Estimation of Multiple Point Sources for Linear Fractional Order Systems Using Modulating Functions
Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem
2017-01-01
This paper proposes an estimation algorithm for the characterization of multiple point inputs for linear fractional order systems. First, using polynomial modulating functions method and a suitable change of variables the problem of estimating
Stability Analysis for Fractional-Order Linear Singular Delay Differential Systems
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Hai Zhang
2014-01-01
Full Text Available We investigate the delay-independently asymptotic stability of fractional-order linear singular delay differential systems. Based on the algebraic approach, the sufficient conditions are presented to ensure the asymptotic stability for any delay parameter. By applying the stability criteria, one can avoid solving the roots of transcendental equations. An example is also provided to illustrate the effectiveness and applicability of the theoretical results.
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Baogui Xin
2012-01-01
Full Text Available Based on linear feedback control technique, a projective synchronization scheme of N-dimensional chaotic fractional-order systems is proposed, which consists of master and slave fractional-order financial systems coupled by linear state error variables. It is shown that the slave system can be projectively synchronized with the master system constructed by state transformation. Based on the stability theory of linear fractional order systems, a suitable controller for achieving synchronization is designed. The given scheme is applied to achieve projective synchronization of chaotic fractional-order financial systems. Numerical simulations are given to verify the effectiveness of the proposed projective synchronization scheme.
Estimation of Multiple Point Sources for Linear Fractional Order Systems Using Modulating Functions
Belkhatir, Zehor
2017-06-28
This paper proposes an estimation algorithm for the characterization of multiple point inputs for linear fractional order systems. First, using polynomial modulating functions method and a suitable change of variables the problem of estimating the locations and the amplitudes of a multi-pointwise input is decoupled into two algebraic systems of equations. The first system is nonlinear and solves for the time locations iteratively, whereas the second system is linear and solves for the input’s amplitudes. Second, closed form formulas for both the time location and the amplitude are provided in the particular case of single point input. Finally, numerical examples are given to illustrate the performance of the proposed technique in both noise-free and noisy cases. The joint estimation of pointwise input and fractional differentiation orders is also presented. Furthermore, a discussion on the performance of the proposed algorithm is provided.
Merrikh-Bayat, Farshad
2011-04-01
One main approach for time-domain simulation of the linear output-feedback systems containing fractional-order controllers is to approximate the transfer function of the controller with an integer-order transfer function and then perform the simulation. In general, this approach suffers from two main disadvantages: first, the internal stability of the resulting feedback system is not guaranteed, and second, the amount of error caused by this approximation is not exactly known. The aim of this paper is to propose an efficient method for time-domain simulation of such systems without facing the above mentioned drawbacks. For this purpose, the fractional-order controller is approximated with an integer-order transfer function (possibly in combination with the delay term) such that the internal stability of the closed-loop system is guaranteed, and then the simulation is performed. It is also shown that the resulting approximate controller can effectively be realized by using the proposed method. Some formulas for estimating and correcting the simulation error, when the feedback system under consideration is subjected to the unit step command or the unit step disturbance, are also presented. Finally, three numerical examples are studied and the results are compared with the Oustaloup continuous approximation method. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.
Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos
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Bin Wang
2015-01-01
Full Text Available This paper investigates fuzzy synchronization for fractional order chaos via linear matrix inequality. Based on generalized Takagi-Sugeno fuzzy model, one efficient stability condition for fractional order chaos synchronization or antisynchronization is given. The fractional order stability condition is transformed into a set of linear matrix inequalities and the rigorous proof details are presented. Furthermore, through fractional order linear time-invariant (LTI interval theory, the approach is developed for fractional order chaos synchronization regardless of the system with uncertain parameters. Three typical examples, including synchronization between an integer order three-dimensional (3D chaos and a fractional order 3D chaos, anti-synchronization of two fractional order hyperchaos, and the synchronization between an integer order 3D chaos and a fractional order 4D chaos, are employed to verify the theoretical results.
Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems
N'Doye, Ibrahima; Laleg-Kirati, Taous-Meriem
2015-01-01
This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.
Fractional-order adaptive fault estimation for a class of nonlinear fractional-order systems
N'Doye, Ibrahima
2015-07-01
This paper studies the problem of fractional-order adaptive fault estimation for a class of fractional-order Lipschitz nonlinear systems using fractional-order adaptive fault observer. Sufficient conditions for the asymptotical convergence of the fractional-order state estimation error, the conventional integer-order and the fractional-order faults estimation error are derived in terms of linear matrix inequalities (LMIs) formulation by introducing a continuous frequency distributed equivalent model and using an indirect Lyapunov approach where the fractional-order α belongs to 0 < α < 1. A numerical example is given to demonstrate the validity of the proposed approach.
Fractional order differentiation by integration: An application to fractional linear systems
Liu, Dayan
2013-02-04
In this article, we propose a robust method to compute the output of a fractional linear system defined through a linear fractional differential equation (FDE) with time-varying coefficients, where the input can be noisy. We firstly introduce an estimator of the fractional derivative of an unknown signal, which is defined by an integral formula obtained by calculating the fractional derivative of a truncated Jacobi polynomial series expansion. We then approximate the FDE by applying to each fractional derivative this formal algebraic integral estimator. Consequently, the fractional derivatives of the solution are applied on the used Jacobi polynomials and then we need to identify the unknown coefficients of the truncated series expansion of the solution. Modulating functions method is used to estimate these coefficients by solving a linear system issued from the approximated FDE and some initial conditions. A numerical result is given to confirm the reliability of the proposed method. © 2013 IFAC.
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Mohammadtaghi Hamidi Beheshti
2010-01-01
Full Text Available We propose a fractional-order controller to stabilize unstable fractional-order open-loop systems with interval uncertainty whereas one does not need to change the poles of the closed-loop system in the proposed method. For this, we will use the robust stability theory of Fractional-Order Linear Time Invariant (FO-LTI systems. To determine the control parameters, one needs only a little knowledge about the plant and therefore, the proposed controller is a suitable choice in the control of interval nonlinear systems and especially in fractional-order chaotic systems. Finally numerical simulations are presented to show the effectiveness of the proposed controller.
N U+02BC Doye, Ibrahima
2018-02-13
In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.
N U+02BC Doye, Ibrahima; Salama, Khaled N.; Laleg-Kirati, Taous-Meriem
2018-01-01
In this paper, we propose a robust fractional-order proportional-integral U+0028 FOPI U+0029 observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities U+0028 LMIs U+0029 approach by using an indirect Lyapunov method. The proposed U+0028 FOPI U+0029 observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional U+0028 FOP U+0029 observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.
Nonlinear dynamics of fractional order Duffing system
International Nuclear Information System (INIS)
Li, Zengshan; Chen, Diyi; Zhu, Jianwei; Liu, Yongjian
2015-01-01
In this paper, we analyze the nonlinear dynamics of fractional order Duffing system. First, we present the fractional order Duffing system and the numerical algorithm. Second, nonlinear dynamic behaviors of Duffing system with a fixed fractional order is studied by using bifurcation diagrams, phase portraits, Poincare maps and time domain waveforms. The fractional order Duffing system shows some interesting dynamical behaviors. Third, a series of Duffing systems with different fractional orders are analyzed by using bifurcation diagrams. The impacts of fractional orders on the tendency of dynamical motion, the periodic windows in chaos, the bifurcation points and the distance between the first and the last bifurcation points are respectively studied, in which some basic laws are discovered and summarized. This paper reflects that the integer order system and the fractional order one have close relationship and an integer order system is a special case of fractional order ones.
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Sayyad Delshad Saleh
2010-01-01
Full Text Available Abstract We propose a fractional-order controller to stabilize unstable fractional-order open-loop systems with interval uncertainty whereas one does not need to change the poles of the closed-loop system in the proposed method. For this, we will use the robust stability theory of Fractional-Order Linear Time Invariant (FO-LTI systems. To determine the control parameters, one needs only a little knowledge about the plant and therefore, the proposed controller is a suitable choice in the control of interval nonlinear systems and especially in fractional-order chaotic systems. Finally numerical simulations are presented to show the effectiveness of the proposed controller.
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Ping Zhou
2012-01-01
Full Text Available The unstable equilibrium points of the fractional-order Lorenz chaotic system can be controlled via fractional-order derivative, and chaos synchronization for the fractional-order Lorenz chaotic system can be achieved via fractional-order derivative. The control and synchronization technique, based on stability theory of fractional-order systems, is simple and theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed method.
Controlling general projective synchronization of fractional order Rossler systems
International Nuclear Information System (INIS)
Shao Shiquan
2009-01-01
This paper proposed a method to achieve general projective synchronization of two fractional order Rossler systems. First, we construct the fractional order Rossler system's corresponding approximation integer order system. Then, a control method based on a partially linear decomposition and negative feedback of state errors was utilized on the integer order system. Numerical simulations show the effectiveness of the proposed method.
Chaos in the fractional order Chen system and its control
International Nuclear Information System (INIS)
Li Chunguang; Chen Guanrong
2004-01-01
In this letter, we study the chaotic behaviors in the fractional order Chen system. We found that chaos exists in the fractional order Chen system with order less than 3. The lowest order we found to have chaos in this system is 2.1. Linear feedback control of chaos in this system is also studied
Function projective lag synchronization of fractional-order chaotic systems
International Nuclear Information System (INIS)
Wang Sha; Yu Yong-Guang; Wang Hu; Rahmani Ahmed
2014-01-01
Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme. (general)
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S. Alonso-Quesada
2010-01-01
Full Text Available This paper presents a strategy for designing a robust discrete-time adaptive controller for stabilizing linear time-invariant (LTI continuous-time dynamic systems. Such systems may be unstable and noninversely stable in the worst case. A reduced-order model is considered to design the adaptive controller. The control design is based on the discretization of the system with the use of a multirate sampling device with fast-sampled control signal. A suitable on-line adaptation of the multirate gains guarantees the stability of the inverse of the discretized estimated model, which is used to parameterize the adaptive controller. A dead zone is included in the parameters estimation algorithm for robustness purposes under the presence of unmodeled dynamics in the controlled dynamic system. The adaptive controller guarantees the boundedness of the system measured signal for all time. Some examples illustrate the efficacy of this control strategy.
Belkhatir, Zehor; Laleg-Kirati, Taous-Meriem
2017-01-01
This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.
Belkhatir, Zehor
2017-05-31
This paper proposes a two-stage estimation algorithm to solve the problem of joint estimation of the parameters and the fractional differentiation orders of a linear continuous-time fractional system with non-commensurate orders. The proposed algorithm combines the modulating functions and the first-order Newton methods. Sufficient conditions ensuring the convergence of the method are provided. An error analysis in the discrete case is performed. Moreover, the method is extended to the joint estimation of smooth unknown input and fractional differentiation orders. The performance of the proposed approach is illustrated with different numerical examples. Furthermore, a potential application of the algorithm is proposed which consists in the estimation of the differentiation orders of a fractional neurovascular model along with the neural activity considered as input for this model.
Identification of fractional order systems using modulating functions method
Liu, Dayan; Laleg-Kirati, Taous-Meriem; Gibaru, O.; Perruquetti, Wilfrid
2013-01-01
can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear
The Active Fractional Order Control for Maglev Suspension System
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Peichang Yu
2015-01-01
Full Text Available Maglev suspension system is the core part of maglev train. In the practical application, the load uncertainties, inherent nonlinearity, and misalignment between sensors and actuators are the main issues that should be solved carefully. In order to design a suitable controller, the attention is paid to the fractional order controller. Firstly, the mathematical model of a single electromagnetic suspension unit is derived. Then, considering the limitation of the traditional PD controller adaptation, the fractional order controller is developed to obtain more excellent suspension specifications and robust performance. In reality, the nonlinearity affects the structure and the precision of the model after linearization, which will degrade the dynamic performance. So, a fractional order controller is addressed to eliminate the disturbance by adjusting the parameters which are added by the fractional order controller. Furthermore, the controller based on LQR is employed to compare with the fractional order controller. Finally, the performance of them is discussed by simulation. The results illustrated the validity of the fractional order controller.
Inverse synchronization of coupled fractional-order systems through ...
Indian Academy of Sciences (India)
netic waves [8], boundary layer effects in ducts [9], dielectric polarization [10], and ... fractional-order systems [27–34] due to its potential applications in secure ..... Now, according to the stability theorem of linear FDEs [61], we can derive the ...
A Solution to the Fundamental Linear Fractional Order Differential Equation
Hartley, Tom T.; Lorenzo, Carl F.
1998-01-01
This paper provides a solution to the fundamental linear fractional order differential equation, namely, (sub c)d(sup q, sub t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the F-function, which generalizes the normal exponential function. The F-function provides the basis for a qth order "fractional pole". Complex plane behavior is elucidated and a simple example, the inductor terminated semi- infinite lossy line, is used to demonstrate the theory.
Synchronization of Coupled Nonidentical Fractional-Order Hyperchaotic Systems
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Zhouchao Wei
2011-01-01
Full Text Available Synchronization of coupled nonidentical fractional-order hyperchaotic systems is addressed by the active sliding mode method. By designing an active sliding mode controller and choosing proper control parameters, the master and slave systems are synchronized. Furthermore, synchronizing fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system is performed to show the effectiveness of the proposed controller.
Zhou, Ping; Bai, Rongji
2014-01-01
Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in 1 < q < 2, one adaptive synchronization approach is established. The adaptive synchronization for the fractional-order Lorenz chaotic system with fractional-order 1 < q < 2 is considered. Numerical simulations show the validity and feasibility of the proposed scheme. PMID:25247207
One Adaptive Synchronization Approach for Fractional-Order Chaotic System with Fractional-Order 1
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Ping Zhou
2014-01-01
Full Text Available Based on a new stability result of equilibrium point in nonlinear fractional-order systems for fractional-order lying in 1fractional-order Lorenz chaotic system with fractional-order 1
Identification of fractional order systems using modulating functions method
Liu, Dayan
2013-06-01
The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville fractional derivatives. First, a new fractional integration by parts formula involving the fractional derivative of a modulating function is given. Then, we apply this formula to a fractional order system, for which the fractional derivatives of the input and the output can be transferred into the ones of the modulating functions. By choosing a set of modulating functions, a linear system of algebraic equations is obtained. Hence, the unknown parameters of a fractional order system can be estimated by solving a linear system. Using this method, we do not need any initial values which are usually unknown and not equal to zero. Also we do not need to estimate the fractional derivatives of noisy output. Moreover, it is shown that the proposed estimators are robust against high frequency sinusoidal noises and the ones due to a class of stochastic processes. Finally, the efficiency and the stability of the proposed method is confirmed by some numerical simulations.
Fractional Order PIλDμ Control for Maglev Guiding System
Hu, Qing; Hu, Yuwei
To effectively suppress the external disturbances and parameter perturbation problem of the maglev guiding system, and improve speed and robustness, the electromagnetic guiding system is exactly linearized using state feedback method, Fractional calculus theory is introduced, the order of integer order PID control was extended to the field of fractional, then fractional order PIλDμ Controller was presented, Due to the extra two adjustable parameters compared with traditional PID controller, fractional order PIλDμ controllers were expected to show better control performance. The results of the computer simulation show that the proposed controller suppresses the external disturbances and parameter perturbation of the system effectively; the system response speed was increased; at the same time, it had flexible structure and stronger robustness.
Fengjiao Wu; Guitao Zhang; Zhengzhong Wang
2016-01-01
The robust fuzzy control for fractional-order hydroturbine regulating system is studied in this paper. First, the more practical fractional-order hydroturbine regulating system with uncertain parameters and random disturbances is presented. Then, on the basis of interval matrix theory and fractional-order stability theorem, a fuzzy control method is proposed for fractional-order hydroturbine regulating system, and the stability condition is expressed as a group of linear matrix inequalities. ...
Stability Analysis of Fractional-Order Nonlinear Systems with Delay
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Yu Wang
2014-01-01
Full Text Available Stability analysis of fractional-order nonlinear systems with delay is studied. We propose the definition of Mittag-Leffler stability of time-delay system and introduce the fractional Lyapunov direct method by using properties of Mittag-Leffler function and Laplace transform. Then some new sufficient conditions ensuring asymptotical stability of fractional-order nonlinear system with delay are proposed firstly. And the application of Riemann-Liouville fractional-order systems is extended by the fractional comparison principle and the Caputo fractional-order systems. Numerical simulations of an example demonstrate the universality and the effectiveness of the proposed method.
Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation
Petráš, Ivo
2011-01-01
"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation" presents a study of fractional-order chaotic systems accompanied by Matlab programs for simulating their state space trajectories, which are shown in the illustrations in the book. Description of the chaotic systems is clearly presented and their analysis and numerical solution are done in an easy-to-follow manner. Simulink models for the selected fractional-order systems are also presented. The readers will understand the fundamentals of the fractional calculus, how real dynamical systems can be described using fractional derivatives and fractional differential equations, how such equations can be solved, and how to simulate and explore chaotic systems of fractional order. The book addresses to mathematicians, physicists, engineers, and other scientists interested in chaos phenomena or in fractional-order systems. It can be used in courses on dynamical systems, control theory, and applied mathematics at graduate or postgraduate level. ...
Dynamics analysis of fractional order Yu-Wang system
Bhalekar, Sachin
2013-10-01
Fractional order version of a dynamical system introduced by Yu and Wang (Engineering, Technology & Applied Science Research, 2, (2012) 209-215) is discussed in this article. The basic dynamical properties of the system are studied. Minimum effective dimension 0.942329 for the existence of chaos in the proposed system is obtained using the analytical result. For chaos detection, we have calculated maximum Lyapunov exponents for various values of fractional order. Feedback control method is then used to control chaos in the system. Further, the system is synchronized with itself and with fractional order financial system using active control technique. Modified Adams-Bashforth-Moulton algorithm is used for numerical simulations.
Taylor–Fourier spectra to study fractional order systems
International Nuclear Information System (INIS)
Barbé, Kurt; Lauwers, Lieve; Fuentes, Lee Gonzales
2016-01-01
In measurement science mathematical models are often used as an indirect measurement of physical properties which are mapped to measurands through the mathematical model. Dynamical systems describing a physical process with a dominant diffusion or dispersion phenomenon requires a large dimensional model due to its long memory. Ignoring a dominant difussion or dispersion component acts as a confounder which may introduce a bias in the estimated quantities of interest. For linear systems it has been observed that fractional order models outperform classical rational forms in terms of the number of parameters for the same fitting error. However it is not straightforward to deal with a fractional order system or long memory effects without prior knowledge. Since the parametric modeling of a fractional system is very involved, we put forward the question whether fractional insight can be gathered in a non-parametric way. In this paper we show that classical Fourier basis leading to the frequency response function lacks fractional insight. To circumvent this problem, we introduce a fractional Taylor–Fourier basis to obtain non-parametric insight in the fractional system. This analysis proposes a novel type of spectrum to visualize the spectral content of a fractional system: Taylor–Fourier spectrum. This spectrum is fully measurement driven which can be used as a first to explore the fractional dynamics of a measured diffusion or dispersion system. (paper)
Synchronization of a new fractional-order hyperchaotic system
International Nuclear Information System (INIS)
Wu Xiangjun; Lu Hongtao; Shen Shilei
2009-01-01
In this letter, a new fractional-order hyperchaotic system is proposed. By utilizing the fractional calculus theory and computer simulations, it is found that hyperchaos exists in the new fractional-order four-dimensional system with order less than 4. The lowest order to have hyperchaos in this system is 2.88. The results are validated by the existence of two positive Lyapunov exponents. Using the pole placement technique, a nonlinear state observer is designed to synchronize a class of nonlinear fractional-order systems. The observer method is used to synchronize two identical fractional-order hyperchaotic systems. In addition, the active control technique is applied to synchronize the new fractional-order hyperchaotic system and the fractional-order Chen hyperchaotic system. The two schemes, based on the stability theory of the fractional-order system, are rather simple, theoretically rigorous and convenient to realize synchronization. They do not require the computation of the conditional Lyapunov exponents. Numerical results are performed to verify the effectiveness of the proposed synchronization schemes.
The adaptive synchronization of fractional-order Liu chaotic system ...
Indian Academy of Sciences (India)
in the world, such as circuits, mathematics, power systems, medicine, electrochemical biology, etc. [1,2]. Thus, chaos is one of the most interesting subjects to attract the experts ... of an integrated fractional-order chaos system was studied.
Dynamic evolution characteristics of a fractional order hydropower station system
Gao, Xiang; Chen, Diyi; Yan, Donglin; Xu, Beibei; Wang, Xiangyu
2018-01-01
This paper investigates the dynamic evolution characteristics of the hydropower station by introducing the fractional order damping forces. A careful analysis of the dynamic characteristics of the generator shaft system is carried out under different values of fractional order. It turns out the vibration state of the axis coordinates has a certain evolution law with the increase of the fractional order. Significantly, the obtained law exists in the horizontal evolution and vertical evolution of the dynamical behaviors. Meanwhile, some interesting dynamical phenomena were found in this process. The outcomes of this study enrich the nonlinear dynamic theory from the engineering practice of hydropower stations.
Generalized Combination Complex Synchronization for Fractional-Order Chaotic Complex Systems
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Cuimei Jiang
2015-07-01
Full Text Available Based on two fractional-order chaotic complex drive systems and one fractional-order chaotic complex response system with different dimensions, we propose generalized combination complex synchronization. In this new synchronization scheme, there are two complex scaling matrices that are non-square matrices. On the basis of the stability theory of fractional-order linear systems, we design a general controller via active control. Additionally, by virtue of two complex scaling matrices, generalized combination complex synchronization between fractional-order chaotic complex systems and real systems is investigated. Finally, three typical examples are given to demonstrate the effectiveness and feasibility of the schemes.
Directory of Open Access Journals (Sweden)
Fengjiao Wu
2016-01-01
Full Text Available The robust fuzzy control for fractional-order hydroturbine regulating system is studied in this paper. First, the more practical fractional-order hydroturbine regulating system with uncertain parameters and random disturbances is presented. Then, on the basis of interval matrix theory and fractional-order stability theorem, a fuzzy control method is proposed for fractional-order hydroturbine regulating system, and the stability condition is expressed as a group of linear matrix inequalities. Furthermore, the proposed method has good robustness which can process external random disturbances and uncertain parameters. Finally, the validity and superiority are proved by the numerical simulations.
Fractional order control and synchronization of chaotic systems
Vaidyanathan, Sundarapandian; Ouannas, Adel
2017-01-01
The book reports on the latest advances in and applications of fractional order control and synchronization of chaotic systems, explaining the concepts involved in a clear, matter-of-fact style. It consists of 30 original contributions written by eminent scientists and active researchers in the field that address theories, methods and applications in a number of research areas related to fractional order control and synchronization of chaotic systems, such as: fractional chaotic systems, hyperchaotic systems, complex systems, fractional order discrete chaotic systems, chaos control, chaos synchronization, jerk circuits, fractional chaotic systems with hidden attractors, neural network, fuzzy logic controllers, behavioral modeling, robust and adaptive control, sliding mode control, different types of synchronization, circuit realization of chaotic systems, etc. In addition to providing readers extensive information on chaos fundamentals, fractional calculus, fractional differential equations, fractional contro...
Designing synchronization schemes for chaotic fractional-order unified systems
International Nuclear Information System (INIS)
Wang Junwei; Zhang Yanbin
2006-01-01
Synchronization in chaotic fractional-order differential systems is studied both theoretically and numerically. Two schemes are designed to achieve chaos synchronization of so-called unified chaotic systems and the corresponding numerical algorithms are established. Some sufficient conditions on synchronization are also derived based on the Laplace transformation theory. Computer simulations are used for demonstration
Study on Fuzzy Adaptive Fractional Order PIλDμ Control for Maglev Guiding System
Hu, Qing; Hu, Yuwei
The mathematical model of the linear elevator maglev guiding system is analyzed in this paper. For the linear elevator needs strong stability and robustness to run, the integer order PID was expanded to the fractional order, in order to improve the steady state precision, rapidity and robustness of the system, enhance the accuracy of the parameter in fractional order PIλDμ controller, the fuzzy control is combined with the fractional order PIλDμ control, using the fuzzy logic achieves the parameters online adjustment. The simulations reveal that the system has faster response speed, higher tracking precision, and has stronger robustness to the disturbance.
Genetic Algorithm-Based Identification of Fractional-Order Systems
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Shengxi Zhou
2013-05-01
Full Text Available Fractional calculus has become an increasingly popular tool for modeling the complex behaviors of physical systems from diverse domains. One of the key issues to apply fractional calculus to engineering problems is to achieve the parameter identification of fractional-order systems. A time-domain identification algorithm based on a genetic algorithm (GA is proposed in this paper. The multi-variable parameter identification is converted into a parameter optimization by applying GA to the identification of fractional-order systems. To evaluate the identification accuracy and stability, the time-domain output error considering the condition variation is designed as the fitness function for parameter optimization. The identification process is established under various noise levels and excitation levels. The effects of external excitation and the noise level on the identification accuracy are analyzed in detail. The simulation results show that the proposed method could identify the parameters of both commensurate rate and non-commensurate rate fractional-order systems from the data with noise. It is also observed that excitation signal is an important factor influencing the identification accuracy of fractional-order systems.
The adaptive synchronization of fractional-order Liu chaotic system ...
Indian Academy of Sciences (India)
In this paper, the chaos control and the synchronization of two fractional-order Liu chaotic systems with unknown parameters are studied. According to the Lyapunov stabilization theory and the adaptive control theorem, the adaptive control rule is obtained for the described error dynamic stabilization. Using the adaptive rule ...
Chaos in a fractional-order Roessler system
International Nuclear Information System (INIS)
Zhang Weiwei; Zhou Shangbo; Li Hua; Zhu Hao
2009-01-01
The dynamic behaviors in the fractional-order Roessler equations were numerically studied. Basic properties of the system have been analyzed by means of Lyapunov exponents and bifurcation diagrams. The parameter and the derivative order ranges used were relatively broad. Regular motions (including period-3 motion) and chaotic motions were examined. The chaotic motion identified was validated by the positive Lyapunov exponent.
Delayed feedback control of fractional-order chaotic systems
International Nuclear Information System (INIS)
Gjurchinovski, A; Urumov, V; Sandev, T
2010-01-01
We study the possibility to stabilize unstable steady states and unstable periodic orbits in chaotic fractional-order dynamical systems by the time-delayed feedback method. By performing a linear stability analysis, we establish the parameter ranges for successful stabilization of unstable equilibria in the plane parameterized by the feedback gain and the time delay. An insight into the control mechanism is gained by analyzing the characteristic equation of the controlled system, showing that the control scheme fails to control unstable equilibria having an odd number of positive real eigenvalues. We demonstrate that the method can also stabilize unstable periodic orbits for a suitable choice of the feedback gain, providing that the time delay is chosen to coincide with the period of the target orbit. In addition, it is shown numerically that delayed feedback control with a sinusoidally modulated time delay significantly enlarges the stability region of steady states in comparison to the classical time-delayed feedback scheme with a constant delay.
A 3D Fractional-Order Chaotic System with Only One Stable Equilibrium and Controlling Chaos
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Shiyun Shen
2017-01-01
Full Text Available One 3D fractional-order chaotic system with only one locally asymptotically stable equilibrium is reported. To verify the chaoticity, the maximum Lyapunov exponent (MAXLE with respect to the fractional-order and chaotic attractors are obtained by numerical calculation for this system. Furthermore, by linear scalar controller consisting of a single state variable, one control scheme for stabilization of the 3D fractional-order chaotic system is suggested. The numerical simulations show the feasibility of the control scheme.
State-Feedback Control for Fractional-Order Nonlinear Systems Subject to Input Saturation
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Junhai Luo
2014-01-01
Full Text Available We give a state-feedback control method for fractional-order nonlinear systems subject to input saturation. First, a sufficient condition is derived for the asymptotical stability of a class of fractional-order nonlinear systems. Then based on Gronwall-Bellman lemma and a sector bounded condition of the saturation function, a linear state-feed back controller is designed. Finally, two simulation examples are presented to show the validity of the proposed method.
Electronic realization of the fractional-order systems
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Františka Dorčáková
2007-10-01
Full Text Available This article is devoted to the electronic (analogue realization of the fractional-order systems – controllers or controlled objects whose we earlier used, identified, and analyzed as a mathematical models only ��� namely a fractional-order differential equation, and solved numerically using a method based on the truncated version of the Grunwald - Letnikov formula for fractional derivative. The electronic realization of the fractional derivative is based on the continued fraction expansion of the rational approximation of the fractional differentiator from which we obtained the values of the resistors and capacitors of the electronic circuit. Along with the mathematical description are presented also simulation and measurement results.
Directory of Open Access Journals (Sweden)
Rafał Stanisławski
2016-01-01
Full Text Available This paper presents new results on modeling and analysis of dynamics of fractional-order discrete-time linear time-invariant single-input single-output (LTI SISO systems by means of new, two-layer, “fractional-order discrete-time Laguerre filters.” It is interesting that the fractionality of the filters at the upper system dynamics layer is directly projected from the lower Laguerre-based approximation layer for the Grünwald-Letnikov difference. A new stability criterion for discrete-time fractional-order Laguerre-based LTI SISO systems is introduced and supplemented with a stability preservation analysis. Both the stability criterion and the stability preservation analysis bring up rather surprising results, which is illustrated with simulation examples.
Chaotic incommensurate fractional order Rössler system: active control and synchronization
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Baleanu Dumitru
2011-01-01
Full Text Available Abstract In this article, we present an active control methodology for controlling the chaotic behavior of a fractional order version of Rössler system. The main feature of the designed controller is its simplicity for practical implementation. Although in controlling such complex system several inputs are used in general to actuate the states, in the proposed design, all states of the system are controlled via one input. Active synchronization of two chaotic fractional order Rössler systems is also investigated via a feedback linearization method. In both control and synchronization, numerical simulations show the efficiency of the proposed methods.
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Yuanhua Li
2015-01-01
Full Text Available Stability and stabilization of fractional-order interval system is investigated. By adding parameters to linear matrix inequalities, necessary and sufficient conditions for stability and stabilization of the system are obtained. The results on stability check for uncertain FO-LTI systems with interval coefficients of dimension n only need to solve one 4n-by-4n LMI. Numerical examples are presented to shown the effectiveness of our results.
Liu, Da-Yan; Tian, Yang; Boutat, Driss; Laleg-Kirati, Taous-Meriem
2015-01-01
This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator.
Liu, Da-Yan
2015-04-30
This paper aims at designing a digital fractional order differentiator for a class of signals satisfying a linear differential equation to estimate fractional derivatives with an arbitrary order in noisy case, where the input can be unknown or known with noises. Firstly, an integer order differentiator for the input is constructed using a truncated Jacobi orthogonal series expansion. Then, a new algebraic formula for the Riemann-Liouville derivative is derived, which is enlightened by the algebraic parametric method. Secondly, a digital fractional order differentiator is proposed using a numerical integration method in discrete noisy case. Then, the noise error contribution is analyzed, where an error bound useful for the selection of the design parameter is provided. Finally, numerical examples illustrate the accuracy and the robustness of the proposed fractional order differentiator.
Chaos in a modified van der Pol system and in its fractional order systems
International Nuclear Information System (INIS)
Ge Zhengming; Zhang, A.-R.
2007-01-01
Chaos in a modified van der Pol system and in its fractional order systems is studied in this paper. It is found that chaos exists both in the system and in the fractional order systems with order from 1.8 down to 0.8 much less than the number of states of the system, two. By phase portraits, Poincare maps and bifurcation diagrams, the chaotic behaviors of fractional order modified van der Pol systems are presented
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Iman Ghasemi
2017-05-01
Full Text Available In this paper, iterative learning control (ILC is combined with an optimal fractional order derivative (BBO-Da-type ILC and optimal fractional and proportional-derivative (BBO-PDa-type ILC. In the update law of Arimoto's derivative iterative learning control, a first order derivative of tracking error signal is used. In the proposed method, fractional order derivative of the error signal is stated in term of 'sa' where to update iterative learning control law. Two types of fractional order iterative learning control namely PDa-type ILC and Da-type ILC are gained for different value of a. In order to improve the performance of closed-loop control system, coefficients of both and learning law i.e. proportional , derivative and are optimized using Biogeography-Based optimization algorithm (BBO. Outcome of the simulation results are compared with those of the conventional fractional order iterative learning control to verify effectiveness of BBO-Da-type ILC and BBO-PDa-type ILC
Static output feedback ℋ ∞ control for a fractional-order glucose-insulin system
N’Doye, Ibrahima
2015-05-23
This paper presents the ℋ∞ static output feedback control of nonlinear fractional-order systems. Based on the extended bounded real lemma, the ℋ∞ control is formulated and sufficient conditions are derived in terms of linear matrix inequalities (LMIs) formulation by using the fractional Lyapunov direct method where the fractional-order α belongs to 0 < α < 1. The control approach is finally applied to the regulation of the glucose level in diabetes type 1 treatment. Therefore, it is attempted to incorporate fractional-order into the mathematical minimal model of glucose-insulin system dynamics and it is still an interesting challenge to show, how the order of a fractional differential system affects the dynamics of the system in the presence of meal disturbance. Numerical simulations are carried out to illustrate our proposed results and show that the nonlinear fractional-order glucose-insulin systems are, at least, as stable as their integer-order counterpart in the presence of exogenous glucose infusion or meal disturbance. © 2015 Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg
Chaos synchronization of the fractional-order Chen's system
International Nuclear Information System (INIS)
Zhu Hao; Zhou Shangbo; He Zhongshi
2009-01-01
In this paper, based on the stability theorem of linear fractional systems, a necessary condition is given to check the chaos synchronization of fractional systems with incommensurate order. Chaos synchronization is studied by utilizing the Pecora-Carroll (PC) method and the coupling method. The necessary condition can also be used as a tool to confirm results of a numerical simulation. Numerical simulation results show the effectiveness of the necessary condition.
Yang, Ningning; Xu, Cheng; Wu, Chaojun; Jia, Rong; Liu, Chongxin
2017-12-01
Memristor is a nonlinear “missing circuit element”, that can easily achieve chaotic oscillation. Memristor-based chaotic systems have received more and more attention. Research shows that fractional-order systems are more close to real systems. As an important parameter, the order can increase the flexibility and degree of freedom of the system. In this paper, a fractional-order generalized memristor, which consists of a diode bridge and a parallel circuit with an equivalent unit circuit and a linear resistance, is proposed. Frequency and electrical characteristics of the fractional-order memristor are analyzed. A chain structure circuit is used to implement the fractional-order unit circuit. Then replacing the conventional Chua’s diode by the fractional-order generalized memristor, a fractional-order memristor-based chaotic circuit is proposed. A large amount of research work has been done to investigate the influence of the order on the dynamical behaviors of the fractional-order memristor-based chaotic circuit. Varying with the order, the system enters the chaotic state from the periodic state through the Hopf bifurcation and period-doubling bifurcation. The chaotic state of the system has two types of attractors: single-scroll and double-scroll attractor. The stability theory of fractional-order systems is used to determine the minimum order occurring Hopf bifurcation. And the influence of the initial value on the system is analyzed. Circuit simulations are designed to verify the results of theoretical analysis and numerical simulation.
Extension of the root-locus method to a certain class of fractional-order systems.
Merrikh-Bayat, Farshad; Afshar, Mahdi; Karimi-Ghartemani, Masoud
2009-01-01
In this paper, the well-known root-locus method is developed for the special subset of linear time-invariant systems commonly known as fractional-order systems. Transfer functions of these systems are rational functions with polynomials of rational powers of the Laplace variable s. Such systems are defined on a Riemann surface because of their multi-valued nature. A set of rules for plotting the root loci on the first Riemann sheet is presented. The important features of the classical root-locus method such as asymptotes, roots condition on the real axis and breakaway points are extended to the fractional case. It is also shown that the proposed method can assess the closed-loop stability of fractional-order systems in the presence of a varying gain in the loop. Moreover, the effect of perturbation on the root loci is discussed. Three illustrative examples are presented to confirm the effectiveness of the proposed algorithm.
Guaranteed Cost Finite-Time Control of Fractional-Order Positive Switched Systems
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Leipo Liu
2017-01-01
Full Text Available The problem of guaranteed cost finite-time control of fractional-order positive switched systems (FOPSS is considered in this paper. Firstly, a new cost function is defined. Then, by constructing linear copositive Lyapunov functions and using the average dwell time (ADT approach, a state feedback controller and a static output feedback controller are constructed, respectively, and sufficient conditions are derived to guarantee that the corresponding closed-loop systems are guaranteed cost finite-time stable (GCFTS. Such conditions can be easily solved by linear programming. Finally, two examples are given to illustrate the effectiveness of the proposed method.
A New Fractional-Order Chaotic Complex System and Its Antisynchronization
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Cuimei Jiang
2014-01-01
with phase portraits, bifurcation diagrams, the histories, and the largest Lyapunov exponents. And we find that chaos exists in this system with orders less than 5 by numerical simulation. Additionally, antisynchronization of different fractional-order chaotic complex systems is considered based on the stability theory of fractional-order systems. This new system and the fractional-order complex Lorenz system can achieve antisynchronization. Corresponding numerical simulations show the effectiveness and feasibility of the scheme.
Parametric Control on Fractional-Order Response for Lü Chaotic System
Moaddy, K; Radwan, A G; Salama, Khaled N.; Momani, S; Hashim, I
2013-01-01
This paper discusses the influence of the fractional order parameter on conventional chaotic systems. These fractional-order parameters increase the system degree of freedom allowing it to enter new domains and thus it can be used as a control for such dynamical systems. This paper investigates the behaviour of the equally-fractional-order Lü chaotic system when changing the fractional-order parameter and determines the fractional-order ranges for chaotic behaviour. Five different parameter values and six fractional-order cases are discussed through this paper. Unlike the conventional parameters, as the fractional-order increases the system response begins with stability, passing by chaotic behaviour then reaches periodic response. As the system parameter α increases, a shift in the fractional order is required to maintain chaotic response.Therefore, the range of chaotic response can be expanded or minimized by controlling the fractional-order parameter. The non-standard finite difference method is used to solve the fractional-order Lü chaotic system numerically to validate these responses.
Parametric Control on Fractional-Order Response for Lü Chaotic System
Moaddy, K
2013-04-10
This paper discusses the influence of the fractional order parameter on conventional chaotic systems. These fractional-order parameters increase the system degree of freedom allowing it to enter new domains and thus it can be used as a control for such dynamical systems. This paper investigates the behaviour of the equally-fractional-order Lü chaotic system when changing the fractional-order parameter and determines the fractional-order ranges for chaotic behaviour. Five different parameter values and six fractional-order cases are discussed through this paper. Unlike the conventional parameters, as the fractional-order increases the system response begins with stability, passing by chaotic behaviour then reaches periodic response. As the system parameter α increases, a shift in the fractional order is required to maintain chaotic response.Therefore, the range of chaotic response can be expanded or minimized by controlling the fractional-order parameter. The non-standard finite difference method is used to solve the fractional-order Lü chaotic system numerically to validate these responses.
Impulsive synchronisation of a class of fractional-order hyperchaotic systems
International Nuclear Information System (INIS)
Wang Xing-Yuan; Zhang Yong-Lei; Lin Da; Zhang Na
2011-01-01
In this paper, an impulsive synchronisation scheme for a class of fractional-order hyperchaotic systems is proposed. The sufficient conditions of a class of integral-order hyperchaotic systems' impulsive synchronisation are illustrated. Furthermore, we apply the sufficient conditions to a class of fractional-order hyperchaotic systems and well achieve impulsive synchronisation of these fractional-order hyperchaotic systems, thereby extending the applicable scope of impulsive synchronisation. Numerical simulations further demonstrate the feasibility and effectiveness of the proposed scheme. (general)
Nonlinear dynamics and chaos in a fractional-order financial system
International Nuclear Information System (INIS)
Chen Weiching
2008-01-01
This study examines the two most attractive characteristics, memory and chaos, in simulations of financial systems. A fractional-order financial system is proposed in this study. It is a generalization of a dynamic financial model recently reported in the literature. The fractional-order financial system displays many interesting dynamic behaviors, such as fixed points, periodic motions, and chaotic motions. It has been found that chaos exists in fractional-order financial systems with orders less than 3. In this study, the lowest order at which this system yielded chaos was 2.35. Period doubling and intermittency routes to chaos in the fractional-order financial system were found
International Nuclear Information System (INIS)
Niu Yu-Jun; Wang Xing-Yuan; Nian Fu-Zhong; Wang Ming-Jun
2010-01-01
Based on the stability theory of the fractional order system, the dynamic behaviours of a new fractional order system are investigated theoretically. The lowest order we found to have chaos in the new three-dimensional system is 2.46, and the period routes to chaos in the new fractional order system are also found. The effectiveness of our analysis results is further verified by numerical simulations and positive largest Lyapunov exponent. Furthermore, a nonlinear feedback controller is designed to achieve the generalized projective synchronization of the fractional order chaotic system, and its validity is proved by Laplace transformation theory. (general)
Synchronization and an application of a novel fractional order King Cobra chaotic system
Energy Technology Data Exchange (ETDEWEB)
Muthukumar, P., E-mail: muthukumardgl@gmail.com; Balasubramaniam, P., E-mail: balugru@gmail.com [Department of Mathematics, Gandhigram Rural Institute‐Deemed University, Gandhigram 624 302, Tamilnadu (India); Ratnavelu, K., E-mail: kuru052001@gmail.com [Faculty of Science, Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur (Malaysia)
2014-09-01
In this paper, we design a new three dimensional King Cobra face shaped fractional order chaotic system. The multi-scale synchronization scheme of two fractional order chaotic systems is described. The necessary conditions for the multi-scale synchronization of two identical fractional order King Cobra chaotic systems are derived through feedback control. A new cryptosystem is proposed for an image encryption and decryption by using synchronized fractional order King Cobra chaotic systems with the supports of multiple cryptographic assumptions. The security of the proposed cryptosystem is analyzed by the well known algebraic attacks. Numerical simulations are given to show the effectiveness of the proposed theoretical results.
Synchronization of Different Fractional Order Time-Delay Chaotic Systems Using Active Control
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Jianeng Tang
2014-01-01
Full Text Available Chaos synchronization of different fractional order time-delay chaotic systems is considered. Based on the Laplace transform theory, the conditions for achieving synchronization of different fractional order time-delay chaotic systems are analyzed by use of active control technique. Then numerical simulations are provided to verify the effectiveness and feasibility of the developed method. At last, effects of the fraction order and the time delay on synchronization are further researched.
Fractional-order sliding mode control for a class of uncertain nonlinear systems based on LQR
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Dong Zhang
2017-03-01
Full Text Available This article presents a new fractional-order sliding mode control (FOSMC strategy based on a linear-quadratic regulator (LQR for a class of uncertain nonlinear systems. First, input/output feedback linearization is used to linearize the nonlinear system and decouple tracking error dynamics. Second, LQR is designed to ensure that the tracking error dynamics converges to the equilibrium point as soon as possible. Based on LQR, a novel fractional-order sliding surface is introduced. Subsequently, the FOSMC is designed to reject system uncertainties and reduce the magnitude of control chattering. Then, the global stability of the closed-loop control system is analytically proved using Lyapunov stability theory. Finally, a typical single-input single-output system and a typical multi-input multi-output system are simulated to illustrate the effectiveness and advantages of the proposed control strategy. The results of the simulation indicate that the proposed control strategy exhibits excellent performance and robustness with system uncertainties. Compared to conventional integer-order sliding mode control, the high-frequency chattering of the control input is drastically depressed.
Consensus Analysis of Fractional-Order Multiagent Systems with Double-Integrator
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Chunde Yang
2017-01-01
Full Text Available In nature, many phenomena can be explained by coordinated behavior of agents with fractional-order dynamics. In this paper, the consensus problem of fractional-order multiagent systems with double-integrator is studied, where the fractional-order satisfies 0<α<2. Based on the fractional-order stability theory, Mittag-Leffler function, and Laplace transform, a necessary and sufficient condition is obtained under the assumption that the directed graph for the communication network contains a directed spanning tree. Finally, an example with simulation is presented to illustrate the theoretical results.
International Nuclear Information System (INIS)
Jia Li-Xin; Dai Hao; Hui Meng
2010-01-01
This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method
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Hua Wang
2016-01-01
Full Text Available This paper proposes a new fractional-order approach for synchronization of a class of fractional-order chaotic systems in the presence of model uncertainties and external disturbances. A simple but practical method to synchronize many familiar fractional-order chaotic systems has been put forward. A new theorem is proposed for a class of cascade fractional-order systems and it is applied in chaos synchronization. Combined with the fact that the states of the fractional chaotic systems are bounded, many coupled items can be taken as zero items. Then, the whole system can be simplified greatly and a simpler controller can be derived. Finally, the validity of the presented scheme is illustrated by numerical simulations of the fractional-order unified system.
Radwan, A.G.; Moaddy, K.; Salama, Khaled N.; Momani, S.; Hashim, I.
2013-01-01
This paper discusses the continuous effect of the fractional order parameter of the Lü system where the system response starts stable, passing by chaotic behavior then reaching periodic response as the fractional-order increases. In addition, this paper presents the concept of synchronization of different fractional order chaotic systems using active control technique. Four different synchronization cases are introduced based on the switching parameters. Also, the static and dynamic synchronizations can be obtained when the switching parameters are functions of time. The nonstandard finite difference method is used for the numerical solution of the fractional order master and slave systems. Many numeric simulations are presented to validate the concept for different fractional order parameters.
Radwan, A.G.
2013-03-13
This paper discusses the continuous effect of the fractional order parameter of the Lü system where the system response starts stable, passing by chaotic behavior then reaching periodic response as the fractional-order increases. In addition, this paper presents the concept of synchronization of different fractional order chaotic systems using active control technique. Four different synchronization cases are introduced based on the switching parameters. Also, the static and dynamic synchronizations can be obtained when the switching parameters are functions of time. The nonstandard finite difference method is used for the numerical solution of the fractional order master and slave systems. Many numeric simulations are presented to validate the concept for different fractional order parameters.
General Output Feedback Stabilization for Fractional Order Systems: An LMI Approach
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Yiheng Wei
2014-01-01
Full Text Available This paper is concerned with the problem of general output feedback stabilization for fractional order linear time-invariant (FO-LTI systems with the fractional commensurate order 0<α<2. The objective is to design suitable output feedback controllers that guarantee the stability of the resulting closed-loop systems. Based on the slack variable method and our previous stability criteria, some new results in the form of linear matrix inequality (LMI are developed to the static and dynamic output feedback controllers synthesis for the FO-LTI system with 0<α<1. Furthermore, the results are extended to stabilize the FO-LTI systems with 1≤α<2. Finally, robust output feedback control is discussed. Numerical examples are given to illustrate the effectiveness of the proposed design methods.
Dynamics of fractional-ordered Chen system with delay
Indian Academy of Sciences (India)
Though this subject has a history of more than 300 years, utility and applicability of fractional calculus to various branches of science and engineering have been real- ... variants of Chen system and see the qualitative changes in attractor and ...
The fractional-order modeling and synchronization of electrically coupled neuron systems
Moaddy, K.
2012-11-01
In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grünwald-Letnikov discretization process which is easily implemented and reliably accurate. © 2011 Elsevier Ltd. All rights reserved.
The fractional-order modeling and synchronization of electrically coupled neuron systems
Moaddy, K.; Radwan, Ahmed G.; Salama, Khaled N.; Momani, Shaher M.; Hashim, Ishak
2012-01-01
In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response. Furthermore, the chaotic synchronization with a gap junction of two or multi-coupled-neurons of fractional-order are discussed. The circuit model, fractional-order state equations and the numerical technique are introduced in this paper for individual and multiple coupled neuron systems with different fractional-orders. Various examples are introduced with different fractional orders using the non-standard finite difference scheme together with the Grünwald-Letnikov discretization process which is easily implemented and reliably accurate. © 2011 Elsevier Ltd. All rights reserved.
Identification of fractional-order systems with unknown initial values and structure
Energy Technology Data Exchange (ETDEWEB)
Du, Wei, E-mail: duwei0203@gmail.com [Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai 200237 (China); Miao, Qingying, E-mail: qymiao@sjtu.edu.cn [School of Continuing Education, Shanghai Jiao Tong University, Shanghai 200030 (China); Tong, Le, E-mail: tongle0328@gmail.com [Faculty of Applied Science and Textiles, The Hong Kong Polytechnic University, Hong Kong (China); Tang, Yang [Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of Education, East China University of Science and Technology, Shanghai 200237 (China)
2017-06-21
In this paper, the identification problem of fractional-order chaotic systems is proposed and investigated via an evolutionary optimization approach. Different with other studies to date, this research focuses on the identification of fractional-order chaotic systems with not only unknown orders and parameters, but also unknown initial values and structure. A group of fractional-order chaotic systems, i.e., Lorenz, Lü, Chen, Rössler, Arneodo and Volta chaotic systems, are set as the system candidate pool. The identification problem of fractional-order chaotic systems in this research belongs to mixed integer nonlinear optimization in essence. A powerful evolutionary algorithm called composite differential evolution (CoDE) is introduced for the identification problem presented in this paper. Extensive experiments are carried out to show that the fractional-order chaotic systems with unknown initial values and structure can be successfully identified by means of CoDE. - Highlights: • Unknown initial values and structure are introduced in the identification of fractional-order chaotic systems; • Only a series of output is utilized in the identification of fractional-order chaotic systems; • CoDE is used for the identification problem and the results are satisfactory when compared with other DE variants.
International Nuclear Information System (INIS)
Ge Zhengming; Hsu Maoyuan
2008-01-01
In this paper, chaos excited chaos synchronizations of generalized van der Pol systems with integral and fractional order are studied. Synchronizations of two identified autonomous generalized van der Pol chaotic systems are obtained by replacing their corresponding exciting terms by the same function of chaotic states of a third nonautonomous or autonomous generalized van der Pol system. Numerical simulations, such as phase portraits, Poincare maps and state error plots are given. It is found that chaos excited chaos synchronizations exist for the fractional order systems with the total fractional order both less than and more than the number of the states of the integer order generalized van der Pol system
Gao, Qiang; Zheng, Liang; Chen, Jilin; Wang, Li; Hou, Yuanlong
2014-01-01
Motion control of gun barrels is an ongoing topic for the development of gun control equipment (GCE) with excellent performances. In this paper, a novel disturbance observer (DOB) based fractional order PD (FOPD) control strategy is proposed for the GCE. By adopting the DOB, the control system behaves as if it were the nominal closed-loop system in the absence of disturbances and uncertainties. The optimal control parameters of the FOPD are determined from the loop-shaping perspective, and the Q-filter of the DOB is deliberately designed with consideration of system robustness. The linear frame of the proposed control system will enable the analysis process more convenient. The disturbance rejection properties and the tracking performances of the control system are investigated by both numerical and experimental tests, the results demonstrate that the proposed DOB based FOPD control system is of more robustness, and it is much more suitable for the gun control system with strong nonlinearity and disturbance.
Complexity Analysis and DSP Implementation of the Fractional-Order Lorenz Hyperchaotic System
Directory of Open Access Journals (Sweden)
Shaobo He
2015-12-01
Full Text Available The fractional-order hyperchaotic Lorenz system is solved as a discrete map by applying the Adomian decomposition method (ADM. Lyapunov Characteristic Exponents (LCEs of this system are calculated according to this deduced discrete map. Complexity of this system versus parameters are analyzed by LCEs, bifurcation diagrams, phase portraits, complexity algorithms. Results show that this system has rich dynamical behaviors. Chaos and hyperchaos can be generated by decreasing fractional order q in this system. It also shows that the system is more complex when q takes smaller values. SE and C 0 complexity algorithms provide a parameter choice criteria for practice applications of fractional-order chaotic systems. The fractional-order system is implemented by digital signal processor (DSP, and a pseudo-random bit generator is designed based on the implemented system, which passes the NIST test successfully.
Using wavelet multi-resolution nature to accelerate the identification of fractional order system
International Nuclear Information System (INIS)
Li Yuan-Lu; Meng Xiao; Ding Ya-Qing
2017-01-01
Because of the fractional order derivatives, the identification of the fractional order system (FOS) is more complex than that of an integral order system (IOS). In order to avoid high time consumption in the system identification, the least-squares method is used to find other parameters by fixing the fractional derivative order. Hereafter, the optimal parameters of a system will be found by varying the derivative order in an interval. In addition, the operational matrix of the fractional order integration combined with the multi-resolution nature of a wavelet is used to accelerate the FOS identification, which is achieved by discarding wavelet coefficients of high-frequency components of input and output signals. In the end, the identifications of some known fractional order systems and an elastic torsion system are used to verify the proposed method. (paper)
The response analysis of fractional-order stochastic system via generalized cell mapping method.
Wang, Liang; Xue, Lili; Sun, Chunyan; Yue, Xiaole; Xu, Wei
2018-01-01
This paper is concerned with the response of a fractional-order stochastic system. The short memory principle is introduced to ensure that the response of the system is a Markov process. The generalized cell mapping method is applied to display the global dynamics of the noise-free system, such as attractors, basins of attraction, basin boundary, saddle, and invariant manifolds. The stochastic generalized cell mapping method is employed to obtain the evolutionary process of probability density functions of the response. The fractional-order ϕ 6 oscillator and the fractional-order smooth and discontinuous oscillator are taken as examples to give the implementations of our strategies. Studies have shown that the evolutionary direction of the probability density function of the fractional-order stochastic system is consistent with the unstable manifold. The effectiveness of the method is confirmed using Monte Carlo results.
Consensus of Fractional-Order Multiagent Systems with Double Integrator under Switching Topologies
Directory of Open Access Journals (Sweden)
Shiyun Shen
2017-01-01
Full Text Available Due to the complexity of the practical environments, many systems can only be described with the fractional-order dynamics. In this paper, the consensus of fractional-order multiagent systems with double integrator under switching topologies is investigated. By applying Mittag-Leffler function, Laplace transform, and dwell time technique, a sufficient condition on consensus is obtained. Finally, a numerical simulation is presented to illustrate the effectiveness of the theoretical result.
Universal block diagram based modeling and simulation schemes for fractional-order control systems.
Bai, Lu; Xue, Dingyü
2017-05-08
Universal block diagram based schemes are proposed for modeling and simulating the fractional-order control systems in this paper. A fractional operator block in Simulink is designed to evaluate the fractional-order derivative and integral. Based on the block, the fractional-order control systems with zero initial conditions can be modeled conveniently. For modeling the system with nonzero initial conditions, the auxiliary signal is constructed in the compensation scheme. Since the compensation scheme is very complicated, therefore the integrator chain scheme is further proposed to simplify the modeling procedures. The accuracy and effectiveness of the schemes are assessed in the examples, the computation results testify the block diagram scheme is efficient for all Caputo fractional-order ordinary differential equations (FODEs) of any complexity, including the implicit Caputo FODEs. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Directory of Open Access Journals (Sweden)
Yu Huang
Full Text Available Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm.
Tabatabaei, Mohammad
2017-07-01
In this paper, a new method for determination of the desired characteristic equation and zero location of commensurate fractional order systems is presented. The concept of the characteristic ratio is extended for zero-including commensurate fractional order systems. The generalized version of characteristic ratios is defined such that the time-scaling property of characteristic ratios is also preserved. The monotonicity of the magnitude frequency response is employed to assign the generalized characteristic ratios for commensurate fractional order transfer functions with one zero. A simple pattern for characteristic ratios is proposed to reach a non-overshooting step response. Then, the proposed pattern is revisited to reach a low overshoot (say for example 2%) step response. Finally, zero-including controllers such as fractional order PI or lag (lead) controllers are designed using generalized characteristic ratios assignment method. Numerical simulations are provided to show the efficiency of the so designed controllers. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Generation of multi-wing chaotic attractor in fractional order system
International Nuclear Information System (INIS)
Zhang Chaoxia; Yu Simin
2011-01-01
Highlights: → We investigate a novel approach for generating multi-wing chaotic attractors. → We introduce a fundamental fractional differential nominal linear system. → A proper nonlinear state feedback controller is designed. → The controlled system can generate fractional-order multi-wing chaotic attractors. - Abstract: In this paper, a novel approach is proposed for generating multi-wing chaotic attractors from the fractional linear differential system via nonlinear state feedback controller equipped with a duality-symmetric multi-segment quadratic function. The main idea is to design a proper nonlinear state feedback controller by using four construction criterions from a fundamental fractional differential nominal linear system, so that the controlled fractional differential system can generate multi-wing chaotic attractors. It is the first time in the literature to report the multi-wing chaotic attractors from an uncoupled fractional differential system. Furthermore, some basic dynamical analysis and numerical simulations are also given, confirming the effectiveness of the proposed method.
International Nuclear Information System (INIS)
Zhang Li-Min; Sun Ke-Hui; Liu Wen-Hao; He Shao-Bo
2017-01-01
In this paper, Adomian decomposition method (ADM) with high accuracy and fast convergence is introduced to solve the fractional-order piecewise-linear (PWL) hyperchaotic system. Based on the obtained hyperchaotic sequences, a novel color image encryption algorithm is proposed by employing a hybrid model of bidirectional circular permutation and DNA masking. In this scheme, the pixel positions of image are scrambled by circular permutation, and the pixel values are substituted by DNA sequence operations. In the DNA sequence operations, addition and substraction operations are performed according to traditional addition and subtraction in the binary, and two rounds of addition rules are used to encrypt the pixel values. The simulation results and security analysis show that the hyperchaotic map is suitable for image encryption, and the proposed encryption algorithm has good encryption effect and strong key sensitivity. It can resist brute-force attack, statistical attack, differential attack, known-plaintext, and chosen-plaintext attacks. (paper)
On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system
Hajipour, Ahamad; Hajipour, Mojtaba; Baleanu, Dumitru
2018-05-01
This manuscript mainly focuses on the construction, dynamic analysis and control of a new fractional-order financial system. The basic dynamical behaviors of the proposed system are studied such as the equilibrium points and their stability, Lyapunov exponents, bifurcation diagrams, phase portraits of state variables and the intervals of system parameters. It is shown that the system exhibits hyperchaotic behavior for a number of system parameters and fractional-order values. To stabilize the proposed hyperchaotic fractional system with uncertain dynamics and disturbances, an efficient adaptive sliding mode controller technique is developed. Using the proposed technique, two hyperchaotic fractional-order financial systems are also synchronized. Numerical simulations are presented to verify the successful performance of the designed controllers.
Parrondo’s paradox for chaos control and anticontrol of fractional-order systems
International Nuclear Information System (INIS)
Danca, Marius-F; Tang, Wallace K S
2016-01-01
We present the generalized forms of Parrondo’s paradox existing in fractional-order nonlinear systems. The generalization is implemented by applying a parameter switching (PS) algorithm to the corresponding initial value problems associated with the fractional-order nonlinear systems. The PS algorithm switches a system parameter within a specific set of N ≥ 2 values when solving the system with some numerical integration method. It is proven that any attractor of the concerned system can be approximated numerically. By replacing the words “winning” and “loosing” in the classical Parrondo’s paradox with “order” and “chaos', respectively, the PS algorithm leads to the generalized Parrondo’s paradox: chaos 1 + chaos 2 + ··· + chaos N = order and order 1 + order 2 + ··· + order N = chaos. Finally, the concept is well demonstrated with the results based on the fractional-order Chen system. (paper)
Parametric study of the fractional-order Chen-Lee system
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Tam, L.M. [Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Av. Padre Tomas Pereira S.J., Taipa, Macau (China)], E-mail: fstlmt@umac.mo; Tou, W.M.S. [Department of Electromechanical Engineering, Faculty of Science and Technology, University of Macau, Av. Padre Tomas Pereira S.J., Taipa, Macau (China)
2008-08-15
The dynamics of fractional-order systems have attracted a great deal of attention in recent years. In this paper, the effects of parameter changes on the dynamics of the fractional-order Chen-Lee system were studied numerically. The parameter ranges used were relatively broad. The order used for the system was fixed at 2.7 (q{sub 1} = q{sub 2} = q{sub 3} = 0.9). The system displays rich dynamic behaviors, such as a fixed point, periodic motion (including period-3 motion), chaotic motion, and transient chaos. The chaotic motion identified was validated by the confirmation of a positive Lyapunov exponent. Period-doubling routes to chaos in the fractional-order Chen-Lee system were also found.
Parametric study of the fractional-order Chen-Lee system
International Nuclear Information System (INIS)
Tam, L.M.; Tou, W.M.S.
2008-01-01
The dynamics of fractional-order systems have attracted a great deal of attention in recent years. In this paper, the effects of parameter changes on the dynamics of the fractional-order Chen-Lee system were studied numerically. The parameter ranges used were relatively broad. The order used for the system was fixed at 2.7 (q 1 = q 2 = q 3 = 0.9). The system displays rich dynamic behaviors, such as a fixed point, periodic motion (including period-3 motion), chaotic motion, and transient chaos. The chaotic motion identified was validated by the confirmation of a positive Lyapunov exponent. Period-doubling routes to chaos in the fractional-order Chen-Lee system were also found
Generation and control of multi-scroll chaotic attractors in fractional order systems
International Nuclear Information System (INIS)
Ahmad, Wajdi M.
2005-01-01
The objective of this paper is twofold: on one hand we demonstrate the generation of multi-scroll attractors in fractional order chaotic systems. Then, we design state feedback controllers to eliminate chaos from the system trajectories. It is demonstrated that modifying the underlying nonlinearity of the fractional chaotic system results in the birth of multiple chaotic attractors, thus forming the so called multi-scroll attractors. The presence of chaotic behavior is evidenced by a positive largest Lyapunov exponent computed for the output time series. We investigate generation and control of multi-scroll attractors in two different models, both of which are fractional order and chaotic: an electronic oscillator, and a mechanical 'jerk' model. The current findings extend previously reported results on generation of n-scroll attractors from the domain of integer order to the domain of fractional order chaotic systems, and addresses the issue of controlling such chaotic behaviors. Our investigations are validated through numerical simulations
Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems
Rajagopal, Karthikeyan; Karthikeyan, Anitha; Duraisamy, Prakash
2017-06-01
In this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. An adaptive controller is derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable.
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Salman IJAZ
2018-05-01
Full Text Available In this paper, a methodology has been developed to address the issue of force fighting and to achieve precise position tracking of control surface driven by two dissimilar actuators. The nonlinear dynamics of both actuators are first approximated as fractional order models. Based on the identified models, three fractional order controllers are proposed for the whole system. Two Fractional Order PID (FOPID controllers are dedicated to improving transient response and are designed in a position feedback configuration. In order to synchronize the actuator dynamics, a third fractional order PI controller is designed, which feeds the force compensation signal in position feedback loop of both actuators. Nelder-Mead (N-M optimization technique is employed in order to optimally tune controller parameters based on the proposed performance criteria. To test the proposed controllers according to real flight condition, an external disturbance of higher amplitude that acts as airload is applied directly on the control surface. In addition, a disturbance signal function of system states is applied to check the robustness of proposed controller. Simulation results on nonlinear system model validated the performance of the proposed scheme as compared to optimal PID and high gain PID controllers. Keywords: Aerospace, Fractional order control, Model identification, Nelder-Mead optimization, Robustness
Chaos in the fractional order logistic delay system: Circuit realization and synchronization
International Nuclear Information System (INIS)
Baskonus, Haci Mehmet; Hammouch, Zakia; Mekkaoui, Toufik; Bulut, Hasan
2016-01-01
In this paper, we present a numerical study and a circuit design to prove existence of chaos in the fractional order Logistic delay system. In addition, we investigate an active control synchronization scheme in this system. Numerical and cicruit simulations show the effectiveness and feasibility of this method.
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Bin Wang
2016-01-01
Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.
Fractional order fuzzy control of hybrid power system with renewable generation using chaotic PSO.
Pan, Indranil; Das, Saptarshi
2016-05-01
This paper investigates the operation of a hybrid power system through a novel fuzzy control scheme. The hybrid power system employs various autonomous generation systems like wind turbine, solar photovoltaic, diesel engine, fuel-cell, aqua electrolyzer etc. Other energy storage devices like the battery, flywheel and ultra-capacitor are also present in the network. A novel fractional order (FO) fuzzy control scheme is employed and its parameters are tuned with a particle swarm optimization (PSO) algorithm augmented with two chaotic maps for achieving an improved performance. This FO fuzzy controller shows better performance over the classical PID, and the integer order fuzzy PID controller in both linear and nonlinear operating regimes. The FO fuzzy controller also shows stronger robustness properties against system parameter variation and rate constraint nonlinearity, than that with the other controller structures. The robustness is a highly desirable property in such a scenario since many components of the hybrid power system may be switched on/off or may run at lower/higher power output, at different time instants. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
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Hongjuan Liu
2014-01-01
Full Text Available A new general and systematic coupling scheme is developed to achieve the modified projective synchronization (MPS of different fractional-order systems under parameter mismatch via the Open-Plus-Closed-Loop (OPCL control. Based on the stability theorem of linear fractional-order systems, some sufficient conditions for MPS are proposed. Two groups of numerical simulations on the incommensurate fraction-order system and commensurate fraction-order system are presented to justify the theoretical analysis. Due to the unpredictability of the scale factors and the use of fractional-order systems, the chaotic data from the MPS is selected to encrypt a plain image to obtain higher security. Simulation results show that our method is efficient with a large key space, high sensitivity to encryption keys, resistance to attack of differential attacks, and statistical analysis.
Static output feedback ℋ ∞ control for a fractional-order glucose-insulin system
N’ Doye, Ibrahima; Voos, Holger; Darouach, Mohamed; Schneider, Jochen G.
2015-01-01
disturbance. Numerical simulations are carried out to illustrate our proposed results and show that the nonlinear fractional-order glucose-insulin systems are, at least, as stable as their integer-order counterpart in the presence of exogenous glucose infusion
Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms
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Abir Lassoued
2017-01-01
Full Text Available A novel hyperchaotic system with fractional-order (FO terms is designed. Its highly complex dynamics are investigated in terms of equilibrium points, Lyapunov spectrum, and attractor forms. It will be shown that the proposed system exhibits larger Lyapunov exponents than related hyperchaotic systems. Finally, to enhance its potential application, a related circuit is designed by using the MultiSIM Software. Simulation results verify the effectiveness of the suggested circuit.
Identification of fractional-order systems with time delays using block pulse functions
Tang, Yinggan; Li, Ning; Liu, Minmin; Lu, Yao; Wang, Weiwei
2017-07-01
In this paper, a novel method based on block pulse functions is proposed to identify continuous-time fractional-order systems with time delays. First, the operational matrices of block pulse functions for fractional integral operator and time delay operator are derived. Then, these operational matrices are applied to convert the continuous-time fractional-order systems with time delays to an algebraic equation. Finally, the system's parameters along with the differentiation orders and the time delays are all simultaneously estimated through minimizing a quadric error function. The proposed method reduces the computation complexity of the identification process, and also it does not require the system's differentiation orders to be commensurate. The effectiveness of the proposed method are demonstrated by several numerical examples.
A novel adaptive-impulsive synchronization of fractional-order chaotic systems
International Nuclear Information System (INIS)
Andrew, Leung Y. T.; Xian-Feng, Li; Yan-Dong, Chu; Hui, Zhang
2015-01-01
A novel adaptive–impulsive scheme is proposed for synchronizing fractional-order chaotic systems without the necessity of knowing the attractors’ bounds in priori. The nonlinear functions in these systems are supposed to satisfy local Lipschitz conditions but which are estimated with adaptive laws. The novelty is that the combination of adaptive control and impulsive control offers a control strategy gathering the advantages of both. In order to guarantee the convergence is no less than an expected exponential rate, a combined feedback strength design is created such that the symmetric axis can shift freely according to the updated transient feedback strength. All of the unknown Lipschitz constants are also updated exponentially in the meantime of achieving synchronization. Two different fractional-order chaotic systems are employed to demonstrate the effectiveness of the novel adaptive–impulsive control scheme. (paper)
Ding, Da-Wei; Liu, Fang-Fang; Chen, Hui; Wang, Nian; Liang, Dong
2017-12-01
In this paper, a simplest fractional-order delayed memristive chaotic system is proposed in order to control the chaos behaviors via sliding mode control strategy. Firstly, we design a sliding mode control strategy for the fractional-order system with time delay to make the states of the system asymptotically stable. Then, we obtain theoretical analysis results of the control method using Lyapunov stability theorem which guarantees the asymptotic stability of the non-commensurate order and commensurate order system with and without uncertainty and an external disturbance. Finally, numerical simulations are given to verify that the proposed sliding mode control method can eliminate chaos and stabilize the fractional-order delayed memristive system in a finite time. Supported by the National Nature Science Foundation of China under Grant No. 61201227, Funding of China Scholarship Council, the Natural Science Foundation of Anhui Province under Grant No. 1208085M F93, 211 Innovation Team of Anhui University under Grant Nos. KJTD007A and KJTD001B
International Nuclear Information System (INIS)
Zhu, Wu; Fang, Jian-an; Tang, Yang; Zhang, Wenbing; Xu, Yulong
2012-01-01
In this Letter, a differential evolution variant, called switching DE (SDE), has been employed to estimate the orders and parameters in incommensurate fractional-order chaotic systems. The proposed algorithm includes a switching population utilization strategy, where the population size is adjusted dynamically based on the solution-searching status. Thus, this adaptive control method realizes the identification of fractional-order Lorenz, Lü and Chen systems in both deterministic and stochastic environments, respectively. Numerical simulations are provided, where comparisons are made with five other State-of-the-Art evolutionary algorithms (EAs) to verify the effectiveness of the proposed method. -- Highlights: ► Switching population utilization strategy is applied for differential evolution. ► The parameters are estimated in both deterministic and stochastic environments. ► Comparisons with five other EAs verify the effectiveness of the proposed method.
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Zhu, Wu, E-mail: dtzhuwu@gmail.com [College of Information Science and Technology, Donghua University, Shanghai 201620 (China); Fang, Jian-an [College of Information Science and Technology, Donghua University, Shanghai 201620 (China); Tang, Yang, E-mail: yang.tang@pik-potsdam.de [Institute of Physics, Humboldt University, Berlin 12489 (Germany); Potsdam Institute for Climate Impact Research, Potsdam 14415 (Germany); Research Institute for Intelligent Control and System, Harbin Institute of Technology, Harbin 150006 (China); Zhang, Wenbing [Institute of Textiles and Clothing, The Hong Kong Polytechnic University, Hong Kong (China); Xu, Yulong [College of Information Science and Technology, Donghua University, Shanghai 201620 (China)
2012-10-01
In this Letter, a differential evolution variant, called switching DE (SDE), has been employed to estimate the orders and parameters in incommensurate fractional-order chaotic systems. The proposed algorithm includes a switching population utilization strategy, where the population size is adjusted dynamically based on the solution-searching status. Thus, this adaptive control method realizes the identification of fractional-order Lorenz, Lü and Chen systems in both deterministic and stochastic environments, respectively. Numerical simulations are provided, where comparisons are made with five other State-of-the-Art evolutionary algorithms (EAs) to verify the effectiveness of the proposed method. -- Highlights: ► Switching population utilization strategy is applied for differential evolution. ► The parameters are estimated in both deterministic and stochastic environments. ► Comparisons with five other EAs verify the effectiveness of the proposed method.
Stabilization and control of fractional order systems a sliding mode approach
Bandyopadhyay, Bijnan
2015-01-01
In the last two decades fractional differential equations have been used more frequently in physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electro chemistry and many others. It opens a new and more realistic way to capture memory dependent phenomena and irregularities inside the systems by using more sophisticated mathematical analysis.This monograph is based on the authors' work on stabilization and control design for continuous and discrete fractional order systems. The initial two chapters and some parts of the third chapter are written in tutorial fashi
A new image encryption algorithm based on the fractional-order hyperchaotic Lorenz system
Wang, Zhen; Huang, Xia; Li, Yu-Xia; Song, Xiao-Na
2013-01-01
We propose a new image encryption algorithm on the basis of the fractional-order hyperchaotic Lorenz system. While in the process of generating a key stream, the system parameters and the derivative order are embedded in the proposed algorithm to enhance the security. Such an algorithm is detailed in terms of security analyses, including correlation analysis, information entropy analysis, run statistic analysis, mean-variance gray value analysis, and key sensitivity analysis. The experimental results demonstrate that the proposed image encryption scheme has the advantages of large key space and high security for practical image encryption.
International Nuclear Information System (INIS)
Kovacic, Ivana
2009-01-01
An analytical approach to determine the approximate solution for the periodic motion of non-conservative oscillators with a fractional-order restoring force and slowly varying parameters is presented. The solution has the form of the first-order differential equation for the amplitude and phase of motion. The method used is based on the combination of the Krylov-Bogoliubov method with Hamilton's variational principle with the uncommutative rule for the variation of velocity. The conservative systems with slowly varying parameters are also considered. The corresponding adiabatic invariant is obtained. Two examples are given to illustrate derived theoretical results.
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Muhammad Asif Zahoor Raja
2011-01-01
Full Text Available A stochastic technique has been developed for the solution of fractional order system represented by Bagley-Torvik equation. The mathematical model of the equation was developed with the help of feed-forward artificial neural networks. The training of the networks was made with evolutionary computational intelligence based on genetic algorithm hybrid with pattern search technique. Designed scheme was successfully applied to different forms of the equation. Results are compared with standard approximate analytic, stochastic numerical solvers and exact solutions.
Image encryption based on a delayed fractional-order chaotic logistic system
International Nuclear Information System (INIS)
Wang Zhen; Li Ning; Huang Xia; Song Xiao-Na
2012-01-01
A new image encryption scheme is proposed based on a delayed fractional-order chaotic logistic system. In the process of generating a key stream, the time-varying delay and fractional derivative are embedded in the proposed scheme to improve the security. Such a scheme is described in detail with security analyses including correlation analysis, information entropy analysis, run statistic analysis, mean-variance gray value analysis, and key sensitivity analysis. Experimental results show that the newly proposed image encryption scheme possesses high security. (general)
Image encryption based on a delayed fractional-order chaotic logistic system
Wang, Zhen; Huang, Xia; Li, Ning; Song, Xiao-Na
2012-05-01
A new image encryption scheme is proposed based on a delayed fractional-order chaotic logistic system. In the process of generating a key stream, the time-varying delay and fractional derivative are embedded in the proposed scheme to improve the security. Such a scheme is described in detail with security analyses including correlation analysis, information entropy analysis, run statistic analysis, mean-variance gray value analysis, and key sensitivity analysis. Experimental results show that the newly proposed image encryption scheme possesses high security.
Khan, Ayub; Tyagi, Arti
2018-05-01
In this paper, we have studied the hybrid projective synchronisation for incommensurate, integer and commensurate fractional-order financial systems with unknown disturbance. To tackle the problem of unknown bounded disturbance, fractional-order disturbance observer is designed to approximate the unknown disturbance. Further, we have introduced simple sliding mode surface and designed adaptive sliding mode controllers incorporating with the designed fractional-order disturbance observer to achieve a bounded hybrid projective synchronisation between two identical fractional-order financial model with different initial conditions. It is shown that the slave system with disturbance can be synchronised with the projection of the master system generated through state transformation. Simulation results are presented to ensure the validity and effectiveness of the proposed sliding mode control scheme in the presence of external bounded unknown disturbance. Also, synchronisation error for commensurate, integer and incommensurate fractional-order financial systems is studied in numerical simulation.
Design of distributed PID-type dynamic matrix controller for fractional-order systems
Wang, Dawei; Zhang, Ridong
2018-01-01
With the continuous requirements for product quality and safety operation in industrial production, it is difficult to describe the complex large-scale processes with integer-order differential equations. However, the fractional differential equations may precisely represent the intrinsic characteristics of such systems. In this paper, a distributed PID-type dynamic matrix control method based on fractional-order systems is proposed. First, the high-order approximate model of integer order is obtained by utilising the Oustaloup method. Then, the step response model vectors of the plant is obtained on the basis of the high-order model, and the online optimisation for multivariable processes is transformed into the optimisation of each small-scale subsystem that is regarded as a sub-plant controlled in the distributed framework. Furthermore, the PID operator is introduced into the performance index of each subsystem and the fractional-order PID-type dynamic matrix controller is designed based on Nash optimisation strategy. The information exchange among the subsystems is realised through the distributed control structure so as to complete the optimisation task of the whole large-scale system. Finally, the control performance of the designed controller in this paper is verified by an example.
A Novel Image Encryption Algorithm Based on a Fractional-Order Hyperchaotic System and DNA Computing
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Taiyong Li
2017-01-01
Full Text Available In the era of the Internet, image encryption plays an important role in information security. Chaotic systems and DNA operations have been proven to be powerful for image encryption. To further enhance the security of image, in this paper, we propose a novel algorithm that combines the fractional-order hyperchaotic Lorenz system and DNA computing (FOHCLDNA for image encryption. Specifically, the algorithm consists of four parts: firstly, we use a fractional-order hyperchaotic Lorenz system to generate a pseudorandom sequence that will be utilized during the whole encryption process; secondly, a simple but effective diffusion scheme is performed to spread the little change in one pixel to all the other pixels; thirdly, the plain image is encoded by DNA rules and corresponding DNA operations are performed; finally, global permutation and 2D and 3D permutation are performed on pixels, bits, and acid bases. The extensive experimental results on eight publicly available testing images demonstrate that the encryption algorithm can achieve state-of-the-art performance in terms of security and robustness when compared with some existing methods, showing that the FOHCLDNA is promising for image encryption.
International Nuclear Information System (INIS)
Wang, Cong; Zhang, Hong-li; Fan, Wen-hui
2017-01-01
In this paper, we propose a new method to improve the safety of secure communication. This method uses the generalized dislocated lag projective synchronization and function projective synchronization to form a new generalized dislocated lag function projective synchronization. Moreover, this paper takes the examples of fractional order Chen system and Lü system with uncertain parameters as illustration. As the parameters of the two systems are uncertain, the nonlinear controller and parameter update algorithms are designed based on the fractional stability theory and adaptive control method. Moreover, this synchronization form and method of control are applied to secure communication via chaotic masking modulation. Many information signals can be recovered and validated. Finally, simulations are used to show the validity and feasibility of the proposed scheme.
Chao, Luo
2015-11-01
In this paper, a novel digital secure communication scheme is firstly proposed. Different from the usual secure communication schemes based on chaotic synchronization, the proposed scheme employs asynchronous communication which avoids the weakness of synchronous systems and is susceptible to environmental interference. Moreover, as to the transmission errors and data loss in the process of communication, the proposed scheme has the ability to be error-checking and error-correcting in real time. In order to guarantee security, the fractional-order complex chaotic system with the shifting of order is utilized to modulate the transmitted signal, which has high nonlinearity and complexity in both frequency and time domains. The corresponding numerical simulations demonstrate the effectiveness and feasibility of the scheme.
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Liu, Xiaojun [State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi' an Jiaotong University, Xi' an 710049 (China); School of Mathematics and Statistics, Tianshui Normal University, Tianshui 741001 (China); Hong, Ling, E-mail: hongling@mail.xjtu.edu.cn; Jiang, Jun [State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi' an Jiaotong University, Xi' an 710049 (China)
2016-08-15
Global bifurcations include sudden changes in chaotic sets due to crises. There are three types of crises defined by Grebogi et al. [Physica D 7, 181 (1983)]: boundary crisis, interior crisis, and metamorphosis. In this paper, by means of the extended generalized cell mapping (EGCM), boundary and interior crises of a fractional-order Duffing system are studied as one of the system parameters or the fractional derivative order is varied. It is found that a crisis can be generally defined as a collision between a chaotic basic set and a basic set, either periodic or chaotic, to cause a sudden discontinuous change in chaotic sets. Here chaotic sets involve three different kinds: a chaotic attractor, a chaotic saddle on a fractal basin boundary, and a chaotic saddle in the interior of a basin and disjoint from the attractor. A boundary crisis results from the collision of a periodic (or chaotic) attractor with a chaotic (or regular) saddle in the fractal (or smooth) boundary. In such a case, the attractor, together with its basin of attraction, is suddenly destroyed as the control parameter passes through a critical value, leaving behind a chaotic saddle in the place of the original attractor and saddle after the crisis. An interior crisis happens when an unstable chaotic set in the basin of attraction collides with a periodic attractor, which causes the appearance of a new chaotic attractor, while the original attractor and the unstable chaotic set are converted to the part of the chaotic attractor after the crisis. These results further demonstrate that the EGCM is a powerful tool to reveal the mechanism of crises in fractional-order systems.
Directory of Open Access Journals (Sweden)
Xueliang Liu
2012-01-01
Full Text Available This paper is concerned with a containment problem of networked fractional-order system with multiple leaders under a fixed directed interaction graph. Based on the neighbor rule, a distributed protocol is proposed in delayed communication channels. By employing the algebraic graph theory, matrix theory, Nyquist stability theorem, and frequency domain method, it is analytically proved that the whole follower agents will flock to the convex hull which is formed by the leaders. Furthermore, a tight upper bound on the communication time-delay that can be tolerated in the dynamic network is obtained. As a special case, the interconnection topology under the undirected case is also discussed. Finally, some numerical examples with simulations are presented to demonstrate the effectiveness and correctness of the theoretical results.
Biswas, Karabi; Caponetto, Riccardo; Mendes Lopes, António; Tenreiro Machado, José António
2017-01-01
This book focuses on two specific areas related to fractional order systems – the realization of physical devices characterized by non-integer order impedance, usually called fractional-order elements (FOEs); and the characterization of vegetable tissues via electrical impedance spectroscopy (EIS) – and provides readers with new tools for designing new types of integrated circuits. The majority of the book addresses FOEs. The interest in these topics is related to the need to produce “analogue” electronic devices characterized by non-integer order impedance, and to the characterization of natural phenomena, which are systems with memory or aftereffects and for which the fractional-order calculus tool is the ideal choice for analysis. FOEs represent the building blocks for designing and realizing analogue integrated electronic circuits, which the authors believe hold the potential for a wealth of mass-market applications. The freedom to choose either an integer- or non-integer-order analogue integrator...
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Sifeu Takougang Kingni
2017-01-01
Full Text Available A linear resistive-capacitive-inductance shunted junction (LRCLSJ model obtained by replacing the nonlinear piecewise resistance of a nonlinear resistive-capacitive-inductance shunted junction (NRCLSJ model by a linear resistance is analyzed in this paper. The LRCLSJ model has two or no equilibrium points depending on the dc bias current. For a suitable choice of the parameters, the LRCLSJ model without equilibrium point can exhibit regular and fast spiking, intrinsic and periodic bursting, and periodic and chaotic behaviors. We show that the LRCLSJ model displays similar dynamical behaviors as the NRCLSJ model. Moreover the coexistence between periodic and chaotic attractors is found in the LRCLSJ model for specific parameters. The lowest order of the commensurate form of the no equilibrium LRCLSJ model to exhibit chaotic behavior is found to be 2.934. Moreover, adaptive finite-time synchronization with parameter estimation is applied to achieve synchronization of unidirectional coupled identical fractional-order form of chaotic no equilibrium LRCLSJ models. Finally, a cryptographic encryption scheme with the help of the finite-time synchronization of fractional-order chaotic no equilibrium LRCLSJ models is illustrated through a numerical example, showing that a high level security device can be produced using this system.
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Li Junyi
2015-01-01
Full Text Available A fractional order PID (FOPID controller, which is suitable for control system designing for being insensitive to the variation in system parameter, is proposed for hydroturbine governing system in the paper. The simultaneous optimization for several parameters of controller, that is, Ki, Kd, Kp, λ, and μ, is done by a recently developed metaheuristic nature-inspired algorithm, namely, the firefly algorithm (FA, for the first time, where the selecting, moving, attractiveness behavior between fireflies and updating of brightness, and decision range are studied in detail to simulate the optimization process. Investigation clearly reveals the advantages of the FOPID controller over the integer controllers in terms of reduced oscillations and settling time. The present work also explores the superiority of FA based optimization technique in finding optimal parameters of the controller. Further, convergence characteristics of the FA are compared with optimum integer order PID (IOPID controller to justify its efficiency. What is more, analysis confirms the robustness of FOPID controller under isolated load operation conditions.
A new color image encryption scheme using CML and a fractional-order chaotic system.
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Xiangjun Wu
Full Text Available The chaos-based image cryptosystems have been widely investigated in recent years to provide real-time encryption and transmission. In this paper, a novel color image encryption algorithm by using coupled-map lattices (CML and a fractional-order chaotic system is proposed to enhance the security and robustness of the encryption algorithms with a permutation-diffusion structure. To make the encryption procedure more confusing and complex, an image division-shuffling process is put forward, where the plain-image is first divided into four sub-images, and then the position of the pixels in the whole image is shuffled. In order to generate initial conditions and parameters of two chaotic systems, a 280-bit long external secret key is employed. The key space analysis, various statistical analysis, information entropy analysis, differential analysis and key sensitivity analysis are introduced to test the security of the new image encryption algorithm. The cryptosystem speed is analyzed and tested as well. Experimental results confirm that, in comparison to other image encryption schemes, the new algorithm has higher security and is fast for practical image encryption. Moreover, an extensive tolerance analysis of some common image processing operations such as noise adding, cropping, JPEG compression, rotation, brightening and darkening, has been performed on the proposed image encryption technique. Corresponding results reveal that the proposed image encryption method has good robustness against some image processing operations and geometric attacks.
Multiobjective Optimization Design of a Fractional Order PID Controller for a Gun Control System
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Qiang Gao
2013-01-01
Full Text Available Motion control of gun barrels is an ongoing topic for the development of gun control equipments possessing excellent performances. In this paper, a typical fractional order PID control strategy is employed for the gun control system. To obtain optimal parameters of the controller, a multiobjective optimization scheme is developed from the loop-shaping perspective. To solve the specified nonlinear optimization problem, a novel Pareto optimal solution based multiobjective differential evolution algorithm is proposed. To enhance the convergent rate of the optimization process, an opposition based learning method is embedded in the chaotic population initialization process. To enhance the robustness of the algorithm for different problems, an adapting scheme of the mutation operation is further employed. With assistance of the evolutionary algorithm, the optimal solution for the specified problem is selected. The numerical simulation results show that the control system can rapidly follow the demand signal with high accuracy and high robustness, demonstrating the efficiency of the proposed controller parameter tuning method.
A New Approach to Rational Discrete-Time Approximations to Continuous-Time Fractional-Order Systems
Matos , Carlos; Ortigueira , Manuel ,
2012-01-01
Part 10: Signal Processing; International audience; In this paper a new approach to rational discrete-time approximations to continuous fractional-order systems of the form 1/(sα+p) is proposed. We will show that such fractional-order LTI system can be decomposed into sub-systems. One has the classic behavior and the other is similar to a Finite Impulse Response (FIR) system. The conversion from continuous-time to discrete-time systems will be done using the Laplace transform inversion integr...
Directory of Open Access Journals (Sweden)
Anitha Karthikeyan
2018-03-01
Full Text Available In this paper we derived the fractional order model of the Permanent Magnet Synchronous Generator (PMSG from its integer model. The PMSG was employing a shaft sensor for the speed sensing and control. But this sensor would increase the hardware complexity as well as the cost of the system. Hence we have developed a Fractional order Nonlinear adaptive control method for speed and current tracking of the PMSG. The objective of an adaptive controller is to first define a virtual control state and force it to become a stabilizing function in accordance with a corresponding error dynamics. In order to study the Lyapunov exponents of the fractional order controller, we proposed a new method which would remove the complexity of finding the sign of the Lyapunov first derivative. The Fractional order control scheme is implemented in LabVIEW for simulation results. The simulation results indicated that the estimated rotor position and speed correspond to their actual values well. Keywords: Chaos suppression, Fractional order systems, Permanent magnet synchronous generator, Speed and current control, Lyapunov stability
Complexity and Hopf Bifurcation Analysis on a Kind of Fractional-Order IS-LM Macroeconomic System
Ma, Junhai; Ren, Wenbo
On the basis of our previous research, we deepen and complete a kind of macroeconomics IS-LM model with fractional-order calculus theory, which is a good reflection on the memory characteristics of economic variables, we also focus on the influence of the variables on the real system, and improve the analysis capabilities of the traditional economic models to suit the actual macroeconomic environment. The conditions of Hopf bifurcation in fractional-order system models are briefly demonstrated, and the fractional order when Hopf bifurcation occurs is calculated, showing the inherent complex dynamic characteristics of the system. With numerical simulation, bifurcation, strange attractor, limit cycle, waveform and other complex dynamic characteristics are given; and the order condition is obtained with respect to time. We find that the system order has an important influence on the running state of the system. The system has a periodic motion when the order meets the conditions of Hopf bifurcation; the fractional-order system gradually stabilizes with the change of the order and parameters while the corresponding integer-order system diverges. This study has certain significance to policy-making about macroeconomic regulation and control.
Ndoye, Ibrahima
2014-12-01
In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown parameters are also adapted to their values. Sufficient conditions for the stability of the adaptive observer error dynamics are derived in terms of linear matrix inequalities. Simulation results for chaotic Lorenz systems with unknown parameters in the presence of external perturbations are given to illustrate the effectiveness of our proposed approach. © 2014 IEEE.
Fractional Order Generalized Information
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José Tenreiro Machado
2014-04-01
Full Text Available This paper formulates a novel expression for entropy inspired in the properties of Fractional Calculus. The characteristics of the generalized fractional entropy are tested both in standard probability distributions and real world data series. The results reveal that tuning the fractional order allow an high sensitivity to the signal evolution, which is useful in describing the dynamics of complex systems. The concepts are also extended to relative distances and tested with several sets of data, confirming the goodness of the generalization.
ℋ∞ Adaptive observer for nonlinear fractional-order systems
Ndoye, Ibrahima
2016-06-23
In this paper, an adaptive observer is proposed for the joint estimation of states and parameters of a fractional nonlinear system with external perturbations. The convergence of the proposed observer is derived in terms of linear matrix inequalities (LMIs) by using an indirect Lyapunov method.The proposed ℋ∞ adaptive observer is also robust against Lipschitz additive nonlinear uncertainty. The performance of the observer is illustrated through some examples including the chaotic Lorenz and Lü\\'s systems. © 2016 John Wiley & Sons, Ltd.
IMC-PID-fractional-order-filter controllers design for integer order systems.
Maâmar, Bettayeb; Rachid, Mansouri
2014-09-01
One of the reasons of the great success of standard PID controllers is the presence of simple tuning rules, of the automatic tuning feature and of tables that simplify significantly their design. For the fractional order case, some tuning rules have been proposed in the literature. However, they are not general because they are valid only for some model cases. In this paper, a new approach is investigated. The fractional property is not especially imposed by the controller structure but by the closed loop reference model. The resulting controller is fractional but it has a very interesting structure for its implementation. Indeed, the controller can be decomposed into two transfer functions: an integer transfer function which is generally an integer PID controller and a simple fractional filter. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
DEFF Research Database (Denmark)
Moafi, Milad; Marzband, Mousa; Savaghebi, Mehdi
2016-01-01
in the islanded Microgrid (MG). To increase performance for a wide range of power system operating conditions, an energy management systems (EMS) is proposed based on a fuzzy fractional order PID (FFOPID) controller. It is able to analyze and simulate the dynamic behavior in grid connected MGs. This controller...... is proposed in the MG encompassing distributed generation resources with “plug and play” ability. The performance of FFOPID controller is verified for frequency control purposes and to support internal bus voltage in both islanded and grid connected operating modes in accordance with the failure time. Energy...... combined with a PID-controller (termed as FLPID) and Fuzzy fractional order PID (termed as FFOPID) are implemented according to the characteristics and limitations of overloading and state of charge (SOC). The obtained results show good performance of FFOPID controllers by improving the transient stability...
International Nuclear Information System (INIS)
Melicio, R.; Mendes, V.M.F.; Catalao, J.P.S.
2010-01-01
This paper presents a new integrated model for the simulation of wind energy systems. The proposed model is more realistic and accurate, considering a variable-speed wind turbine, two-mass rotor, permanent magnet synchronous generator (PMSG), different power converter topologies, and filters. Additionally, a new control strategy is proposed for the variable-speed operation of wind turbines with PMSG/full-power converter topology, based on fractional-order controllers. Comprehensive simulation studies are carried out with matrix and multilevel power converter topologies, in order to adequately assert the system performance in what regards the quality of the energy injected into the electric grid. Finally, conclusions are duly drawn.
Energy Technology Data Exchange (ETDEWEB)
Melicio, R.; Catalao, J.P.S. [Department of Electromechanical Engineering, University of Beira Interior, R. Fonte do Lameiro, 6201-001 Covilha (Portugal); Mendes, V.M.F. [Department of Electrical Engineering and Automation, Instituto Superior de Engenharia de Lisboa, R. Conselheiro Emidio Navarro, 1950-062 Lisbon (Portugal)
2010-06-15
This paper presents a new integrated model for the simulation of wind energy systems. The proposed model is more realistic and accurate, considering a variable-speed wind turbine, two-mass rotor, permanent magnet synchronous generator (PMSG), different power converter topologies, and filters. Additionally, a new control strategy is proposed for the variable-speed operation of wind turbines with PMSG/full-power converter topology, based on fractional-order controllers. Comprehensive simulation studies are carried out with matrix and multilevel power converter topologies, in order to adequately assert the system performance in what regards the quality of the energy injected into the electric grid. Finally, conclusions are duly drawn. (author)
DEFF Research Database (Denmark)
Huang, Sunhua; Zhou, Bin; Li, Canbing
2018-01-01
represent complex dynamic behaviours with chaotic and unstable states on the energy conservation, carbon emissions, economic growth, and renewable energy development, and have a great impact on the formulation of government energy policies. Furthermore, based on the fractional Lyapunov stability and robust......, and the fractional-order model of the energy-saving and emission-reduction system (FOESERS) is formulated. With the proposed FOESERS, all of the equilibrium points and the corresponding eigenvalues are obtained, and the instability region and the state trajectories of FOESERS are also given. The FOESERS can...
International Nuclear Information System (INIS)
Beddar, Antar; Bouzekri, Hacene; Babes, Badreddine; Afghoul, Hamza
2016-01-01
Highlights: • Fuzzy fractional order PI+I for wind energy conversion system is developed. • Investigation of the control methods performances under wind and load variations. • PSO algorithm with frequency method are used for parameters tuning. • Experimental results are presented. - Abstract: In this paper, fuzzy fractional order PI+I (FFOPI+I) controller for grid connected Variable Speed Wind Energy Conversion System (VS-WECS) is proposed. The FFOPI+I controller is applied to control a Permanent Magnet Synchronous Generator (PMSG) connected to the grid and nonlinear load through a back-to-back AC-DC-AC PWM converter. The control strategy of the Machine Side Converter (MSC) aims, at first, to extract a maximum power under fluctuating wind speed. Then, the Grid Side Converter (GSC) is controlled to improve the power quality and ensure sinusoidal current in the grid side. The FFOPI+I controller implements a Fuzzy Logic Controller (FLC) in parallel with Fractional Order PI (FOPI) and conventional PI controllers by having a commune proportional gain. The FLC changes the integral gains at runtime. The initial parameters of the FFOPI+I controller were calculated using a frequency method to create a search space then the PSO algorithm is used to select the optimal parameters. To evaluate the performance of the proposed controller in steady and transient states, an experimental test bench has been built in laboratory using dSPACE1104 card. The experimental results demonstrate the effectiveness and feasibility of the FFOPI+I over FOPI and conventional PI controllers by realizing maximum power extraction and improving the grid-side power factor for a wide range of wind speed.
Ndoye, Ibrahima; Voos, Holger; Laleg-Kirati, Taous-Meriem; Darouach, Mohamed
2014-01-01
In this paper, an adaptive observer design with parameter identification for a nonlinear system with external perturbations and unknown parameters is proposed. The states of the nonlinear system are estimated by a nonlinear observer and the unknown
On nonlinear control design for autonomous chaotic systems of integer and fractional orders
International Nuclear Information System (INIS)
Ahmad, Wajdi M.; Harb, Ahmad M.
2003-01-01
In this paper, we address the problem of chaos control for autonomous nonlinear chaotic systems. We use the recursive 'backstepping' method of nonlinear control design to derive the nonlinear controllers. The controller effect is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. We study two nonlinear chaotic systems: an electronic chaotic oscillator model, and a mechanical chaotic 'jerk' model. We demonstrate the robustness of the derived controllers against system order reduction arising from the use of fractional integrators in the system models. Our results are validated via numerical simulations
Fractional Order Element Based Impedance Matching
Radwan, Ahmed Gomaa; Salama, Khaled N.; Shamim, Atif
2014-01-01
Disclosed are various embodiments of methods and systems related to fractional order element based impedance matching. In one embodiment, a method includes aligning a traditional Smith chart (|.alpha.|=1) with a fractional order Smith chart (|.alpha
Fractional Order Element Based Impedance Matching
Radwan, Ahmed Gomaa
2014-06-24
Disclosed are various embodiments of methods and systems related to fractional order element based impedance matching. In one embodiment, a method includes aligning a traditional Smith chart (|.alpha.|=1) with a fractional order Smith chart (|.alpha.|.noteq.1). A load impedance is located on the traditional Smith chart and projected onto the fractional order Smith chart. A fractional order matching element is determined by transitioning along a matching circle of the fractional order Smith chart based at least in part upon characteristic line impedance. In another embodiment, a system includes a fractional order impedance matching application executed in a computing device. The fractional order impedance matching application includes logic that obtains a first set of Smith chart coordinates at a first order, determines a second set of Smith chart coordinates at a second order, and determines a fractional order matching element from the second set of Smith chart coordinates.
Directory of Open Access Journals (Sweden)
S. J. Sadati
2012-01-01
Full Text Available A fractional-order controller will be proposed to regulate the inlet oxygen into the heart-lung machine. An analytical approach will be explained to satisfy some requirements together with practical implementation of some restrictions for the first time. Primarily a nonlinear single-input single-output (SISO time-delay model which was obtained previously in the literature is introduced for the oxygen generation process in the heart-lung machine system and we will complete it by adding some new states to control it. Thereafter, the system is linearized using the state feedback linearization approach to find a third-order time-delay dynamics. Consequently classical PID and fractional order controllers are gained to assess the quality of the proposed technique. A set of optimal parameters of those controllers are achieved through the genetic algorithm optimization procedure through minimizing a cost function. Our design method focuses on minimizing some famous performance criterions such as IAE, ISE, and ITSE. In the genetic algorithm, the controller parameters are chosen as a random population. The best relevant values are achieved by reducing the cost function. A time-domain simulation signifies the performance of controller with respect to a traditional optimized PID controller.
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Qiang Gao
2015-12-01
Full Text Available Aiming at balancing and positioning of a new electro-hydraulic servo system with iso-actuation configuration, an extended state observer–based fractional order proportional–integral–derivative controller is proposed in this study. To meet the lightweight requirements of heavy barrel weapons with large diameters, an electro-hydraulic servo system with a three-chamber hydraulic cylinder is especially designed. In the electro-hydraulic servo system, the balance chamber of the hydraulic cylinder is used to realize active balancing of the unbalanced forces, while the driving chambers consisting of the upper and lower chambers are adopted for barrel positioning and dynamic compensation of external disturbances. Compared with conventional proportional–integral–derivative controllers, the fractional order proportional–integral–derivative possesses another two adjustable parameters by expanding integer order to arbitrary order calculus, resulting in more flexibility and stronger robustness of the control system. To better compensate for strong external disturbances and system nonlinearities, the extended state observer strategy is further introduced to the fractional order proportional–integral–derivative control system. Numerical simulation and bench test indicate that the extended state observer–based fractional order proportional–integral–derivative significantly outperforms proportional–integral–derivative and fractional order proportional–integral–derivative control systems with better control accuracy and higher system robustness, well demonstrating the feasibility and effectiveness of the proposed extended state observer–based fractional order proportional–integral–derivative control strategy.
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Lakhdar Chaib
2017-06-01
Full Text Available This paper proposes a novel robust power system stabilizer (PSS, based on hybridization of fractional order PID controller (PIλDμ and PSS for optimal stabilizer (FOPID-PSS for the first time, using a new metaheuristic optimization Bat algorithm (BA inspired by the echolocation behavior to improve power system stability. The problem of FOPID-PSS design is transformed as an optimization problem based on performance indices (PI, including Integral Absolute Error (IAE, Integral Squared Error (ISE, Integral of the Time-Weighted Absolute Error (ITAE and Integral of Time multiplied by the Squared Error (ITSE, where, BA is employed to obtain the optimal stabilizer parameters. In order to examine the robustness of FOPID-PSS, it has been tested on a Single Machine Infinite Bus (SMIB power system under different disturbances and operating conditions. The performance of the system with FOPID-PSS controller is compared with a PID-PSS and PSS. Further, the simulation results obtained with the proposed BA based FOPID-PSS are compared with those obtained with FireFly algorithm (FFA based FOPID-PSS. Simulation results show the effectiveness of BA for FOPID-PSS design, and superior robust performance for enhancement power system stability compared to other with different cases.
Xie, Yuanlong; Tang, Xiaoqi; Song, Bao; Zhou, Xiangdong; Guo, Yixuan
2018-04-01
In this paper, data-driven adaptive fractional order proportional integral (AFOPI) control is presented for permanent magnet synchronous motor (PMSM) servo system perturbed by measurement noise and data dropouts. The proposed method directly exploits the closed-loop process data for the AFOPI controller design under unknown noise distribution and data missing probability. Firstly, the proposed method constructs the AFOPI controller tuning problem as a parameter identification problem using the modified l p norm virtual reference feedback tuning (VRFT). Then, iteratively reweighted least squares is integrated into the l p norm VRFT to give a consistent compensation solution for the AFOPI controller. The measurement noise and data dropouts are estimated and eliminated by feedback compensation periodically, so that the AFOPI controller is updated online to accommodate the time-varying operating conditions. Moreover, the convergence and stability are guaranteed by mathematical analysis. Finally, the effectiveness of the proposed method is demonstrated both on simulations and experiments implemented on a practical PMSM servo system. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Kingni, Sifeu Takougang; Pham, Viet-Thanh; Jafari, Sajad; Woafo, Paul
2017-01-01
A three-dimensional autonomous chaotic system with an infinite number of equilibrium points located on a line and a hyperbola is proposed in this paper. To analyze the dynamical behaviors of the proposed system, mathematical tools such as Routh-Hurwitz criteria, Lyapunov exponents and bifurcation diagram are exploited. For a suitable choice of the parameters, the proposed system can generate periodic oscillations and chaotic attractors of different shapes such as bistable and monostable chaotic attractors. In addition, an electronic circuit is designed and implemented to verify the feasibility of the proposed system. A good qualitative agreement is shown between the numerical simulations and the Orcard-PSpice results. Moreover, the fractional-order form of the proposed system is studied using analog and numerical simulations. It is found that chaos, periodic oscillations and periodic spiking exist in this proposed system with order less than three. Then an electronic circuit is designed for the commensurate fractional order α = 0.98, from which we can observe that a chaotic attractor exists in the fractional-order form of the proposed system. Finally, the problem of drive-response generalized projective synchronization of the fractional-order form of the chaotic proposed autonomous system is considered.
Wang, Fei; Yang, Yongqing
2017-09-01
In this paper, we study the leader-following exponential consensus of multi-agent system. Each agent in the system is described by nonlinear fractional order differential equation. Both the internal delay and coupling delay are taken into consideration. The heterogeneous impulsive control is used for ensuring the consensus of all agents. Based on Lyapunov function method and matrix analysis, some sufficient conditions for exponential consensus are obtained. Finally, some illustrative examples are given to show the effectiveness of the obtained results.
Fractional Order Models of Industrial Pneumatic Controllers
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Abolhassan Razminia
2014-01-01
Full Text Available This paper addresses a new approach for modeling of versatile controllers in industrial automation and process control systems such as pneumatic controllers. Some fractional order dynamical models are developed for pressure and pneumatic systems with bellows-nozzle-flapper configuration. In the light of fractional calculus, a fractional order derivative-derivative (FrDD controller and integral-derivative (FrID are remodeled. Numerical simulations illustrate the application of the obtained theoretical results in simple examples.
Ferroelectric Fractional-Order Capacitors
Agambayev, Agamyrat
2017-07-25
Poly(vinylidene fluoride)-based polymers and their blends are used to fabricate electrostatic fractional-order capacitors. This simple but effective method allows us to precisely tune the constant phase angle of the resulting fractional-order capacitor by changing the blend composition. Additionally, we have derived an empirical relation between the ratio of the blend constituents and the constant phase angle to facilitate the design of a fractional order capacitor with a desired constant phase angle. The structural composition of the fabricated blends is investigated using Fourier transform infrared spectroscopy and X-ray diffraction techniques.
Ferroelectric Fractional-Order Capacitors
Agambayev, Agamyrat; Patole, Shashikant P.; Farhat, Mohamed; Elwakil, Ahmed; Bagci, Hakan; Salama, Khaled N.
2017-01-01
Poly(vinylidene fluoride)-based polymers and their blends are used to fabricate electrostatic fractional-order capacitors. This simple but effective method allows us to precisely tune the constant phase angle of the resulting fractional-order capacitor by changing the blend composition. Additionally, we have derived an empirical relation between the ratio of the blend constituents and the constant phase angle to facilitate the design of a fractional order capacitor with a desired constant phase angle. The structural composition of the fabricated blends is investigated using Fourier transform infrared spectroscopy and X-ray diffraction techniques.
International Nuclear Information System (INIS)
Chen, Zhihuan; Yuan, Xiaohui; Ji, Bin; Wang, Pengtao; Tian, Hao
2014-01-01
Highlights: • Multi-objective optimization based fractional order controller is designed for HTRS. • NSGAII is improved by iterative chaotic map with infinite collapses (ICMIC) operator. • ISE and ITSE are as chosen as objective functions in tuning parameters of HTRS. • FOPID controller outperforms the PID controller under various running conditions. • Trade-off between speed of reference tracking and damping of oscillation are shown. - Abstract: Fractional-order PID (FOPID) controller is a generalization of traditional PID controller using fractional calculus. Compared to the traditional PID controller, in FOPID controller, the order of derivative portion and integral portion is not integer, which provides more flexibility in achieving control objectives. Design stage of such an FOPID controller consists of determining five parameters, i.e. proportional, integral and derivative gains {Kp, Ki, Kd}, and extra integration and differentiation orders {λ,μ}, which has a large difference comparing with the conventional PID tuning rules, thus a suitable optimization algorithm is essential to the parameters tuning of FOPID controller. This paper focuses on the design of the FOPID controller using chaotic non-dominated sorting genetic algorithm II (NSGAII) for hydraulic turbine regulating system (HTRS). The parameters chosen of the FOPID controller is formulated as a multi-objective optimization problem, in which the objective functions are composed by the integral of the squared error (ISE) and integral of the time multiplied squared error (ITSE). The chaotic NSGAII algorithm, which is an incorporation of chaotic behaviors into NSGAII, is used as the optimizer to search true Pareto-front of the FOPID controller and designers can implement each of them based on objective functions priority. The designed chaotic NSGAII based FOPID controller procedure is applied to a HTRS system. A comparison study between the optimum integer order PID controller and optimum
Hyperchaotic Chameleon: Fractional Order FPGA Implementation
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Karthikeyan Rajagopal
2017-01-01
Full Text Available There are many recent investigations on chaotic hidden attractors although hyperchaotic hidden attractor systems and their relationships have been less investigated. In this paper, we introduce a hyperchaotic system which can change between hidden attractor and self-excited attractor depending on the values of parameters. Dynamic properties of these systems are investigated. Fractional order models of these systems are derived and their bifurcation with fractional orders is discussed. Field programmable gate array (FPGA implementations of the systems with their power and resource utilization are presented.
Energy Technology Data Exchange (ETDEWEB)
Wu, Yimin [School of Mathematics and Statistics, Suzhou University, Suzhou 234000 (China); Lv, Hui, E-mail: lvhui207@gmail.com [Department of Applied Mathematics, Huainan Normal University, Huainan 232038 (China)
2016-08-15
In this paper, we consider the control problem of a class of uncertain fractional-order chaotic systems preceded by unknown backlash-like hysteresis nonlinearities based on backstepping control algorithm. We model the hysteresis by using a differential equation. Based on the fractional Lyapunov stability criterion and the backstepping algorithm procedures, an adaptive neural network controller is driven. No knowledge of the upper bound of the disturbance and system uncertainty is required in our controller, and the asymptotical convergence of the tracking error can be guaranteed. Finally, we give two simulation examples to confirm our theoretical results.
Projective synchronization of a complex network with different fractional order chaos nodes
International Nuclear Information System (INIS)
Wang Ming-Jun; Wang Xing-Yuan; Niu Yu-Jun
2011-01-01
Based on the stability theory of the linear fractional order system, projective synchronization of a complex network is studied in the paper, and the coupling functions of the connected nodes are identified. With this method, the projective synchronization of the network with different fractional order chaos nodes can be achieved, besides, the number of the nodes does not affect the stability of the whole network. In the numerical simulations, the chaotic fractional order Lü system, Liu system and Coullet system are chosen as examples to show the effectiveness of the scheme. (general)
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Guan-Chun Chen
2015-01-01
Full Text Available This study proposes virtual-reality (VR simulator system for double interventional cardiac catheterization (ICC using fractional-order vascular access tracker and haptic force producer. An endoscope or a catheter for diagnosis and surgery of cardiovascular disease has been commonly used in minimally invasive surgery. It needs specific skills and experiences for young surgeons or postgraduate year (PGY students to operate a Berman catheter and a pigtail catheter in the inside of the human body and requires avoiding damaging vessels. To improve the training in inserting catheters, a double-catheter mechanism is designed for the ICC procedures. A fractional-order vascular access tracker is used to trace the senior surgeons’ consoled trajectories and transmit the frictional feedback and visual feedback during the insertion of catheters. Based on the clinical feeling through the aortic arch, vein into the ventricle, or tortuous blood vessels, haptic force producer is used to mock the elasticity of the vessel wall using voice coil motors (VCMs. The VR establishment with surgeons’ consoled vessel trajectories and hand feeling is achieved, and the experimental results show the effectiveness for the double ICC procedures.
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Javad Morsali
2017-02-01
Full Text Available In this paper, fractional order proportional-integral-differential (FOPID controller is employed in the design of thyristor controlled series capacitor (TCSC-based damping controller in coordination with the secondary integral controller as automatic generation control (AGC loop. In doing so, the contribution of the TCSC in tie-line power exchange is extracted mathematically for small load disturbance. Adjustable parameters of the proposed FOPID-based TCSC damping controller and the AGC loop are optimized concurrently via an improved particle swarm optimization (IPSO algorithm which is reinforced by chaotic parameter and crossover operator to obtain a globally optimal solution. The powerful FOMCON toolbox is used along with MATLAB for handling fractional order modeling and control. An interconnected multi-source power system is simulated regarding the physical constraints of generation rate constraint (GRC nonlinearity and governor dead band (GDB effect. Simulation results using FOMCON toolbox demonstrate that the proposed FOPID-based TCSC damping controller achieves the greatest dynamic performance under different load perturbation patterns in comparison with phase lead-lag and classical PID-based TCSC damping controllers, all in coordination with the integral AGC. Moreover, sensitivity analyses are performed to show the robustness of the proposed controller under various uncertainty scenarios.
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Sadalla Talar
2017-12-01
Full Text Available The paper aims at presenting the influence of an open-loop time delay on the stability and tracking performance of a second-order open-loop system and continuoustime fractional-order PI controller. The tuning method of this controller is based on Hermite- Biehler and Pontryagin theorems, and the tracking performance is evaluated on the basis of two integral performance indices, namely IAE and ISE. The paper extends the results and methodology presented in previous work of the authors to analysis of the influence of time delay on the closed-loop system taking its destabilizing properties into account, as well as concerning possible application of the presented results and used models.
International Nuclear Information System (INIS)
Khanzadeh, Alireza; Pourgholi, Mahdi
2016-01-01
A main problem associated with the synchronization of two chaotic systems is that the time in which complete synchronization will occur is not specified. Synchronization time is either infinitely large or is finite but only its upper bound is known and this bound depends on the systems' initial conditions. In this paper we propose a method for synchronizing of two chaotic systems precisely at a time which we want. To this end, time-varying switching surfaces sliding mode control is used and the control law based on Lyapunov stability theorem is derived which is able to synchronize two fractional-order chaotic systems precisely at a pre specified time without concerning about their initial conditions. Moreover, by eliminating the reaching phase in the proposed synchronization scheme, robustness against existence of uncertainties and exogenous disturbances is obtained. Because of the existence of fractional integral of the sign function instead of the sign function in the control equation, the necessity for infinitely fast switching be obviated in this method. To show the effectiveness of the proposed method the illustrative examples under different situations are provided and the simulation results are reported.
Dynamical models of happiness with fractional order
Song, Lei; Xu, Shiyun; Yang, Jianying
2010-03-01
This present study focuses on a dynamical model of happiness described through fractional-order differential equations. By categorizing people of different personality and different impact factor of memory (IFM) with different set of model parameters, it is demonstrated via numerical simulations that such fractional-order models could exhibit various behaviors with and without external circumstance. Moreover, control and synchronization problems of this model are discussed, which correspond to the control of emotion as well as emotion synchronization in real life. This study is an endeavor to combine the psychological knowledge with control problems and system theories, and some implications for psychotherapy as well as hints of a personal approach to life are both proposed.
Fractional-Order Control of Pneumatic Position Servosystems
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Cao Junyi
2011-01-01
Full Text Available A fractional-order control strategy for pneumatic position servosystem is presented in this paper. The idea of the fractional calculus application to control theory was introduced in many works, and its advantages were proved. However, the realization of fractional-order controllers for pneumatic position servosystems has not been investigated. Based on the relationship between the pressure in cylinder and the rate of mass flow into the cylinder, the dynamic model of pneumatic position servo system is established. The fractional-order controller for pneumatic position servo and its implementation in industrial computer is designed. The experiments with fractional-order controller are carried out under various conditions, which include sine position signal with different frequency and amplitude, step position signal, and variety inertial load. The results show the effectiveness of the proposed scheme and verify their fine control performance for pneumatic position servo system.
Fractional-order in a macroeconomic dynamic model
David, S. A.; Quintino, D. D.; Soliani, J.
2013-10-01
In this paper, we applied the Riemann-Liouville approach in order to realize the numerical simulations to a set of equations that represent a fractional-order macroeconomic dynamic model. It is a generalization of a dynamic model recently reported in the literature. The aforementioned equations have been simulated for several cases involving integer and non-integer order analysis, with some different values to fractional order. The time histories and the phase diagrams have been plotted to visualize the effect of fractional order approach. The new contribution of this work arises from the fact that the macroeconomic dynamic model proposed here involves the public sector deficit equation, which renders the model more realistic and complete when compared with the ones encountered in the literature. The results reveal that the fractional-order macroeconomic model can exhibit a real reasonable behavior to macroeconomics systems and might offer greater insights towards the understanding of these complex dynamic systems.
Sasano, Koji; Okajima, Hiroshi; Matsunaga, Nobutomo
Recently, the fractional order PID (FO-PID) control, which is the extension of the PID control, has been focused on. Even though the FO-PID requires the high-order filter, it is difficult to realize the high-order filter due to the memory limitation of digital computer. For implementation of FO-PID, approximation of the fractional integrator and differentiator are required. Short memory principle (SMP) is one of the effective approximation methods. However, there is a disadvantage that the approximated filter with SMP cannot eliminate the steady-state error. For this problem, we introduce the distributed implementation of the integrator and the dynamic quantizer to make the efficient use of permissible memory. The objective of this study is to clarify how to implement the accurate FO-PID with limited memories. In this paper, we propose the implementation method of FO-PID with memory constraint using dynamic quantizer. And the trade off between approximation of fractional elements and quantized data size are examined so as to close to the ideal FO-PID responses. The effectiveness of proposed method is evaluated by numerical example and experiment in the temperature control of heat plate.
On some fractional order hardy inequalities
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Kufner Alois
1997-01-01
Full Text Available Weighted inequalities for fractional derivatives ( fractional order Hardy-type inequalities have recently been proved in [4] and [1]. In this paper, new inequalities of this type are proved and applied. In particular, the general mixed norm case and a general twodimensional weight are considered. Moreover, an Orlicz norm version and a multidimensional fractional order Hardy inequality are proved. The connections to related results are pointed out.
International Nuclear Information System (INIS)
Craiem, Damian; Magin, Richard L
2010-01-01
New lumped-element models of red blood cell mechanics can be constructed using fractional order generalizations of springs and dashpots. Such 'spring-pots' exhibit a fractional order viscoelastic behavior that captures a wide spectrum of experimental results through power-law expressions in both the time and frequency domains. The system dynamics is fully described by linear fractional order differential equations derived from first order stress–strain relationships using the tools of fractional calculus. Changes in the composition or structure of the membrane are conveniently expressed in the fractional order of the model system. This approach provides a concise way to describe and quantify the biomechanical behavior of membranes, cells and tissues. (perspective)
Craiem, Damian; Magin, Richard L
2010-01-20
New lumped-element models of red blood cell mechanics can be constructed using fractional order generalizations of springs and dashpots. Such 'spring-pots' exhibit a fractional order viscoelastic behavior that captures a wide spectrum of experimental results through power-law expressions in both the time and frequency domains. The system dynamics is fully described by linear fractional order differential equations derived from first order stress-strain relationships using the tools of fractional calculus. Changes in the composition or structure of the membrane are conveniently expressed in the fractional order of the model system. This approach provides a concise way to describe and quantify the biomechanical behavior of membranes, cells and tissues.
Robust fractional order differentiators using generalized modulating functions method
Liu, Dayan; Laleg-Kirati, Taous-Meriem
2015-01-01
This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.
Robust fractional order differentiators using generalized modulating functions method
Liu, Dayan
2015-02-01
This paper aims at designing a fractional order differentiator for a class of signals satisfying a linear differential equation with unknown parameters. A generalized modulating functions method is proposed first to estimate the unknown parameters, then to derive accurate integral formulae for the left-sided Riemann-Liouville fractional derivatives of the studied signal. Unlike the improper integral in the definition of the left-sided Riemann-Liouville fractional derivative, the integrals in the proposed formulae can be proper and be considered as a low-pass filter by choosing appropriate modulating functions. Hence, digital fractional order differentiators applicable for on-line applications are deduced using a numerical integration method in discrete noisy case. Moreover, some error analysis are given for noise error contributions due to a class of stochastic processes. Finally, numerical examples are given to show the accuracy and robustness of the proposed fractional order differentiators.
Subharmonic Resonance of Van Der Pol Oscillator with Fractional-Order Derivative
Directory of Open Access Journals (Sweden)
Yongjun Shen
2014-01-01
Full Text Available The subharmonic resonance of van der Pol (VDP oscillator with fractional-order derivative is studied by the averaging method. At first, the first-order approximate solutions are obtained by the averaging method. Then the definitions of equivalent linear damping coefficient (ELDC and equivalent linear stiffness coefficient (ELSC for subharmonic resonance are established, and the effects of the fractional-order parameters on the ELDC, the ELSC, and the dynamical characteristics of system are also analysed. Moreover, the amplitude-frequency equation and phase-frequency equation of steady-state solution for subharmonic resonance are established. The corresponding stability condition is presented based on Lyapunov theory, and the existence condition for subharmonic resonance (ECSR is also obtained. At last, the comparisons of the fractional-order and the traditional integer-order VDP oscillator are fulfilled by the numerical simulation. The effects of the parameters in fractional-order derivative on the steady-state amplitude, the amplitude-frequency curves, and the system stability are also studied.
Quasi-projective synchronization of fractional-order complex-valued recurrent neural networks.
Yang, Shuai; Yu, Juan; Hu, Cheng; Jiang, Haijun
2018-08-01
In this paper, without separating the complex-valued neural networks into two real-valued systems, the quasi-projective synchronization of fractional-order complex-valued neural networks is investigated. First, two new fractional-order inequalities are established by using the theory of complex functions, Laplace transform and Mittag-Leffler functions, which generalize traditional inequalities with the first-order derivative in the real domain. Additionally, different from hybrid control schemes given in the previous work concerning the projective synchronization, a simple and linear control strategy is designed in this paper and several criteria are derived to ensure quasi-projective synchronization of the complex-valued neural networks with fractional-order based on the established fractional-order inequalities and the theory of complex functions. Moreover, the error bounds of quasi-projective synchronization are estimated. Especially, some conditions are also presented for the Mittag-Leffler synchronization of the addressed neural networks. Finally, some numerical examples with simulations are provided to show the effectiveness of the derived theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.
Continuous fractional-order Zero Phase Error Tracking Control.
Liu, Lu; Tian, Siyuan; Xue, Dingyu; Zhang, Tao; Chen, YangQuan
2018-04-01
A continuous time fractional-order feedforward control algorithm for tracking desired time varying input signals is proposed in this paper. The presented controller cancels the phase shift caused by the zeros and poles of controlled closed-loop fractional-order system, so it is called Fractional-Order Zero Phase Tracking Controller (FZPETC). The controlled systems are divided into two categories i.e. with and without non-cancellable (non-minimum-phase) zeros which stand in unstable region or on stability boundary. Each kinds of systems has a targeted FZPETC design control strategy. The improved tracking performance has been evaluated successfully by applying the proposed controller to three different kinds of fractional-order controlled systems. Besides, a modified quasi-perfect tracking scheme is presented for those systems which may not have available future tracking trajectory information or have problem in high frequency disturbance rejection if the perfect tracking algorithm is applied. A simulation comparison and a hardware-in-the-loop thermal peltier platform are shown to validate the practicality of the proposed quasi-perfect control algorithm. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.
Martínez-Guerra, Rafael; Gómez-Cortés, Gian Carlo
2015-01-01
This book provides a general overview of several concepts of synchronization and brings together related approaches to secure communication in chaotic systems. This is achieved using a combination of analytic, algebraic, geometrical and asymptotical methods to tackle the dynamical feedback stabilization problem. In particular, differential-geometric and algebraic differential concepts reveal important structural properties of chaotic systems and serve as guide for the construction of design procedures for a wide variety of chaotic systems. The basic differential algebraic and geometric concepts are presented in the first few chapters in a novel way as design tools, together with selected experimental studies demonstrating their importance. The subsequent chapters treat recent applications. Written for graduate students in applied physical sciences, systems engineers, and applied mathematicians interested in synchronization of chaotic systems and in secure communications, this self-contained text requires only...
Fractional-order RC and RL circuits
Radwan, Ahmed Gomaa
2012-05-30
This paper is a step forward to generalize the fundamentals of the conventional RC and RL circuits in fractional-order sense. The effect of fractional orders is the key factor for extra freedom, more flexibility, and novelty. The conditions for RC and RL circuits to act as pure imaginary impedances are derived, which are unrealizable in the conventional case. In addition, the sensitivity analyses of the magnitude and phase response with respect to all parameters showing the locations of these critical values are discussed. A qualitative revision for the fractional RC and RL circuits in the frequency domain is provided. Numerical and PSpice simulations are included to validate this study. © Springer Science+Business Media, LLC 2012.
Adaptive control and synchronization of a fractional-order chaotic ...
Indian Academy of Sciences (India)
In this paper, the chaotic dynamics of a three-dimensional fractional-order chaotic sys- tem is investigated. ... So, the fractional description is closer to reality. One of the ..... For the augmented systems (14) and (16), the candidate function can.
Saad, K. M.
2018-03-01
In this work we extend the standard model for a cubic isothermal auto-catalytic chemical system (CIACS) to a new model of a fractional cubic isothermal auto-catalytic chemical system (FCIACS) based on Caputo (C), Caputo-Fabrizio (CF) and Atangana-Baleanu in the Liouville-Caputo sense (ABC) fractional time derivatives, respectively. We present approximate solutions for these extended models using the q -homotopy analysis transform method ( q -HATM). We solve the FCIACS with the C derivative and compare our results with those obtained using the CF and ABC derivatives. The ranges of convergence of the solutions are found and the optimal values of h , the auxiliary parameter, are derived. Finally, these solutions are compared with numerical solutions of the various models obtained using finite differences and excellent agreement is found.
Modeling and analysis of fractional order DC-DC converter.
Radwan, Ahmed G; Emira, Ahmed A; AbdelAty, Amr M; Azar, Ahmad Taher
2017-07-11
Due to the non-idealities of commercial inductors, the demand for a better model that accurately describe their dynamic response is elevated. So, the fractional order models of Buck, Boost and Buck-Boost DC-DC converters are presented in this paper. The detailed analysis is made for the two most common modes of converter operation: Continuous Conduction Mode (CCM) and Discontinuous Conduction Mode (DCM). Closed form time domain expressions are derived for inductor currents, voltage gain, average current, conduction time and power efficiency where the effect of the fractional order inductor is found to be strongly present. For example, the peak inductor current at steady state increases with decreasing the inductor order. Advanced Design Systems (ADS) circuit simulations are used to verify the derived formulas, where the fractional order inductor is simulated using Valsa Constant Phase Element (CPE) approximation and Generalized Impedance Converter (GIC). Different simulation results are introduced with good matching to the theoretical formulas for the three DC-DC converter topologies under different fractional orders. A comprehensive comparison with the recently published literature is presented to show the advantages and disadvantages of each approach. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Non linear system become linear system
Directory of Open Access Journals (Sweden)
Petre Bucur
2007-01-01
Full Text Available The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding features.
Fractional order absolute vibration suppression (AVS) controllers
Halevi, Yoram
2017-04-01
Absolute vibration suppression (AVS) is a control method for flexible structures. The first step is an accurate, infinite dimension, transfer function (TF), from actuation to measurement. This leads to the collocated, rate feedback AVS controller that in some cases completely eliminates the vibration. In case of the 1D wave equation, the TF consists of pure time delays and low order rational terms, and the AVS controller is rational. In all other cases, the TF and consequently the controller are fractional order in both the delays and the "rational parts". The paper considers stability, performance and actual implementation in such cases.
Fractional Processes and Fractional-Order Signal Processing Techniques and Applications
Sheng, Hu; Qiu, TianShuang
2012-01-01
Fractional processes are widely found in science, technology and engineering systems. In Fractional Processes and Fractional-order Signal Processing, some complex random signals, characterized by the presence of a heavy-tailed distribution or non-negligible dependence between distant observations (local and long memory), are introduced and examined from the ‘fractional’ perspective using simulation, fractional-order modeling and filtering and realization of fractional-order systems. These fractional-order signal processing (FOSP) techniques are based on fractional calculus, the fractional Fourier transform and fractional lower-order moments. Fractional Processes and Fractional-order Signal Processing: • presents fractional processes of fixed, variable and distributed order studied as the output of fractional-order differential systems; • introduces FOSP techniques and the fractional signals and fractional systems point of view; • details real-world-application examples of FOSP techniques to demonstr...
Numerical Analysis of Fractional Order Epidemic Model of Childhood Diseases
Directory of Open Access Journals (Sweden)
Fazal Haq
2017-01-01
Full Text Available The fractional order Susceptible-Infected-Recovered (SIR epidemic model of childhood disease is considered. Laplace–Adomian Decomposition Method is used to compute an approximate solution of the system of nonlinear fractional differential equations. We obtain the solutions of fractional differential equations in the form of infinite series. The series solution of the proposed model converges rapidly to its exact value. The obtained results are compared with the classical case.
Implementation of fractional order integrator/differentiator on field programmable gate array
K.P.S. Rana; V. Kumar; N. Mittra; N. Pramanik
2016-01-01
Concept of fractional order calculus is as old as the regular calculus. With the advent of high speed and cost effective computing power, now it is possible to model the real world control and signal processing problems using fractional order calculus. For the past two decades, applications of fractional order calculus, in system modeling, control and signal processing, have grown rapidly. This paper presents a systematic procedure for hardware implementation of the basic operators of fractio...
Dynamic behaviours and control of fractional-order memristor-based ...
Indian Academy of Sciences (India)
Dynamics of fractional-order memristor circuit system and its control are investigated in this paper. With the help of stability theory of fractional-order systems, stability of its equilibrium points is analysed. Then, the chaotic behaviours are validated using phase portraits, the Lyapunov exponents and bifurcation diagrams with ...
Callier, Frank M.; Desoer, Charles A.
1991-01-01
The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.
Chaos control via a simple fractional-order controller
International Nuclear Information System (INIS)
Tavazoei, Mohammad Saleh; Haeri, Mohammad
2008-01-01
In this Letter, we propose a fractional-order controller to stabilize the unstable fixed points of an unstable open-loop system. Also, we show that this controller has strong ability to eliminate chaotic oscillations or reduce them to regular oscillations in the chaotic systems. This controller has simple structure and is designed very easily. To determine the control parameters, one needs only a little knowledge about the plant and therefore, the proposed controller is a suitable choice in the control of uncertain chaotic systems
Institute of Scientific and Technical Information of China (English)
孙永辉; 高振阳; 卫志农; 孙国强
2016-01-01
Based on the measurement noise as the non-Gaussian L ´evy noise, a novel Kalman filter for the discrete linear stochastic fractional order system is proposed. By eliminating the maximum, the approximated Gaussian white noise can be obtained. Based on the principle of least square, an improved Kalman filter can be developed for the discrete linear stochastic fractional order system with measurement L´evy noise. Compared to the traditional method, the proposed method gets better performance. Finally, simulation results show the effectiveness and usefulness of the proposed algorithm.%针对量测噪声模型为非高斯L ´evy噪声，研究离散线性随机分数阶系统的卡尔曼滤波设计问题。通过剔除极大值的方法得到近似高斯白噪声的L´evy噪声，基于最小二乘原理，提出一种考虑非高斯L´evy量测噪声下的改进分数阶卡尔曼滤波算法。与传统的分数阶卡尔曼滤波相比，改进的分数阶卡尔曼滤波对非高斯L´evy噪声具有更好的滤波效果。最后，通过模拟仿真验证了所提出算法的正确性和有效性。
Digital Fractional Order Controllers Realized by PIC Microprocessor: Experimental Results
Petras, I.; Grega, S.; Dorcak, L.
2003-01-01
This paper deals with the fractional-order controllers and their possible hardware realization based on PIC microprocessor and numerical algorithm coded in PIC Basic. The mathematical description of the digital fractional -order controllers and approximation in the discrete domain are presented. An example of realization of the particular case of digital fractional-order PID controller is shown and described.
On Fractional Order Hybrid Differential Equations
Directory of Open Access Journals (Sweden)
Mohamed A. E. Herzallah
2014-01-01
Full Text Available We develop the theory of fractional hybrid differential equations with linear and nonlinear perturbations involving the Caputo fractional derivative of order 0<α<1. Using some fixed point theorems we prove the existence of mild solutions for two types of hybrid equations. Examples are given to illustrate the obtained results.
Hipergeometric solutions to some nonhomogeneous equations of fractional order
Olivares, Jorge; Martin, Pablo; Maass, Fernando
2017-12-01
In this paper a study is performed to the solution of the linear non homogeneous fractional order alpha differential equation equal to I 0(x), where I 0(x) is the modified Bessel function of order zero, the initial condition is f(0)=0 and 0 definition for the fractional derivatives is considered. Fractional derivatives have become important in physical and chemical phenomena as visco-elasticity and visco-plasticity, anomalous diffusion and electric circuits. In particular in this work the values of alpha=1/2, 1/4 and 3/4. are explicitly considered . In these cases Laplace transform is applied, and later the inverse Laplace transform leads to the solutions of the differential equation, which become hypergeometric functions.
Veeraian, Parthasarathi; Gandhi, Uma; Mangalanathan, Umapathy
2018-04-01
Seismic transducers are widely used for measurement of displacement, velocity, and acceleration. This paper presents the design of seismic transducer in the fractional domain for the measurement of displacement and acceleration. The fractional order transfer function for seismic displacement and acceleration transducer are derived using Grünwald-Letnikov derivative. Frequency response analysis of fractional order seismic displacement transducer (FOSDT) and fractional order seismic acceleration transducer (FOSAT) are carried out for different damping ratio with the different fractional order, and the maximum dynamic measurement range is identified. The results demonstrate that fractional order seismic transducer has increased dynamic measurement range and less phase distortion as compared to the conventional seismic transducer even with a lower damping ratio. Time response of FOSDT and FOSAT are derived analytically in terms of Mittag-Leffler function, the effect of fractional behavior in the time domain is evaluated from the impulse and step response. The fractional order system is found to have significantly reduced overshoot as compared to the conventional transducer. The fractional order seismic transducer design proposed in this paper is illustrated with a design example for FOSDT and FOSAT. Finally, an electrical equivalent of FOSDT and FOSAT is considered, and its frequency response is found to be in close agreement with the proposed fractional order seismic transducer.
Fractional Order Differentiation by Integration and Error Analysis in Noisy Environment
Liu, Dayan
2015-03-31
The integer order differentiation by integration method based on the Jacobi orthogonal polynomials for noisy signals was originally introduced by Mboup, Join and Fliess. We propose to extend this method from the integer order to the fractional order to estimate the fractional order derivatives of noisy signals. Firstly, two fractional order differentiators are deduced from the Jacobi orthogonal polynomial filter, using the Riemann-Liouville and the Caputo fractional order derivative definitions respectively. Exact and simple formulae for these differentiators are given by integral expressions. Hence, they can be used for both continuous-time and discrete-time models in on-line or off-line applications. Secondly, some error bounds are provided for the corresponding estimation errors. These bounds allow to study the design parameters\\' influence. The noise error contribution due to a large class of stochastic processes is studied in discrete case. The latter shows that the differentiator based on the Caputo fractional order derivative can cope with a class of noises, whose mean value and variance functions are polynomial time-varying. Thanks to the design parameters analysis, the proposed fractional order differentiators are significantly improved by admitting a time-delay. Thirdly, in order to reduce the calculation time for on-line applications, a recursive algorithm is proposed. Finally, the proposed differentiator based on the Riemann-Liouville fractional order derivative is used to estimate the state of a fractional order system and numerical simulations illustrate the accuracy and the robustness with respect to corrupting noises.
Fractional order PID controller for load frequency control
International Nuclear Information System (INIS)
Sondhi, Swati; Hote, Yogesh V.
2014-01-01
Highlights: • The manuscript shows the design of FOPID controller for the load frequency control. • Performance of FOPID is given for non-reheated, reheated and hydro turbine. • Performance of FOPID is compared to IMC-PID and reduced order IMC-PID design scheme. • Performance of FOPID is better than the existing techniques. - Abstract: Load frequency control (LFC) plays a very important role in providing quality power both in the case of isolated as well as interconnected power systems. In order to maintain good quality power supply, the LFC should possess robustness toward the parametric uncertainty of the system and good disturbance rejection capability. The fractional order controller has the properties such as, eliminating steady state error, robustness toward plant gain variations and also good disturbance rejection. This makes the fractional order PID (FOPID) controller quite suitable for the LFC. Therefore, in this paper a FOPID is designed for single area LFC for all three types of turbines i.e., non-reheated, reheated and hydro turbines. It is observed that the FOPID controller shows better robustness toward ±50% parametric uncertainty and disturbance rejection capability than the existing techniques. Finally, the optimization of controller parameters and robustness evaluation of the control technique is done on the basis of the integral error criterion
SOLVING FRACTIONAL-ORDER COMPETITIVE LOTKA-VOLTERRA MODEL BY NSFD SCHEMES
Directory of Open Access Journals (Sweden)
S.ZIBAEI
2016-12-01
Full Text Available In this paper, we introduce fractional-order into a model competitive Lotka- Volterra prey-predator system. We will discuss the stability analysis of this fractional system. The non-standard nite difference (NSFD scheme is implemented to study the dynamic behaviors in the fractional-order Lotka-Volterra system. Proposed non-standard numerical scheme is compared with the forward Euler and fourth order Runge-Kutta methods. Numerical results show that the NSFD approach is easy and accurate for implementing when applied to fractional-order Lotka-Volterra model.
Electronically Tunable Fully Integrated Fractional-Order Resonator
Tsirimokou, Georgia
2017-03-20
A fully integrated implementation of a parallel fractional-order resonator which employs together a fractional order capacitor and a fractional-order inductor is proposed in this paper. The design utilizes current-controlled Operational Transconductance Amplifiers as building blocks, designed and fabricated in AMS 0:35m CMOS process, and based on a second-order approximation of a fractional-order differentiator/ integrator magnitude optimized in the range 10Hz–700Hz. An attractive benefit of the proposed scheme is its electronic tuning capability.
Electronically Tunable Fully Integrated Fractional-Order Resonator
Tsirimokou, Georgia; Psychalinos, Costas; Elwakil, Ahmed S.; Salama, Khaled N.
2017-01-01
A fully integrated implementation of a parallel fractional-order resonator which employs together a fractional order capacitor and a fractional-order inductor is proposed in this paper. The design utilizes current-controlled Operational Transconductance Amplifiers as building blocks, designed and fabricated in AMS 0:35m CMOS process, and based on a second-order approximation of a fractional-order differentiator/ integrator magnitude optimized in the range 10Hz–700Hz. An attractive benefit of the proposed scheme is its electronic tuning capability.
Stability analysis of fractional-order Hopfield neural networks with time delays.
Wang, Hu; Yu, Yongguang; Wen, Guoguang
2014-07-01
This paper investigates the stability for fractional-order Hopfield neural networks with time delays. Firstly, the fractional-order Hopfield neural networks with hub structure and time delays are studied. Some sufficient conditions for stability of the systems are obtained. Next, two fractional-order Hopfield neural networks with different ring structures and time delays are developed. By studying the developed neural networks, the corresponding sufficient conditions for stability of the systems are also derived. It is shown that the stability conditions are independent of time delays. Finally, numerical simulations are given to illustrate the effectiveness of the theoretical results obtained in this paper. Copyright © 2014 Elsevier Ltd. All rights reserved.
Fractional Order PID Control of Rotor Suspension by Active Magnetic Bearings
Directory of Open Access Journals (Sweden)
Parinya Anantachaisilp
2017-01-01
Full Text Available One of the key issues in control design for Active Magnetic Bearing (AMB systems is the tradeoff between the simplicity of the controller structure and the performance of the closed-loop system. To achieve this tradeoff, this paper proposes the design of a fractional order Proportional-Integral-Derivative (FOPID controller. The FOPID controller consists of only two additional parameters in comparison with a conventional PID controller. The feasibility of FOPID for AMB systems is investigated for rotor suspension in both the radial and axial directions. Tuning methods are developed based on the evolutionary algorithms for searching the optimal values of the controller parameters. The resulting FOPID controllers are then tested and compared with a conventional PID controller, as well as with some advanced controllers such as Linear Quadratic Gausian (LQG and H ∞ controllers. The comparison is made in terms of various stability and robustness specifications, as well as the dimensions of the controllers as implemented. Lastly, to validate the proposed method, experimental testing is carried out on a single-stage centrifugal compressor test rig equipped with magnetic bearings. The results show that, with a proper selection of gains and fractional orders, the performance of the resulting FOPID is similar to those of the advanced controllers.
Kumar, Anupam; Kumar, Vijay
2017-05-01
In this paper, a novel concept of an interval type-2 fractional order fuzzy PID (IT2FO-FPID) controller, which requires fractional order integrator and fractional order differentiator, is proposed. The incorporation of Takagi-Sugeno-Kang (TSK) type interval type-2 fuzzy logic controller (IT2FLC) with fractional controller of PID-type is investigated for time response measure due to both unit step response and unit load disturbance. The resulting IT2FO-FPID controller is examined on different delayed linear and nonlinear benchmark plants followed by robustness analysis. In order to design this controller, fractional order integrator-differentiator operators are considered as design variables including input-output scaling factors. A new hybridized algorithm named as artificial bee colony-genetic algorithm (ABC-GA) is used to optimize the parameters of the controller while minimizing weighted sum of integral of time absolute error (ITAE) and integral of square of control output (ISCO). To assess the comparative performance of the IT2FO-FPID, authors compared it against existing controllers, i.e., interval type-2 fuzzy PID (IT2-FPID), type-1 fractional order fuzzy PID (T1FO-FPID), type-1 fuzzy PID (T1-FPID), and conventional PID controllers. Furthermore, to show the effectiveness of the proposed controller, the perturbed processes along with the larger dead time are tested. Moreover, the proposed controllers are also implemented on multi input multi output (MIMO), coupled, and highly complex nonlinear two-link robot manipulator system in presence of un-modeled dynamics. Finally, the simulation results explicitly indicate that the performance of the proposed IT2FO-FPID controller is superior to its conventional counterparts in most of the cases. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Lin, Chia-Hung; Huang, Cong-Hui; Du, Yi-Chun; Chen, Jian-Liung
2011-01-01
Highlights: → The FOICM can shorten the tracking time less than traditional methods. → The proposed method can work under lower solar radiation including thin and heavy clouds. → The FOICM algorithm can achieve MPPT for radiation and temperature changes. → It is easy to implement in a single-chip microcontroller or embedded system. -- Abstract: This paper proposes maximum photovoltaic power tracking (MPPT) for the photovoltaic (PV) array using the fractional-order incremental conductance method (FOICM). Since the PV array has low conversion efficiency, and the output power of PV array depends on the operation environments, such as various solar radiation, environment temperature, and weather conditions. Maximum charging power can be increased to a battery using a MPPT algorithm. The energy conversion of the absorbed solar light and cell temperature is directly transferred to the semiconductor, but electricity conduction has anomalous diffusion phenomena in inhomogeneous material. FOICM can provide a dynamic mathematical model to describe non-linear characteristics. The fractional-order incremental change as dynamic variable is used to adjust the PV array voltage toward the maximum power point. For a small-scale PV conversion system, the proposed method is validated by simulation with different operation environments. Compared with traditional methods, experimental results demonstrate the short tracking time and the practicality in MPPT of PV array.
Pitchfork bifurcation and vibrational resonance in a fractional-order ...
Indian Academy of Sciences (India)
The fractional-order damping mainly determines the pattern of the vibrational resonance. There is a bifurcation point of the fractional order which, in the case of double-well potential, transforms vibrational resonance pattern from a single resonance to a double resonance, while in the case of single-well potential, transforms ...
Fractional order differentiation by integration with Jacobi polynomials
Liu, Dayan
2012-12-01
The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.
Fractional order differentiation by integration with Jacobi polynomials
Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid; Laleg-Kirati, Taous-Meriem
2012-01-01
The differentiation by integration method with Jacobi polynomials was originally introduced by Mboup, Join and Fliess [22], [23]. This paper generalizes this method from the integer order to the fractional order for estimating the fractional order derivatives of noisy signals. The proposed fractional order differentiator is deduced from the Jacobi orthogonal polynomial filter and the Riemann-Liouville fractional order derivative definition. Exact and simple formula for this differentiator is given where an integral formula involving Jacobi polynomials and the noisy signal is used without complex mathematical deduction. Hence, it can be used both for continuous-time and discrete-time models. The comparison between our differentiator and the recently introduced digital fractional order Savitzky-Golay differentiator is given in numerical simulations so as to show its accuracy and robustness with respect to corrupting noises. © 2012 IEEE.
Butterworth passive filter in the fractional-order
Sołtan, Ahmed
2011-12-01
In this paper, the generalized analysis of the first Butterworth filter based on two passive elements is introduced in the fractional-order sense. The fractional-order condition of the Butterworth circuit is presented for the first time where it will lead us back to the known condition of the integer-order circuit when the two fractional-orders equal one. Therefore, the conventional behavior of the integer-order circuit is a narrow subset of the fractional-order ones. The circuit is studied under same and different order cases, and verified through their numerical simulations. Stability analysis is also introduced showing the poles location in the fractional-order versus integer order cases. © 2011 IEEE.
Dynamical response of Mathieu–Duffing oscillator with fractional-order delayed feedback
International Nuclear Information System (INIS)
Wen, Shao-Fang; Shen, Yong-Jun; Yang, Shao-Pu; Wang, Jun
2017-01-01
Highlights: • The analytical solution for Mathieu–Duffing oscillator with fractional-order delayed feedback is obtained. • The fractional-order delayed feedback has both the functions of delayed velocity feedback and delayed displacement feedback. • The special effects of time delay on nonzero periodic solutions are analyzed in detail. • The effects of the fractional-order parameters on system response are characterized. - Abstract: In this paper, the dynamical response of Mathieu–Duffing oscillator under fractional-order delayed feedback is investigated. At first, the approximate analytical solution and the amplitude-frequency equation are obtained based on the averaging method. The equivalent stiffness coefficient and equivalent damping coefficient are defined by the feedback coefficient, fractional order and time delay et al. The effects of feedback coefficient, fractional order and time delay on these two equivalent parameters are analyzed. It is found that the fractional-order delayed feedback has not only the function of delayed velocity feedback, but also the function of delayed displacement feedback. Then, the comparison of the amplitude-frequency curves obtained by the analytical and numerical solutions verifies the correctness and satisfactory precision of the approximate analytical solution. The effects of the parameters in the fractional-order delayed feedback on the complex dynamical behaviors of Mathieu–Duffing oscillator are studied. It could be found that fractional-order delayed feedback has important influences on the dynamical behavior of Mathieu–Duffing oscillator, and the results are very helpful to design, analyze or control in vibration engineering.
Novel Fractional Order Calculus Extended PN for Maneuvering Targets
Directory of Open Access Journals (Sweden)
Jikun Ye
2017-01-01
Full Text Available Based on the theory of fractional order calculus (FOC, a novel extended proportional guidance (EPN law for intercepting the maneuvering target is proposed. In the first part, considering the memory function and filter characteristic of FOC, the novel extended PN guidance algorithm is developed based on the conventional PN after introducing the properties and operation rules of FOC. Further, with the help of FOC theory, the average load and ballistics characteristics of proposed guidance law are analyzed. Then, using the small offset kinematic model, the robustness of the new guidance law against autopilot parameters is studied theoretically by analyzing the sensitivity of the closed loop guidance system. At last, representative numerical results show that the designed guidance law obtains a better performance than the traditional PN for maneuvering target.
Spiking and bursting patterns of fractional-order Izhikevich model
Teka, Wondimu W.; Upadhyay, Ranjit Kumar; Mondal, Argha
2018-03-01
Bursting and spiking oscillations play major roles in processing and transmitting information in the brain through cortical neurons that respond differently to the same signal. These oscillations display complex dynamics that might be produced by using neuronal models and varying many model parameters. Recent studies have shown that models with fractional order can produce several types of history-dependent neuronal activities without the adjustment of several parameters. We studied the fractional-order Izhikevich model and analyzed different kinds of oscillations that emerge from the fractional dynamics. The model produces a wide range of neuronal spike responses, including regular spiking, fast spiking, intrinsic bursting, mixed mode oscillations, regular bursting and chattering, by adjusting only the fractional order. Both the active and silent phase of the burst increase when the fractional-order model further deviates from the classical model. For smaller fractional order, the model produces memory dependent spiking activity after the pulse signal turned off. This special spiking activity and other properties of the fractional-order model are caused by the memory trace that emerges from the fractional-order dynamics and integrates all the past activities of the neuron. On the network level, the response of the neuronal network shifts from random to scale-free spiking. Our results suggest that the complex dynamics of spiking and bursting can be the result of the long-term dependence and interaction of intracellular and extracellular ionic currents.
Outer synchronization between two different fractional-order general complex dynamical networks
International Nuclear Information System (INIS)
Xiang-Jun, Wu; Hong-Tao, Lu
2010-01-01
Outer synchronization between two different fractional-order general complex dynamical networks is investigated in this paper. Based on the stability theory of the fractional-order system, the sufficient criteria for outer synchronization are derived analytically by applying the nonlinear control and the bidirectional coupling methods. The proposed synchronization method is applicable to almost all kinds of coupled fractional-order general complex dynamical networks. Neither a symmetric nor irreducible coupling configuration matrix is required. In addition, no constraint is imposed on the inner-coupling matrix. Numerical examples are also provided to demonstrate the validity of the presented synchronization scheme. Numeric evidence shows that both the feedback strength k and the fractional order α can be chosen appropriately to adjust the synchronization effect effectively. (general)
Saha, Suman; Das, Saptarshi; Das, Shantanu; Gupta, Amitava
2012-09-01
A novel conformal mapping based fractional order (FO) methodology is developed in this paper for tuning existing classical (Integer Order) Proportional Integral Derivative (PID) controllers especially for sluggish and oscillatory second order systems. The conventional pole placement tuning via Linear Quadratic Regulator (LQR) method is extended for open loop oscillatory systems as well. The locations of the open loop zeros of a fractional order PID (FOPID or PIλDμ) controller have been approximated in this paper vis-à-vis a LQR tuned conventional integer order PID controller, to achieve equivalent integer order PID control system. This approach eases the implementation of analog/digital realization of a FOPID controller with its integer order counterpart along with the advantages of fractional order controller preserved. It is shown here in the paper that decrease in the integro-differential operators of the FOPID/PIλDμ controller pushes the open loop zeros of the equivalent PID controller towards greater damping regions which gives a trajectory of the controller zeros and dominant closed loop poles. This trajectory is termed as "M-curve". This phenomena is used to design a two-stage tuning algorithm which reduces the existing PID controller's effort in a significant manner compared to that with a single stage LQR based pole placement method at a desired closed loop damping and frequency.
International Nuclear Information System (INIS)
Sandev, D. Trivche
2010-01-01
The fractional calculus basis, Mittag-Leffler functions, various relaxation-oscillation and diffusion-wave fractional order equation and systems of fractional order equations are considered in this thesis. To solve these fractional order equations analytical methods, such as the Laplace transform method and method of separation of variables are employed. Some applications of the fractional calculus are considered, particularly physical system with anomalous diffusive behavior. (Author)
Adaptive control and synchronization of a fractional-order chaotic ...
Indian Academy of Sciences (India)
Fractional order; adaptive scheme; control; synchronization. ... College of Physics and Electronics, Hunan Institute of Science and Technology, ... of Information and Communication Engineering, Hunan Institute of Science and Technology, ...
Tunable fractional-order capacitor using layered ferroelectric polymers
Agambayev, Agamyrat; Patole, Shashikant P.; Bagci, Hakan; Salama, Khaled N.
2017-01-01
Pairs of various Polyvinylidene fluoride P(VDF)-based polymers are used for fabricating bilayer fractional order capacitors (FOCs). The polymer layers are constructed using a simple drop casting approach. The resulting FOC has two advantages: It can
Fractional-Order Control of Pneumatic Position Servosystems
Junyi, Cao; Binggang, Cao
2011-01-01
A fractional-order control strategy for pneumatic position servosystem is presented in this paper. The idea of the fractional calculus application to control theory was introduced in many works, and its advantages were proved. However, the realization of fractional-order controllers for pneumatic position servosystems has not been investigated. Based on the relationship between the pressure in cylinder and the rate of mass flow into the cylinder, the dynamic model of pneumatic position servo ...
Linearization of the Lorenz system
International Nuclear Information System (INIS)
Li, Chunbiao; Sprott, Julien Clinton; Thio, Wesley
2015-01-01
A partial and complete piecewise linearized version of the Lorenz system is proposed. The linearized versions have an independent total amplitude control parameter. Additional further linearization leads naturally to a piecewise linear version of the diffusionless Lorenz system. A chaotic circuit with a single amplitude controller is then implemented using a new switch element, producing a chaotic oscillation that agrees with the numerical calculation for the piecewise linear diffusionless Lorenz system. - Highlights: • A partial and complete piecewise linearized version of the Lorenz system are addressed. • The linearized versions have an independent total amplitude control parameter. • A piecewise linear version of the diffusionless Lorenz system is derived by further linearization. • A corresponding chaotic circuit without any multiplier is implemented for the chaotic oscillation
Linearization of the Lorenz system
Energy Technology Data Exchange (ETDEWEB)
Li, Chunbiao, E-mail: goontry@126.com [School of Electronic & Information Engineering, Nanjing University of Information Science & Technology, Nanjing 210044 (China); Engineering Technology Research and Development Center of Jiangsu Circulation Modernization Sensor Network, Jiangsu Institute of Commerce, Nanjing 211168 (China); Sprott, Julien Clinton [Department of Physics, University of Wisconsin–Madison, Madison, WI 53706 (United States); Thio, Wesley [Department of Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210 (United States)
2015-05-08
A partial and complete piecewise linearized version of the Lorenz system is proposed. The linearized versions have an independent total amplitude control parameter. Additional further linearization leads naturally to a piecewise linear version of the diffusionless Lorenz system. A chaotic circuit with a single amplitude controller is then implemented using a new switch element, producing a chaotic oscillation that agrees with the numerical calculation for the piecewise linear diffusionless Lorenz system. - Highlights: • A partial and complete piecewise linearized version of the Lorenz system are addressed. • The linearized versions have an independent total amplitude control parameter. • A piecewise linear version of the diffusionless Lorenz system is derived by further linearization. • A corresponding chaotic circuit without any multiplier is implemented for the chaotic oscillation.
An extended integrable fractional-order KP soliton hierarchy
International Nuclear Information System (INIS)
Li Li
2011-01-01
In this Letter, we consider the modified derivatives and integrals of fractional-order pseudo-differential operators. A sequence of Lax KP equations hierarchy and extended fractional KP (fKP) hierarchy are introduced, and the fKP hierarchy has Lax presentations with the extended Lax operators. In the case of the extension with the half-order pseudo-differential operators, a new integrable fKP hierarchy is obtained. A few particular examples of fractional order will be listed, together with their Lax pairs.
An extended integrable fractional-order KP soliton hierarchy
Energy Technology Data Exchange (ETDEWEB)
Li Li, E-mail: li07099@163.co [College of Maths and Systematic Science, Shenyang Normal University, Shenyang 110034 (China)
2011-01-17
In this Letter, we consider the modified derivatives and integrals of fractional-order pseudo-differential operators. A sequence of Lax KP equations hierarchy and extended fractional KP (fKP) hierarchy are introduced, and the fKP hierarchy has Lax presentations with the extended Lax operators. In the case of the extension with the half-order pseudo-differential operators, a new integrable fKP hierarchy is obtained. A few particular examples of fractional order will be listed, together with their Lax pairs.
Fractional order PID controller for improvement of PMSM speed control in aerospace applications
Energy Technology Data Exchange (ETDEWEB)
Saraji, Ali Motalebi [Young Researchers and Elite Club, AliAbad Katoul Branch, Islamic Azad University, AliAbad Katoul (Iran, Islamic Republic of); Ghanbari, Mahmood [Department of Electrical Engineering, AliAbad Katoul Branch, Islamic Azad University, AliAbad Katoul (Iran, Islamic Republic of)
2014-12-10
Because of the benefits reduced size, cost and maintenance, noise, CO2 emissions and increased control flexibility and precision, to meet these expectations, electrical equipment increasingly utilize in modern aircraft systems and aerospace industry rather than conventional mechanic, hydraulic, and pneumatic power systems. Electric motor drives are capable of converting electrical power to drive actuators, pumps, compressors, and other subsystems at variable speeds. In the past decades, permanent magnet synchronous motor (PMSM) and brushless dc (BLDC) motor were investigated for aerospace applications such as aircraft actuators. In this paper, the fractional-order PID controller is used in the design of speed loop of PMSM speed control system. Having more parameters for tuning fractional order PID controller lead to good performance ratio to integer order. This good performance is shown by comparison fractional order PID controller with the conventional PI and tuned PID controller by Genetic algorithm in MATLAB soft wear.
Fractional order PID controller for improvement of PMSM speed control in aerospace applications
International Nuclear Information System (INIS)
Saraji, Ali Motalebi; Ghanbari, Mahmood
2014-01-01
Because of the benefits reduced size, cost and maintenance, noise, CO2 emissions and increased control flexibility and precision, to meet these expectations, electrical equipment increasingly utilize in modern aircraft systems and aerospace industry rather than conventional mechanic, hydraulic, and pneumatic power systems. Electric motor drives are capable of converting electrical power to drive actuators, pumps, compressors, and other subsystems at variable speeds. In the past decades, permanent magnet synchronous motor (PMSM) and brushless dc (BLDC) motor were investigated for aerospace applications such as aircraft actuators. In this paper, the fractional-order PID controller is used in the design of speed loop of PMSM speed control system. Having more parameters for tuning fractional order PID controller lead to good performance ratio to integer order. This good performance is shown by comparison fractional order PID controller with the conventional PI and tuned PID controller by Genetic algorithm in MATLAB soft wear
Dynamical systems and linear algebra
Colonius, Fritz (Prof.)
2007-01-01
Dynamical systems and linear algebra / F. Colonius, W. Kliemann. - In: Handbook of linear algebra / ed. by Leslie Hogben. - Boca Raton : Chapman & Hall/CRC, 2007. - S. 56,1-56,22. - (Discrete mathematics and its applications)
Directory of Open Access Journals (Sweden)
Jian Liu
2014-11-01
Full Text Available This paper introduces a type of modified hybrid projective synchronization with complex transformationmatrix (CMHPS for different dimensional fractional-order complex chaos and fractional-order real hyper-chaos. The transformationmatrix in this type of chaotic synchronization is a non-square matrix, and its elements are complex numbers. Based on the stability theory of fractional-order systems, by employing the feedback control technique, necessary and sufficient criteria on CMHPS are derived. Furthermore, CMHPS between fractional-order real hyper-chaotic Rössler system and other two different dimensional fractional-order complex Lorenz-like chaotic systems is provided as two examples to discuss reduced order and increased order synchronization, respectively.
New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis.
Ingo, Carson; Magin, Richard L; Parrish, Todd B
2014-11-01
Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag-Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.
New Insights into the Fractional Order Diffusion Equation Using Entropy and Kurtosis
Directory of Open Access Journals (Sweden)
Carson Ingo
2014-11-01
Full Text Available Fractional order derivative operators offer a concise description to model multi-scale, heterogeneous and non-local systems. Specifically, in magnetic resonance imaging, there has been recent work to apply fractional order derivatives to model the non-Gaussian diffusion signal, which is ubiquitous in the movement of water protons within biological tissue. To provide a new perspective for establishing the utility of fractional order models, we apply entropy for the case of anomalous diffusion governed by a fractional order diffusion equation generalized in space and in time. This fractional order representation, in the form of the Mittag–Leffler function, gives an entropy minimum for the integer case of Gaussian diffusion and greater values of spectral entropy for non-integer values of the space and time derivatives. Furthermore, we consider kurtosis, defined as the normalized fourth moment, as another probabilistic description of the fractional time derivative. Finally, we demonstrate the implementation of anomalous diffusion, entropy and kurtosis measurements in diffusion weighted magnetic resonance imaging in the brain of a chronic ischemic stroke patient.
FPGA implementation of fractional-order discrete memristor chaotic ...
Indian Academy of Sciences (India)
Anitha Karthikeyan
Corresponding author. E-mail: rkarthiekeyan@gmail.com. MS received 10 August 2017; revised 4 September 2017; accepted 5 September 2017; published online 30 December 2017. Abstract. A new fourth-order memristor chaotic oscillator is taken to investigate its fractional-order discrete synchronisation.
Approximation of Analytic Functions by Bessel's Functions of Fractional Order
Directory of Open Access Journals (Sweden)
Soon-Mo Jung
2011-01-01
Full Text Available We will solve the inhomogeneous Bessel's differential equation x2y″(x+xy′(x+(x2-ν2y(x=∑m=0∞amxm, where ν is a positive nonintegral number and apply this result for approximating analytic functions of a special type by the Bessel functions of fractional order.
Fractional-order integral and derivative controller for temperature ...
Indian Academy of Sciences (India)
ideal transfer function as a reference model, for a temperature profile tracking. ... tant, and in process industry (Tsai & Lu 1998), the most common control task is to ..... be solved for fractional order α using numerical classical approach in MATLAB. ..... discrepancy between simulation and experimental results may be due to ...
ECG artifact cancellation in surface EMG signals by fractional order calculus application.
Miljković, Nadica; Popović, Nenad; Djordjević, Olivera; Konstantinović, Ljubica; Šekara, Tomislav B
2017-03-01
New aspects for automatic electrocardiography artifact removal from surface electromyography signals by application of fractional order calculus in combination with linear and nonlinear moving window filters are explored. Surface electromyography recordings of skeletal trunk muscles are commonly contaminated with spike shaped artifacts. This artifact originates from electrical heart activity, recorded by electrocardiography, commonly present in the surface electromyography signals recorded in heart proximity. For appropriate assessment of neuromuscular changes by means of surface electromyography, application of a proper filtering technique of electrocardiography artifact is crucial. A novel method for automatic artifact cancellation in surface electromyography signals by applying fractional order calculus and nonlinear median filter is introduced. The proposed method is compared with the linear moving average filter, with and without prior application of fractional order calculus. 3D graphs for assessment of window lengths of the filters, crest factors, root mean square differences, and fractional calculus orders (called WFC and WRC graphs) have been introduced. For an appropriate quantitative filtering evaluation, the synthetic electrocardiography signal and analogous semi-synthetic dataset have been generated. The examples of noise removal in 10 able-bodied subjects and in one patient with muscle dystrophy are presented for qualitative analysis. The crest factors, correlation coefficients, and root mean square differences of the recorded and semi-synthetic electromyography datasets showed that the most successful method was the median filter in combination with fractional order calculus of the order 0.9. Statistically more significant (p ECG peak reduction was obtained by the median filter application compared to the moving average filter in the cases of low level amplitude of muscle contraction compared to ECG spikes. The presented results suggest that the
Marinangeli, L.; Alijani, F.; HosseinNia, S. Hassan
2018-01-01
In this paper, Active Vibration Control (AVC) of a rectangular carbon fibre composite plate with free edges is presented. The plate is subjected to out-of-plane excitation by a modal vibration exciter and controlled by Macro Fibre Composite (MFC) transducers. Vibration measurements are performed by using a Laser Doppler Vibrometer (LDV) system. A fractional-order Positive Position Feedback (PPF) compensator is proposed, implemented and compared to the standard integer-order PPF. MFC actuator and sensor are positioned on the plate based on maximal modal strain criterion, so as to control the second natural mode of the plate. Both integer and fractional-order PPF allowed for the effective control of the second mode of vibration. However, the newly proposed fractional-order controller is found to be more efficient in achieving the same performance with less actuation voltage. Moreover, it shows promising performance in reducing spillover effect due to uncontrolled modes.
Li, Mingjie; Zhou, Ping; Zhao, Zhicheng; Zhang, Jinggang
2016-03-01
Recently, fractional order (FO) processes with dead-time have attracted more and more attention of many researchers in control field, but FO-PID controllers design techniques available for the FO processes with dead-time suffer from lack of direct systematic approaches. In this paper, a simple design and parameters tuning approach of two-degree-of-freedom (2-DOF) FO-PID controller based on internal model control (IMC) is proposed for FO processes with dead-time, conventional one-degree-of-freedom control exhibited the shortcoming of coupling of robustness and dynamic response performance. 2-DOF control can overcome the above weakness which means it realizes decoupling of robustness and dynamic performance from each other. The adjustable parameter η2 of FO-PID controller is directly related to the robustness of closed-loop system, and the analytical expression is given between the maximum sensitivity specification Ms and parameters η2. In addition, according to the dynamic performance requirement of the practical system, the parameters η1 can also be selected easily. By approximating the dead-time term of the process model with the first-order Padé or Taylor series, the expressions for 2-DOF FO-PID controller parameters are derived for three classes of FO processes with dead-time. Moreover, compared with other methods, the proposed method is simple and easy to implement. Finally, the simulation results are given to illustrate the effectiveness of this method. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
Ullah, Asmat; Chen, Wen; Khan, Mushtaq Ahmad
2017-07-01
This paper introduces a fractional order total variation (FOTV) based model with three different weights in the fractional order derivative definition for multiplicative noise removal purpose. The fractional-order Euler Lagrange equation which is a highly non-linear partial differential equation (PDE) is obtained by the minimization of the energy functional for image restoration. Two numerical schemes namely an iterative scheme based on the dual theory and majorization- minimization algorithm (MMA) are used. To improve the restoration results, we opt for an adaptive parameter selection procedure for the proposed model by applying the trial and error method. We report numerical simulations which show the validity and state of the art performance of the fractional-order model in visual improvement as well as an increase in the peak signal to noise ratio comparing to corresponding methods. Numerical experiments also demonstrate that MMAbased methodology is slightly better than that of an iterative scheme.
Wei, Zhouchao; Rajagopal, Karthikeyan; Zhang, Wei; Kingni, Sifeu Takougang; Akgül, Akif
2018-04-01
Hidden hyperchaotic attractors can be generated with three positive Lyapunov exponents in the proposed 5D hyperchaotic Burke-Shaw system with only one stable equilibrium. To the best of our knowledge, this feature has rarely been previously reported in any other higher-dimensional systems. Unidirectional linear error feedback coupling scheme is used to achieve hyperchaos synchronisation, which will be estimated by using two indicators: the normalised average root-mean squared synchronisation error and the maximum cross-correlation coefficient. The 5D hyperchaotic system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integration. In addition, fractional-order hidden hyperchaotic system will be considered from the following three aspects: stability, bifurcation analysis and FPGA implementation. Such implementations in real time represent hidden hyperchaotic attractors with important consequences for engineering applications.
Das, Saptarshi; Pan, Indranil; Das, Shantanu
2013-07-01
Fuzzy logic based PID controllers have been studied in this paper, considering several combinations of hybrid controllers by grouping the proportional, integral and derivative actions with fuzzy inferencing in different forms. Fractional order (FO) rate of error signal and FO integral of control signal have been used in the design of a family of decomposed hybrid FO fuzzy PID controllers. The input and output scaling factors (SF) along with the integro-differential operators are tuned with real coded genetic algorithm (GA) to produce optimum closed loop performance by simultaneous consideration of the control loop error index and the control signal. Three different classes of fractional order oscillatory processes with various levels of relative dominance between time constant and time delay have been used to test the comparative merits of the proposed family of hybrid fractional order fuzzy PID controllers. Performance comparison of the different FO fuzzy PID controller structures has been done in terms of optimal set-point tracking, load disturbance rejection and minimal variation of manipulated variable or smaller actuator requirement etc. In addition, multi-objective Non-dominated Sorting Genetic Algorithm (NSGA-II) has been used to study the Pareto optimal trade-offs between the set point tracking and control signal, and the set point tracking and load disturbance performance for each of the controller structure to handle the three different types of processes. Copyright © 2013 ISA. Published by Elsevier Ltd. All rights reserved.
Chen, Jiejie; Chen, Boshan; Zeng, Zhigang
2018-04-01
This paper investigates O(t -α )-synchronization and adaptive Mittag-Leffler synchronization for the fractional-order memristive neural networks with delays and discontinuous neuron activations. Firstly, based on the framework of Filippov solution and differential inclusion theory, using a Razumikhin-type method, some sufficient conditions ensuring the global O(t -α )-synchronization of considered networks are established via a linear-type discontinuous control. Next, a new fractional differential inequality is established and two new discontinuous adaptive controller is designed to achieve Mittag-Leffler synchronization between the drive system and the response systems using this inequality. Finally, two numerical simulations are given to show the effectiveness of the theoretical results. Our approach and theoretical results have a leading significance in the design of synchronized fractional-order memristive neural networks circuits involving discontinuous activations and time-varying delays. Copyright © 2018 Elsevier Ltd. All rights reserved.
General solution of the Bagley-Torvik equation with fractional-order derivative
Wang, Z. H.; Wang, X.
2010-05-01
This paper investigates the general solution of the Bagley-Torvik equation with 1/2-order derivative or 3/2-order derivative. This fractional-order differential equation is changed into a sequential fractional-order differential equation (SFDE) with constant coefficients. Then the general solution of the SFDE is expressed as the linear combination of fundamental solutions that are in terms of α-exponential functions, a kind of functions that play the same role of the classical exponential function. Because the number of fundamental solutions of the SFDE is greater than 2, the general solution of the SFDE depends on more than two free (independent) constants. This paper shows that the general solution of the Bagley-Torvik equation involves actually two free constants only, and it can be determined fully by the initial displacement and initial velocity.
Energy Technology Data Exchange (ETDEWEB)
Saha Ray, S., E-mail: santanusaharay@yahoo.com; Patra, A.
2014-10-15
Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet collocation method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: In this paper the numerical solution for the fractional order stationary neutron transport equation is presented using Haar wavelet Collocation Method (HWCM). Haar wavelet collocation method is efficient and powerful in solving wide class of linear and nonlinear differential equations. This paper intends to provide an application of Haar wavelets to nuclear science problems. This paper describes the application of Haar wavelets for the numerical solution of fractional order stationary neutron transport equation in homogeneous medium with isotropic scattering. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency and applicability of the method, two test problems are discussed.
Fractional-Order Identification and Control of Heating Processes with Non-Continuous Materials
Directory of Open Access Journals (Sweden)
Riccardo Caponetto
2016-11-01
Full Text Available The paper presents a fractional order model of a heating process and a comparison of fractional and standard PI controllers in its closed loop system. Preliminarily, an enhanced fractional order model for the heating process on non-continuous materials has been identified through a fitting algorithm on experimental data. Experimentation has been carried out on a finite length beam filled with three non-continuous materials (air, styrofoam, metal buckshots in order to identify a model in the frequency domain and to obtain a relationship between the fractional order of the heating process and the different materials’ properties. A comparison between the experimental model and the theoretical one has been performed, proving a significant enhancement of the fitting performances. Moreover the obtained modelling results confirm the fractional nature of the heating processes when diffusion occurs in non-continuous composite materials, and they show how the model’s fractional order can be used as a characteristic parameter for non-continuous materials with different composition and structure. Finally, three different kinds of controllers have been applied and compared in order to keep constant the beam temperature constant at a fixed length.
Feedback systems for linear colliders
Hendrickson, L; Himel, Thomas M; Minty, Michiko G; Phinney, N; Raimondi, Pantaleo; Raubenheimer, T O; Shoaee, H; Tenenbaum, P G
1999-01-01
Feedback systems are essential for stable operation of a linear collider, providing a cost-effective method for relaxing tight tolerances. In the Stanford Linear Collider (SLC), feedback controls beam parameters such as trajectory, energy, and intensity throughout the accelerator. A novel dithering optimization system which adjusts final focus parameters to maximize luminosity contributed to achieving record performance in the 1997-98 run. Performance limitations of the steering feedback have been investigated, and improvements have been made. For the Next Linear Collider (NLC), extensive feedback systems are planned as an intregal part of the design. Feedback requiremetns for JLC (the Japanese Linear Collider) are essentially identical to NLC; some of the TESLA requirements are similar but there are significant differences. For NLC, algorithms which incorporate improvements upon the SLC implementation are being prototyped. Specialized systems for the damping rings, rf and interaction point will operate at hi...
Theory of fractional order elements based impedance matching networks
Radwan, Ahmed G.
2011-03-01
Fractional order circuit elements (inductors and capacitors) based impedance matching networks are introduced for the first time. In comparison to the conventional integer based L-type matching networks, fractional matching networks are much simpler and versatile. Any complex load can be matched utilizing a single series fractional element, which generally requires two elements for matching in the conventional approach. It is shown that all the Smith chart circles (resistance and reactance) are actually pairs of completely identical circles. They appear to be single for the conventional integer order case, where the identical circles completely overlap each other. The concept is supported by design equations and impedance matching examples. © 2010 IEEE.
Performance Analysis of Fractional-Order PID Controller for a Parabolic Distributed Solar Collector
Elmetennani, Shahrazed
2017-09-01
This paper studies the performance of a fractional-order proportional integral derivative (FOPID) controller designed for parabolic distributed solar collectors. The control problem addressed in concentrated solar collectors aims at forcing the produced heat to follow a desired reference despite the unevenly varying solar irradiance. In addition to the unpredictable variations of the energy source, the parabolic solar collectors are subject to inhomogeneous distributed efficiency parameters affecting the heat production. The FOPID controller is well known for its simplicity with better tuning flexibility along with robustness with respect to disturbances. Thus, we propose a control strategy based on FOPID to achieve the control objectives. First, the FOPID controller is designed based on a linear approximate model describing the system dynamics under nominal working conditions. Then, the FOPID gains and differentiation orders are optimally tuned in order to fulfill the robustness design specifications by solving a nonlinear optimization problem. Numerical simulations are carried out to evaluate the performance of the proposed FOPID controller. A comparison to the robust integer order PID is also provided. Robustness tests are performed for the nominal model to show the effectiveness of the FOPID. Furthermore, the proposed FOPID is numerically tested to control the distributed solar collector under real working conditions.
Zou, Changfu; Zhang, Lei; Hu, Xiaosong; Wang, Zhenpo; Wik, Torsten; Pecht, Michael
2018-06-01
Electrochemical energy storage systems play an important role in diverse applications, such as electrified transportation and integration of renewable energy with the electrical grid. To facilitate model-based management for extracting full system potentials, proper mathematical models are imperative. Due to extra degrees of freedom brought by differentiation derivatives, fractional-order models may be able to better describe the dynamic behaviors of electrochemical systems. This paper provides a critical overview of fractional-order techniques for managing lithium-ion batteries, lead-acid batteries, and supercapacitors. Starting with the basic concepts and technical tools from fractional-order calculus, the modeling principles for these energy systems are presented by identifying disperse dynamic processes and using electrochemical impedance spectroscopy. Available battery/supercapacitor models are comprehensively reviewed, and the advantages of fractional types are discussed. Two case studies demonstrate the accuracy and computational efficiency of fractional-order models. These models offer 15-30% higher accuracy than their integer-order analogues, but have reasonable complexity. Consequently, fractional-order models can be good candidates for the development of advanced battery/supercapacitor management systems. Finally, the main technical challenges facing electrochemical energy storage system modeling, state estimation, and control in the fractional-order domain, as well as future research directions, are highlighted.
Das, Saptarshi; Pan, Indranil; Das, Shantanu
2015-09-01
An optimal trade-off design for fractional order (FO)-PID controller is proposed with a Linear Quadratic Regulator (LQR) based technique using two conflicting time domain objectives. A class of delayed FO systems with single non-integer order element, exhibiting both sluggish and oscillatory open loop responses, have been controlled here. The FO time delay processes are handled within a multi-objective optimization (MOO) formalism of LQR based FOPID design. A comparison is made between two contemporary approaches of stabilizing time-delay systems withinLQR. The MOO control design methodology yields the Pareto optimal trade-off solutions between the tracking performance and total variation (TV) of the control signal. Tuning rules are formed for the optimal LQR-FOPID controller parameters, using median of the non-dominated Pareto solutions to handle delayed FO processes. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
Feedback Systems for Linear Colliders
International Nuclear Information System (INIS)
1999-01-01
Feedback systems are essential for stable operation of a linear collider, providing a cost-effective method for relaxing tight tolerances. In the Stanford Linear Collider (SLC), feedback controls beam parameters such as trajectory, energy, and intensity throughout the accelerator. A novel dithering optimization system which adjusts final focus parameters to maximize luminosity contributed to achieving record performance in the 1997-98 run. Performance limitations of the steering feedback have been investigated, and improvements have been made. For the Next Linear Collider (NLC), extensive feedback systems are planned as an integral part of the design. Feedback requirements for JLC (the Japanese Linear Collider) are essentially identical to NLC; some of the TESLA requirements are similar but there are significant differences. For NLC, algorithms which incorporate improvements upon the SLC implementation are being prototyped. Specialized systems for the damping rings, rf and interaction point will operate at high bandwidth and fast response. To correct for the motion of individual bunches within a train, both feedforward and feedback systems are planned. SLC experience has shown that feedback systems are an invaluable operational tool for decoupling systems, allowing precision tuning, and providing pulse-to-pulse diagnostics. Feedback systems for the NLC will incorporate the key SLC features and the benefits of advancing technologies
Window observers for linear systems
Directory of Open Access Journals (Sweden)
Utkin Vadim
2000-01-01
Full Text Available Given a linear system x ˙ = A x + B u with output y = C x and a window function ω ( t , i.e., ∀ t , ω ( t ∈ {0,1 }, and assuming that the window function is Lebesgue measurable, we refer to the following observer, x ˆ = A x + B u + ω ( t L C ( x − x ˆ as a window observer. The stability issue is treated in this paper. It is proven that for linear time-invariant systems, the window observer can be stabilized by an appropriate design under a very mild condition on the window functions, albeit for linear time-varying system, some regularity of the window functions is required to achieve observer designs with the asymptotic stability. The corresponding design methods are developed. An example is included to illustrate the possible applications
Mata-Machuca, Juan L.; Aguilar-López, Ricardo
2018-01-01
This work deals with the adaptative synchronization of complex dynamical networks with fractional-order nodes and its application in secure communications employing chaotic parameter modulation. The complex network is composed of multiple fractional-order systems with mismatch parameters and the coupling functions are given to realize the network synchronization. We introduce a fractional algebraic synchronizability condition (FASC) and a fractional algebraic identifiability condition (FAIC) which are used to know if the synchronization and parameters estimation problems can be solved. To overcome these problems, an adaptative synchronization methodology is designed; the strategy consists in proposing multiple receiver systems which tend to follow asymptotically the uncertain transmitters systems. The coupling functions and parameters of the receiver systems are adjusted continually according to a convenient sigmoid-like adaptative controller (SLAC), until the measurable output errors converge to zero, hence, synchronization between transmitter and receivers is achieved and message signals are recovered. Indeed, the stability analysis of the synchronization error is based on the fractional Lyapunov direct method. Finally, numerical results corroborate the satisfactory performance of the proposed scheme by means of the synchronization of a complex network consisting of several fractional-order unified chaotic systems.
Tunable fractional-order capacitor using layered ferroelectric polymers
Agambayev, Agamyrat
2017-09-05
Pairs of various Polyvinylidene fluoride P(VDF)-based polymers are used for fabricating bilayer fractional order capacitors (FOCs). The polymer layers are constructed using a simple drop casting approach. The resulting FOC has two advantages: It can be easily integrated with printed circuit boards, and its constant phase angle (CPA) can be tuned by changing the thickness ratio of the layers. Indeed, our experiments show that the CPA of the fabricated FOCs can be tuned within the range from -83° to -65° in the frequency band changing from 150 kHz to 10 MHz. Additionally, we provide an empirical formula describing the relationship between the thickness ratio and the CPA, which is highly useful for designing FOCs with the desired CPA.
Fractional Order Stochastic Differential Equation with Application in European Option Pricing
Directory of Open Access Journals (Sweden)
Qing Li
2014-01-01
Full Text Available Memory effect is an important phenomenon in financial systems, and a number of research works have been carried out to study the long memory in the financial markets. In recent years, fractional order ordinary differential equation is used as an effective instrument for describing the memory effect in complex systems. In this paper, we establish a fractional order stochastic differential equation (FSDE model to describe the effect of trend memory in financial pricing. We, then, derive a European option pricing formula based on the FSDE model and prove the existence of the trend memory (i.e., the mean value function in the option pricing formula when the Hurst index is between 0.5 and 1. In addition, we make a comparison analysis between our proposed model, the classic Black-Scholes model, and the stochastic model with fractional Brownian motion. Numerical results suggest that our model leads to more accurate and lower standard deviation in the empirical study.
The synchronisation of fractional-order hyperchaos compound system
Indian Academy of Sciences (India)
Naeimadeen Noghredani
2018-01-24
Jan 24, 2018 ... ... Engineering, Faculty of Engineering, Ferdowsi University of Mashhad (FUM) Campus, ... effectiveness of the proposed synchronisation scheme using MATLAB. .... component synchronisation in secure communication.
Zheng, Mingwen; Li, Lixiang; Peng, Haipeng; Xiao, Jinghua; Yang, Yixian; Zhang, Yanping; Zhao, Hui
2018-06-01
This paper mainly studies the finite-time stability and synchronization problems of memristor-based fractional-order fuzzy cellular neural network (MFFCNN). Firstly, we discuss the existence and uniqueness of the Filippov solution of the MFFCNN according to the Banach fixed point theorem and give a sufficient condition for the existence and uniqueness of the solution. Secondly, a sufficient condition to ensure the finite-time stability of the MFFCNN is obtained based on the definition of finite-time stability of the MFFCNN and Gronwall-Bellman inequality. Thirdly, by designing a simple linear feedback controller, the finite-time synchronization criterion for drive-response MFFCNN systems is derived according to the definition of finite-time synchronization. These sufficient conditions are easy to verify. Finally, two examples are given to show the effectiveness of the proposed results.
Nasser Eddine, Achraf; Huard, Benoît; Gabano, Jean-Denis; Poinot, Thierry
2018-06-01
This paper deals with the initialization of a non linear identification algorithm used to accurately estimate the physical parameters of Lithium-ion battery. A Randles electric equivalent circuit is used to describe the internal impedance of the battery. The diffusion phenomenon related to this modeling is presented using a fractional order method. The battery model is thus reformulated into a transfer function which can be identified through Levenberg-Marquardt algorithm to ensure the algorithm's convergence to the physical parameters. An initialization method is proposed in this paper by taking into account previously acquired information about the static and dynamic system behavior. The method is validated using noisy voltage response, while precision of the final identification results is evaluated using Monte-Carlo method.
PSO Based Optimal Design of Fractional Order Controller for Industrial Application
Rohit Gupta; Ruchika
2016-01-01
In this paper, a PSO based fractional order PID (FOPID) controller is proposed for concentration control of an isothermal Continuous Stirred Tank Reactor (CSTR) problem. CSTR is used to carry out chemical reactions in industries, which possesses complex nonlinear dynamic characteristics. Particle Swarm Optimization algorithm technique, which is an evolutionary optimization technique based on the movement and intelligence of swarm is proposed for tuning of the controller for this system. Compa...
Fractional-order gradient descent learning of BP neural networks with Caputo derivative.
Wang, Jian; Wen, Yanqing; Gou, Yida; Ye, Zhenyun; Chen, Hua
2017-05-01
Fractional calculus has been found to be a promising area of research for information processing and modeling of some physical systems. In this paper, we propose a fractional gradient descent method for the backpropagation (BP) training of neural networks. In particular, the Caputo derivative is employed to evaluate the fractional-order gradient of the error defined as the traditional quadratic energy function. The monotonicity and weak (strong) convergence of the proposed approach are proved in detail. Two simulations have been implemented to illustrate the performance of presented fractional-order BP algorithm on three small datasets and one large dataset. The numerical simulations effectively verify the theoretical observations of this paper as well. Copyright © 2017 Elsevier Ltd. All rights reserved.
Riemann-Liouville integrals of fractional order and extended KP hierarchy
International Nuclear Information System (INIS)
Kamata, Masaru; Nakamula, Atsushi
2002-01-01
An attempt to formulate the extensions of the KP hierarchy by introducing fractional-order pseudo-differential operators is given. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the supersymmetric extensions of the KP hierarchy is obtained. Unlike the supersymmetric extensions, no Grassmannian variable appears in the hierarchy considered here. More general hierarchies constructed by the 1/Nth-order pseudo-differential operators, their integrability and the reduction procedure are also investigated. In addition to finding the new extensions of the KP hierarchy, a brief introduction to the Riemann-Liouville integral is provided to yield a candidate for the fractional-order pseudo-differential operators
Systems of Inhomogeneous Linear Equations
Scherer, Philipp O. J.
Many problems in physics and especially computational physics involve systems of linear equations which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the dimension of the system is not too large standard methods like Gaussian elimination or QR decomposition are sufficient. Systems with a tridiagonal matrix are important for cubic spline interpolation and numerical second derivatives. They can be solved very efficiently with a specialized Gaussian elimination method. Practical applications often involve very large dimensions and require iterative methods. Convergence of Jacobi and Gauss-Seidel methods is slow and can be improved by relaxation or over-relaxation. An alternative for large systems is the method of conjugate gradients.
Directory of Open Access Journals (Sweden)
Yaoyao Wang
2014-01-01
Full Text Available For the 4-DOF (degrees of freedom trajectory tracking control problem of underwater remotely operated vehicles (ROVs in the presence of model uncertainties and external disturbances, a novel output feedback fractional-order nonsingular terminal sliding mode control (FO-NTSMC technique is introduced in light of the equivalent output injection sliding mode observer (SMO and TSMC principle and fractional calculus technology. The equivalent output injection SMO is applied to reconstruct the full states in finite time. Meanwhile, the FO-NTSMC algorithm, based on a new proposed fractional-order switching manifold, is designed to stabilize the tracking error to equilibrium points in finite time. The corresponding stability analysis of the closed-loop system is presented using the fractional-order version of the Lyapunov stability theory. Comparative numerical simulation results are presented and analyzed to demonstrate the effectiveness of the proposed method. Finally, it is noteworthy that the proposed output feedback FO-NTSMC technique can be used to control a broad range of nonlinear second-order dynamical systems in finite time.
Zhang, Xinxin; Niu, Peifeng; Ma, Yunpeng; Wei, Yanqiao; Li, Guoqiang
2017-10-01
This paper is concerned with the stability analysis issue of fractional-order impulsive neural networks. Under the one-side Lipschitz condition or the linear growth condition of activation function, the existence of solution is analyzed respectively. In addition, the existence, uniqueness and global Mittag-Leffler stability of equilibrium point of the fractional-order impulsive neural networks with one-side Lipschitz condition are investigated by the means of contraction mapping principle and Lyapunov direct method. Finally, an example with numerical simulation is given to illustrate the validity and feasibility of the proposed results. Copyright © 2017 Elsevier Ltd. All rights reserved.
Linear collider systems and costs
International Nuclear Information System (INIS)
Loew, G.A.
1993-05-01
The purpose of this paper is to examine some of the systems and sub-systems involved in so-called ''conventional'' e + e - linear colliders and to study how their design affects the overall cost of these machines. There are presently a total of at least six 500 GeV c. of m. linear collider projects under study in the world. Aside from TESLA (superconducting linac at 1.3 GHz) and CLIC (two-beam accelerator with main linac at 30GHz), the other four proposed e + e - linear colliders can be considered ''conventional'' in that their main linacs use the proven technique of driving room temperature accelerator sections with pulsed klystrons and modulators. The centrally distinguishing feature between these projects is their main linac rf frequency: 3 GHz for the DESY machine, 11.424 GHz for the SLAC and JLC machines, and 14 GHz for the VLEPP machine. The other systems, namely the electron and positron sources, preaccelerators, compressors, damping rings and final foci, are fairly similar from project to project. Probably more than 80% of the cost of these linear colliders will be incurred in the two main linacs facing each other and it is therefore in their design and construction that major savings or extra costs may be found
Fractional-order mathematical model of an irrigation main canal pool
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Shlomi N. Calderon-Valdez
2015-09-01
Full Text Available In this paper a fractional order model for an irrigation main canal is proposed. It is based on the experiments developed in a laboratory prototype of a hydraulic canal and the application of a direct system identification methodology. The hydraulic processes that take place in this canal are equivalent to those that occur in real main irrigation canals and the results obtained here can therefore be easily extended to real canals. The accuracy of the proposed fractional order model is compared by deriving two other integer-order models of the canal of a complexity similar to that proposed here. The parameters of these three mathematical models have been identified by minimizing the Integral Square Error (ISE performance index existing between the models and the real-time experimental data obtained from the canal prototype. A comparison of the performances of these three models shows that the fractional-order model has the lowest error and therefore the higher accuracy. Experiments showed that our model outperformed the accuracy of the integer-order models by about 25%, which is a significant improvement as regards to capturing the canal dynamics.
Magin, Richard L.; Akpa, Belinda S.; Neuberger, Thomas; Webb, Andrew G.
2011-12-01
We report the appearance of anomalous water diffusion in hydrophilic Sephadex gels observed using pulse field gradient (PFG) nuclear magnetic resonance (NMR). The NMR diffusion data was collected using a Varian 14.1 Tesla imaging system with a home-built RF saddle coil. A fractional order analysis of the data was used to characterize heterogeneity in the gels for the dynamics of water diffusion in this restricted environment. Several recent studies of anomalous diffusion have used the stretched exponential function to model the decay of the NMR signal, i.e., exp[-( bD) α], where D is the apparent diffusion constant, b is determined the experimental conditions (gradient pulse separation, durations and strength), and α is a measure of structural complexity. In this work, we consider a different case where the spatial Laplacian in the Bloch-Torrey equation is generalized to a fractional order model of diffusivity via a complexity parameter, β, a space constant, μ, and a diffusion coefficient, D. This treatment reverts to the classical result for the integer order case. The fractional order decay model was fit to the diffusion-weighted signal attenuation for a range of b-values (0 < b < 4000 s mm -2). Throughout this range of b values, the parameters β, μ and D, were found to correlate with the porosity and tortuosity of the gel structure.
Design of fractional order differentiator using type-III and type-IV discrete cosine transform
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Manjeet Kumar
2017-02-01
Full Text Available In this paper, an interpolation method based on discrete cosine transform (DCT is employed for digital finite impulse response-fractional order differentiator (FIR-FOD design. Here, a fractional order digital differentiator is modeled as finite impulse response (FIR system to get an optimized frequency response that approximates the ideal response of a fractional order differentiator. Next, DCT-III and DCT-IV are utilized to determine the filter coefficients of FIR filter that compute the Fractional derivative of a given signal. To improve the frequency response of the proposed FIR-FOD, the filter coefficients are further modified using windows. Several design examples are presented to demonstrate the superiority of the proposed method. The simulation results have also been compared with the existing FIR-FOD design methods such as DFT interpolation, radial basis function (RBF interpolation, DCT-II interpolation and DST interpolation methods. The result reveals that the proposed FIR-FOD design technique using DCT-III and DCT-IV outperforms DFT interpolation, RBF interpolation, DCT-II interpolation and DST interpolation methods in terms of magnitude error.
Experimental Characterization of Ionic Polymer Metal Composite as a Novel Fractional Order Element
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Riccardo Caponetto
2013-01-01
Full Text Available Ionic polymer metal composites (IPMCs are electroactive materials made of ionic polymer thin membranes with platinum metallization on their surfaces. They are interesting materials due to not only their electromechanical applications as transducers but also to their electrochemical features and the relationship between the ionic/solvent current and the potential field. Their electrochemical properties thus suggest the possibility for exploiting them as compact fractional-order elements (FOEs with a view of defining fabrication processes and production strategies that assure the desired performances. In this paper, the experimental electrical characterization of a brand new IPMC setup in a fixed sandwich configuration is proposed. Two IPMC devices with different platinum absorption times (5 h and 20 h are characterized through experimental data: first, a preliminary linearity study is performed for a fixed input voltage amplitude in order to determine the frequency region where IPMC can be approximated as linear; then, a frequency analysis is carried out in order to identify a coherent fractional-order dynamics in the bode diagrams. Such analyses take the first steps towards a simplified model of IPMC as a compact electronic FOE for which the fractional exponent value depends on fabrication parameters as the absorption time.
Incorporation of fractional-order dynamics into an existing PI/PID DC motor control loop.
Tepljakov, Aleksei; Gonzalez, Emmanuel A; Petlenkov, Eduard; Belikov, Juri; Monje, Concepción A; Petráš, Ivo
2016-01-01
The problem of changing the dynamics of an existing DC motor control system without the need of making internal changes is considered in the paper. In particular, this paper presents a method for incorporating fractional-order dynamics in an existing DC motor control system with internal PI or PID controller, through the addition of an external controller into the system and by tapping its original input and output signals. Experimental results based on the control of a real test plant from MATLAB/Simulink environment are presented, indicating the validity of the proposed approach. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
Linear operator inequalities for strongly stable weakly regular linear systems
Curtain, RF
2001-01-01
We consider the question of the existence of solutions to certain linear operator inequalities (Lur'e equations) for strongly stable, weakly regular linear systems with generating operators A, B, C, 0. These operator inequalities are related to the spectral factorization of an associated Popov
Directory of Open Access Journals (Sweden)
Teerawat Sangpet
2014-01-01
Full Text Available Noncollocated control of flexible structures results in nonminimum-phase systems because the separation between the actuator and the sensor creates an input-output delay. The delay can deteriorate stability of closed-loop systems. This paper presents a simple approach to improve the delay-margin of the noncollocated vibration control of piezo-actuated flexible beams using a fractional-order controller. Results of real life experiments illustrate efficiency of the controller and show that the fractional-order controller has better stability robustness than the integer-order controller.
On the fragility of fractional-order PID controllers for FOPDT processes.
Padula, Fabrizio; Visioli, Antonio
2016-01-01
This paper analyzes the fragility issue of fractional-order proportional-integral-derivative controllers applied to integer first-order plus-dead-time processes. In particular, the effects of the variations of the controller parameters on the achieved control system robustness and performance are investigated. Results show that this kind of controllers is more fragile with respect to the standard proportional-integral-derivative controllers and therefore a significant attention should be paid by the user in their tuning. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
Wang, Zhen; Wang, Xiaohong; Li, Yuxia; Huang, Xia
2017-12-01
In this paper, the problems of stability and Hopf bifurcation in a class of fractional-order complex-valued single neuron model with time delay are addressed. With the help of the stability theory of fractional-order differential equations and Laplace transforms, several new sufficient conditions, which ensure the stability of the system are derived. Taking the time delay as the bifurcation parameter, Hopf bifurcation is investigated and the critical value of the time delay for the occurrence of Hopf bifurcation is determined. Finally, two representative numerical examples are given to show the effectiveness of the theoretical results.
Improved Fractional Order VSS Inc-Cond MPPT Algorithm for Photovoltaic Scheme
Directory of Open Access Journals (Sweden)
R. Arulmurugan
2014-01-01
Full Text Available Nowadays a hot topic among the research community is the harnessing energy from the free sunlight which is abundant and pollution-free. The availability of cheap solar photovoltaic (PV modules has to harvest solar energy with better efficiency. The nature of solar modules is nonlinear and therefore the proper impedance matching is essential. The proper impedance matching ensures the extraction of the maximum power from solar PV module. Maximum power point tracking (MPPT algorithm is acting as a significant part in solar power generating system because it varies in the output power from a PV generating set for various climatic conditions. This paper suggested a new improved work for MPPT of PV energy system by using the optimized novel improved fractional order variable step size (FOVSS incremental conductance (Inc-Cond algorithm. The new proposed controller combines the merits of both improved fractional order (FO and variable step size (VSS Inc-Cond which is well suitable for design control and execution. The suggested controller results in attaining the desired transient reaction under changing operating points. MATLAB simulation effort shows MPPT controller and a DC to DC Luo converter feeding a battery load is achieved. The laboratory experimental results demonstrate that the new proposed MPPT controller in the photovoltaic generating system is valid.
Global asymptotical ω-periodicity of a fractional-order non-autonomous neural networks.
Chen, Boshan; Chen, Jiejie
2015-08-01
We study the global asymptotic ω-periodicity for a fractional-order non-autonomous neural networks. Firstly, based on the Caputo fractional-order derivative it is shown that ω-periodic or autonomous fractional-order neural networks cannot generate exactly ω-periodic signals. Next, by using the contraction mapping principle we discuss the existence and uniqueness of S-asymptotically ω-periodic solution for a class of fractional-order non-autonomous neural networks. Then by using a fractional-order differential and integral inequality technique, we study global Mittag-Leffler stability and global asymptotical periodicity of the fractional-order non-autonomous neural networks, which shows that all paths of the networks, starting from arbitrary points and responding to persistent, nonconstant ω-periodic external inputs, asymptotically converge to the same nonconstant ω-periodic function that may be not a solution. Copyright © 2015 Elsevier Ltd. All rights reserved.
A New Model of the Fractional Order Dynamics of the Planetary Gears
Directory of Open Access Journals (Sweden)
Vera Nikolic-Stanojevic
2013-01-01
Full Text Available A theoretical model of planetary gears dynamics is presented. Planetary gears are parametrically excited by the time-varying mesh stiffness that fluctuates as the number of gear tooth pairs in contact changes during gear rotation. In the paper, it has been indicated that even the small disturbance in design realizations of this gear cause nonlinear properties of dynamics which are the source of vibrations and noise in the gear transmission. Dynamic model of the planetary gears with four degrees of freedom is used. Applying the basic principles of analytical mechanics and taking the initial and boundary conditions into consideration, it is possible to obtain the system of equations representing physical meshing process between the two or more gears. This investigation was focused to a new model of the fractional order dynamics of the planetary gear. For this model analytical expressions for the corresponding fractional order modes like one frequency eigen vibrational modes are obtained. For one planetary gear, eigen fractional modes are obtained, and a visualization is presented. By using MathCAD the solution is obtained.
Wu, L.; Liu, S.; Yang, Yingjie
2016-01-01
Traditional integer order buffer operator is extended to fractional order buffer operator, the corresponding relationship between the weakening buffer operator and the strengthening buffer operator is revealed. Fractional order buffer operator not only can generalize the weakening buffer operator and the strengthening buffer operator, but also realize tiny adjustment of buffer effect. The effectiveness of GM(1,1) with the fractional order buffer operator is validated by six cases.
Numerical Inversion for the Multiple Fractional Orders in the Multiterm TFDE
Sun, Chunlong; Li, Gongsheng; Jia, Xianzheng
2017-01-01
The fractional order in a fractional diffusion model is a key parameter which characterizes the anomalous diffusion behaviors. This paper deals with an inverse problem of determining the multiple fractional orders in the multiterm time-fractional diffusion equation (TFDE for short) from numerics. The homotopy regularization algorithm is applied to solve the inversion problem using the finite data at one interior point in the space domain. The inversion fractional orders with random noisy data...
Dynamic linearization system for a radiation gauge
International Nuclear Information System (INIS)
Panarello, J.A.
1977-01-01
The linearization system and process converts a high resolution non-linear analog input signal, representative of the thickness of an object, into a high resolution linear analog output signal suitable for use in driving a variety of output devices. The system requires only a small amount of memory for storing pre-calculated non-linear correction coefficients. The system channels the input signal to separate circuit paths so that it may be used directly to; locate an appropriate correction coefficient; develop a correction term after an appropriate correction coefficient is located; and develop a linearized signal having the same high resolution inherent in the input signal. The system processes the linearized signal to compensate for the possible errors introduced by radiation source noise. The processed linearized signal is the high resolution linear analog output signal which accurately represents the thickness of the object being gauged
Linear quadratic optimization for positive LTI system
Muhafzan, Yenti, Syafrida Wirma; Zulakmal
2017-05-01
Nowaday the linear quadratic optimization subject to positive linear time invariant (LTI) system constitute an interesting study considering it can become a mathematical model of variety of real problem whose variables have to nonnegative and trajectories generated by these variables must be nonnegative. In this paper we propose a method to generate an optimal control of linear quadratic optimization subject to positive linear time invariant (LTI) system. A sufficient condition that guarantee the existence of such optimal control is discussed.
Asymptotical Behavior of the Solution of a SDOF Linear Fractionally Damped Vibration System
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Z.H. Wang
2011-01-01
Full Text Available Fractional-order derivative has been shown an adequate tool to the study of so-called "anomalous" social and physical behaviors, in reflecting their non-local, frequency- and history-dependent properties, and it has been used to model practical systems in engineering successfully, including the famous Bagley-Torvik equation modeling forced motion of a rigid plate immersed in Newtonian fluid. The solutions of the initial value problems of linear fractional differential equations are usually expressed in terms of Mittag-Leffler functions or some other kind of power series. Such forms of solutions are not good for engineers not only in understanding the solutions but also in investigation. This paper proves that for the linear SDOF oscillator with a damping described by fractional-order derivative whose order is between 1 and 2, the solution of its initial value problem free of external excitation consists of two parts, the first one is the 'eigenfunction expansion' that is similar to the case without fractional-order derivative, and the second one is a definite integral that is independent of the eigenvalues (or characteristic roots. The integral disappears in the classical linear oscillator and it can be neglected from the solution when stationary solution is addressed. Moreover, the response of the fractionally damped oscillator under harmonic excitation is calculated in a similar way, and it is found that the fractional damping with order between 1 and 2 can be used to produce oscillation with large amplitude as well as to suppress oscillation, depending on the ratio of the excitation frequency and the natural frequency.
Song, Shuai; Song, Xiaona; Balsera, Ines Tejado
2017-05-01
This paper investigates the mixed H∞ and passive projective synchronization problem for fractional-order (FO) memristor-based neural networks with time delays. Our aim is to design a controller such that, though the unavoidable phenomena of time delay and external disturbances is fully considered, the resulting closed-loop system is stable with a mixed H∞ and passive performance level. By combining sliding mode control and adaptive control methods, a novel adaptive sliding mode control strategy is designed for the synchronization of time-delayed FO dynamic networks. Via the application of FO system stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequalities. Based on the conditions, a desired controller which can guarantee the stability of the closed-loop system and also ensure a mixed H∞ and passive performance level is designed. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method.
Experimental demonstration of fractional-order oscillators of orders 2.6 and 2.7
Elwakil, A.S.; Agambayev, Agamyrat; Allagui, A.; Salama, Khaled N.
2017-01-01
The purpose of this work is to provide an experimental demonstration for the development of sinusoidal oscillations in a fractional-order Hartley-like oscillator. Solid-state fractional-order electric double-layer capacitors were first fabricated using graphene-percolated P(VDF-TrFE-CFE) composite structure, and then characterized by using electrochemical impedance spectroscopy. The devices exhibit the fractional orders of 0.6 and 0.74 respectively (using the model Zc=Rs+1/(jω)αCα), with the corresponding pseudocapacitances of approximately 93nFsec−0.4 and 1.5nFsec−0.26 over the frequency range 200kHz–6MHz (Rs < 15Ω). Then, we verified using these fractional-order devices integrated in a Hartley-like circuit that the fractional-order oscillatory behaviors are of orders 2.6 and 2.74.
Experimental demonstration of fractional-order oscillators of orders 2.6 and 2.7
Elwakil, A.S.
2017-02-07
The purpose of this work is to provide an experimental demonstration for the development of sinusoidal oscillations in a fractional-order Hartley-like oscillator. Solid-state fractional-order electric double-layer capacitors were first fabricated using graphene-percolated P(VDF-TrFE-CFE) composite structure, and then characterized by using electrochemical impedance spectroscopy. The devices exhibit the fractional orders of 0.6 and 0.74 respectively (using the model Zc=Rs+1/(jω)αCα), with the corresponding pseudocapacitances of approximately 93nFsec−0.4 and 1.5nFsec−0.26 over the frequency range 200kHz–6MHz (Rs < 15Ω). Then, we verified using these fractional-order devices integrated in a Hartley-like circuit that the fractional-order oscillatory behaviors are of orders 2.6 and 2.74.
An Adaptive Pseudospectral Method for Fractional Order Boundary Value Problems
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Mohammad Maleki
2012-01-01
Full Text Available An adaptive pseudospectral method is presented for solving a class of multiterm fractional boundary value problems (FBVP which involve Caputo-type fractional derivatives. The multiterm FBVP is first converted into a singular Volterra integrodifferential equation (SVIDE. By dividing the interval of the problem to subintervals, the unknown function is approximated using a piecewise interpolation polynomial with unknown coefficients which is based on shifted Legendre-Gauss (ShLG collocation points. Then the problem is reduced to a system of algebraic equations, thus greatly simplifying the problem. Further, some additional conditions are considered to maintain the continuity of the approximate solution and its derivatives at the interface of subintervals. In order to convert the singular integrals of SVIDE into nonsingular ones, integration by parts is utilized. In the method developed in this paper, the accuracy can be improved either by increasing the number of subintervals or by increasing the degree of the polynomial on each subinterval. Using several examples including Bagley-Torvik equation the proposed method is shown to be efficient and accurate.
Comparison of the methods for discrete approximation of the fractional-order operator
Directory of Open Access Journals (Sweden)
Zborovjan Martin
2003-12-01
Full Text Available In this paper we will present some alternative types of discretization methods (discrete approximation for the fractional-order (FO differentiator and their application to the FO dynamical system described by the FO differential equation (FDE. With analytical solution and numerical solution by power series expansion (PSE method are compared two effective methods - the Muir expansion of the Tustin operator and continued fraction expansion method (CFE with the Tustin operator and the Al-Alaoui operator. Except detailed mathematical description presented are also simulation results. From the Bode plots of the FO differentiator and FDE and from the solution in the time domain we can see, that the CFE is a more effective method according to the PSE method, but there are some restrictions for the choice of the time step. The Muir expansion is almost unusable.
On pole structure assignment in linear systems
Czech Academy of Sciences Publication Activity Database
Loiseau, J.-J.; Zagalak, Petr
2009-01-01
Roč. 82, č. 7 (2009), s. 1179-1192 ISSN 0020-7179 R&D Projects: GA ČR(CZ) GA102/07/1596 Institutional research plan: CEZ:AV0Z10750506 Keywords : linear systems * linear state feedback * pole structure assignment Subject RIV: BC - Control Systems Theory Impact factor: 1.124, year: 2009 http://library.utia.cas.cz/separaty/2009/AS/zagalak-on pole structure assignment in linear systems.pdf
International Nuclear Information System (INIS)
Song Xiao-Na; Song Shuai; Liu Lei-Po; Tejado Balsera, Inés
2017-01-01
This paper investigates the mixed H ∞ and passive projective synchronization problem for fractional-order (FO) memristor-based neural networks. Our aim is to design a controller such that, though the unavoidable phenomena of time-delay and parameter uncertainty are fully considered, the resulting closed-loop system is asymptotically stable with a mixed H ∞ and passive performance level. By combining active and adaptive control methods, a novel hybrid control strategy is designed, which can guarantee the robust stability of the closed-loop system and also ensure a mixed H ∞ and passive performance level. Via the application of FO Lyapunov stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequality techniques. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method. (paper)
Displacement measurement system for linear array detector
International Nuclear Information System (INIS)
Zhang Pengchong; Chen Ziyu; Shen Ji
2011-01-01
It presents a set of linear displacement measurement system based on encoder. The system includes displacement encoders, optical lens and read out circuit. Displacement read out unit includes linear CCD and its drive circuit, two amplifier circuits, second order Butterworth low-pass filter and the binarization circuit. The coding way is introduced, and various parts of the experimental signal waveforms are given, and finally a linear experimental test results are given. The experimental results are satisfactory. (authors)
Numerical solution of large sparse linear systems
International Nuclear Information System (INIS)
Meurant, Gerard; Golub, Gene.
1982-02-01
This note is based on one of the lectures given at the 1980 CEA-EDF-INRIA Numerical Analysis Summer School whose aim is the study of large sparse linear systems. The main topics are solving least squares problems by orthogonal transformation, fast Poisson solvers and solution of sparse linear system by iterative methods with a special emphasis on preconditioned conjuguate gradient method [fr
Balanced truncation for linear switched systems
DEFF Research Database (Denmark)
Petreczky, Mihaly; Wisniewski, Rafal; Leth, John-Josef
2013-01-01
In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems from Shaker and Wisniewski (2011, 2009) and . This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems (Wood et al., 1996) [3]. Specifically...
The Oscillation of a Class of the Fractional-Order Delay Differential Equations
Directory of Open Access Journals (Sweden)
Qianli Lu
2014-01-01
Full Text Available Several oscillation results are proposed including necessary and sufficient conditions for the oscillation of fractional-order delay differential equations with constant coefficients, the sufficient or necessary and sufficient conditions for the oscillation of fractional-order delay differential equations by analysis method, and the sufficient or necessary and sufficient conditions for the oscillation of delay partial differential equation with three different boundary conditions. For this, α-exponential function which is a kind of functions that play the same role of the classical exponential functions of fractional-order derivatives is used.
Numerical Inversion for the Multiple Fractional Orders in the Multiterm TFDE
Directory of Open Access Journals (Sweden)
Chunlong Sun
2017-01-01
Full Text Available The fractional order in a fractional diffusion model is a key parameter which characterizes the anomalous diffusion behaviors. This paper deals with an inverse problem of determining the multiple fractional orders in the multiterm time-fractional diffusion equation (TFDE for short from numerics. The homotopy regularization algorithm is applied to solve the inversion problem using the finite data at one interior point in the space domain. The inversion fractional orders with random noisy data give good approximations to the exact order demonstrating the efficiency of the inversion algorithm and numerical stability of the inversion problem.
Observability of linear systems with saturated outputs
Koplon, R.; Sontag, E.D.; Hautus, M.L.J.
1994-01-01
We present necessary and sufficient conditions for observability of the class of output-saturated systems. These are linear systems whose output passes through a saturation function before it can be measured.
Belkhatir, Zehor
2015-11-05
This paper deals with the joint estimation of the unknown input and the fractional differentiation orders of a linear fractional order system. A two-stage algorithm combining the modulating functions with a first-order Newton method is applied to solve this estimation problem. First, the modulating functions approach is used to estimate the unknown input for a given fractional differentiation orders. Then, the method is combined with a first-order Newton technique to identify the fractional orders jointly with the input. To show the efficiency of the proposed method, numerical examples illustrating the estimation of the neural activity, considered as input of a fractional model of the neurovascular coupling, along with the fractional differentiation orders are presented in both noise-free and noisy cases.
Performance Analysis of Fractional-Order PID Controller for a Parabolic Distributed Solar Collector
Elmetennani, Shahrazed; N'Doye, Ibrahima; Salama, Khaled N.; Laleg-Kirati, Taous-Meriem
2017-01-01
This paper studies the performance of a fractional-order proportional integral derivative (FOPID) controller designed for parabolic distributed solar collectors. The control problem addressed in concentrated solar collectors aims at forcing
On Existence of Solutions to the Caputo Type Fractional Order Three-Point Boundary Value Problems
Directory of Open Access Journals (Sweden)
B.M.B. Krushna
2016-10-01
Full Text Available In this paper, we establish the existence of solutions to the fractional order three-point boundary value problems by utilizing Banach contraction principle and Schaefer's fixed point theorem.
Ebrahimkhani, Sadegh
2016-07-01
Wind power plants have nonlinear dynamics and contain many uncertainties such as unknown nonlinear disturbances and parameter uncertainties. Thus, it is a difficult task to design a robust reliable controller for this system. This paper proposes a novel robust fractional-order sliding mode (FOSM) controller for maximum power point tracking (MPPT) control of doubly fed induction generator (DFIG)-based wind energy conversion system. In order to enhance the robustness of the control system, uncertainties and disturbances are estimated using a fractional order uncertainty estimator. In the proposed method a continuous control strategy is developed to achieve the chattering free fractional order sliding-mode control, and also no knowledge of the uncertainties and disturbances or their bound is assumed. The boundedness and convergence properties of the closed-loop signals are proven using Lyapunov׳s stability theory. Simulation results in the presence of various uncertainties were carried out to evaluate the effectiveness and robustness of the proposed control scheme. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
Fractional-Order Total Variation Image Restoration Based on Primal-Dual Algorithm
Chen, Dali; Chen, YangQuan; Xue, Dingyu
2013-01-01
This paper proposes a fractional-order total variation image denoising algorithm based on the primal-dual method, which provides a much more elegant and effective way of treating problems of the algorithm implementation, ill-posed inverse, convergence rate, and blocky effect. The fractional-order total variation model is introduced by generalizing the first-order model, and the corresponding saddle-point and dual formulation are constructed in theory. In order to guarantee $O(1/{N}^{2})$ conv...
International Nuclear Information System (INIS)
Xu Chang-Jin; Li Pei-Luan; Pang Yi-Cheng
2017-01-01
This paper is concerned with fractional-order bidirectional associative memory (BAM) neural networks with time delays. Applying Laplace transform, the generalized Gronwall inequality and estimates of Mittag–Leffler functions, some sufficient conditions which ensure the finite-time stability of fractional-order bidirectional associative memory neural networks with time delays are obtained. Two examples with their simulations are given to illustrate the theoretical findings. Our results are new and complement previously known results. (paper)
A Novel Sigma-Delta Modulator with Fractional-Order Digital Loop Integrator
Directory of Open Access Journals (Sweden)
Chi Xu
2017-01-01
Full Text Available This paper proposes using a fractional-order digital loop integrator to improve the robust stability of Sigma-Delta modulator, thus extending the integer-order Sigma-Delta modulator to a non-integer-order (fractional-order one in the Sigma-Delta ADC design field. The proposed fractional-order Sigma-Delta modulator has reasonable noise characteristics, dynamic range, and bandwidth; moreover the signal-to-noise ratio (SNR is improved remarkably. In particular, a 2nd-order digital loop integrator and a digital PIλDμ controller are combined to work as the fractional-order digital loop integrator, which is realized using FPGA; this will reduce the ASIC analog circuit layout design and chip testing difficulties. The parameters of the proposed fractional-order Sigma-Delta modulator are tuned by using swarm intelligent algorithm, which offers opportunity to simplify the process of tuning parameters and further improve the noise performance. Simulation results are given and they demonstrate the efficiency of the proposed fractional-order Sigma-Delta modulator.
Generalized modeling of the fractional-order memcapacitor and its character analysis
Guo, Zhang; Si, Gangquan; Diao, Lijie; Jia, Lixin; Zhang, Yanbin
2018-06-01
Memcapacitor is a new type of memory device generalized from the memristor. This paper proposes a generalized fractional-order memcapacitor model by introducing the fractional calculus into the model. The generalized formulas are studied and the two fractional-order parameter α, β are introduced where α mostly affects the fractional calculus value of charge q within the generalized Ohm's law and β generalizes the state equation which simulates the physical mechanism of a memcapacitor into the fractional sense. This model will be reduced to the conventional memcapacitor as α = 1 , β = 0 and to the conventional memristor as α = 0 , β = 1 . Then the numerical analysis of the fractional-order memcapacitor is studied. And the characteristics and output behaviors of the fractional-order memcapacitor applied with sinusoidal charge are derived. The analysis results have shown that there are four basic v - q and v - i curve patterns when the fractional order α, β respectively equal to 0 or 1, moreover all v - q and v - i curves of the other fractional-order models are transition curves between the four basic patterns.
Isolators Including Main Spring Linear Guide Systems
Goold, Ryan (Inventor); Buchele, Paul (Inventor); Hindle, Timothy (Inventor); Ruebsamen, Dale Thomas (Inventor)
2017-01-01
Embodiments of isolators, such as three parameter isolators, including a main spring linear guide system are provided. In one embodiment, the isolator includes first and second opposing end portions, a main spring mechanically coupled between the first and second end portions, and a linear guide system extending from the first end portion, across the main spring, and toward the second end portion. The linear guide system expands and contracts in conjunction with deflection of the main spring along the working axis, while restricting displacement and rotation of the main spring along first and second axes orthogonal to the working axis.
Linear systems a measurement based approach
Bhattacharyya, S P; Mohsenizadeh, D N
2014-01-01
This brief presents recent results obtained on the analysis, synthesis and design of systems described by linear equations. It is well known that linear equations arise in most branches of science and engineering as well as social, biological and economic systems. The novelty of this approach is that no models of the system are assumed to be available, nor are they required. Instead, a few measurements made on the system can be processed strategically to directly extract design values that meet specifications without constructing a model of the system, implicitly or explicitly. These new concepts are illustrated by applying them to linear DC and AC circuits, mechanical, civil and hydraulic systems, signal flow block diagrams and control systems. These applications are preliminary and suggest many open problems. The results presented in this brief are the latest effort in this direction and the authors hope these will lead to attractive alternatives to model-based design of engineering and other systems.
Dominant pole placement with fractional order PID controllers: D-decomposition approach.
Mandić, Petar D; Šekara, Tomislav B; Lazarević, Mihailo P; Bošković, Marko
2017-03-01
Dominant pole placement is a useful technique designed to deal with the problem of controlling a high order or time-delay systems with low order controller such as the PID controller. This paper tries to solve this problem by using D-decomposition method. Straightforward analytic procedure makes this method extremely powerful and easy to apply. This technique is applicable to a wide range of transfer functions: with or without time-delay, rational and non-rational ones, and those describing distributed parameter systems. In order to control as many different processes as possible, a fractional order PID controller is introduced, as a generalization of classical PID controller. As a consequence, it provides additional parameters for better adjusting system performances. The design method presented in this paper tunes the parameters of PID and fractional PID controller in order to obtain good load disturbance response with a constraint on the maximum sensitivity and sensitivity to noise measurement. Good set point response is also one of the design goals of this technique. Numerous examples taken from the process industry are given, and D-decomposition approach is compared with other PID optimization methods to show its effectiveness. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
Final focus systems for linear colliders
International Nuclear Information System (INIS)
Erickson, R.A.
1987-11-01
The final focus system of a linear collider must perform two primary functions, it must focus the two opposing beams so that their transverse dimensions at the interaction point are small enough to yield acceptable luminosity, and it must steer the beams together to maintain collisions. In addition, the final focus system must transport the outgoing beams to a location where they can be recycled or safely dumped. Elementary optical considerations for linear collider final focus systems are discussed, followed by chromatic aberrations. The design of the final focus system of the SLAC Linear Collider (SLC) is described. Tuning and diagnostics and steering to collision are discussed. Most of the examples illustrating the concepts covered are drawn from the SLC, but the principles and conclusions are said to be generally applicable to other linear collider designs as well. 26 refs., 17 figs
On deformations of linear differential systems
Gontsov, R.R.; Poberezhnyi, V.A.; Helminck, G.F.
2011-01-01
This article concerns deformations of meromorphic linear differential systems. Problems relating to their existence and classification are reviewed, and the global and local behaviour of solutions to deformation equations in a neighbourhood of their singular set is analysed. Certain classical
Superconducting linear accelerator system for NSC
Indian Academy of Sciences (India)
59, No. 5. — journal of. November 2002 physics pp. 849–858. Superconducting linear accelerator system for NSC ... cryogenics facility, RF electronics development, facilities for fabricating niobium resonators indige- ... Prototype resonator was.
Jian, Jigui; Wan, Peng
2017-07-01
This paper deals with the problem on Lagrange α-exponential stability and α-exponential convergence for a class of fractional-order complex-valued neural networks. To this end, some new fractional-order differential inequalities are established, which improve and generalize previously known criteria. By using the new inequalities and coupling with the Lyapunov method, some effective criteria are derived to guarantee Lagrange α-exponential stability and α-exponential convergence of the addressed network. Moreover, the framework of the α-exponential convergence ball is also given, where the convergence rate is related to the parameters and the order of differential of the system. These results here, which the existence and uniqueness of the equilibrium points need not to be considered, generalize and improve the earlier publications and can be applied to monostable and multistable fractional-order complex-valued neural networks. Finally, one example with numerical simulations is given to show the effectiveness of the obtained results. Copyright © 2017 Elsevier Ltd. All rights reserved.
Fast Solvers for Dense Linear Systems
Energy Technology Data Exchange (ETDEWEB)
Kauers, Manuel [Research Institute for Symbolic Computation (RISC), Altenbergerstrasse 69, A4040 Linz (Austria)
2008-10-15
It appears that large scale calculations in particle physics often require to solve systems of linear equations with rational number coefficients exactly. If classical Gaussian elimination is applied to a dense system, the time needed to solve such a system grows exponentially in the size of the system. In this tutorial paper, we present a standard technique from computer algebra that avoids this exponential growth: homomorphic images. Using this technique, big dense linear systems can be solved in a much more reasonable time than using Gaussian elimination over the rationals.
Signals and transforms in linear systems analysis
Wasylkiwskyj, Wasyl
2013-01-01
Signals and Transforms in Linear Systems Analysis covers the subject of signals and transforms, particularly in the context of linear systems theory. Chapter 2 provides the theoretical background for the remainder of the text. Chapter 3 treats Fourier series and integrals. Particular attention is paid to convergence properties at step discontinuities. This includes the Gibbs phenomenon and its amelioration via the Fejer summation techniques. Special topics include modulation and analytic signal representation, Fourier transforms and analytic function theory, time-frequency analysis and frequency dispersion. Fundamentals of linear system theory for LTI analogue systems, with a brief account of time-varying systems, are covered in Chapter 4 . Discrete systems are covered in Chapters 6 and 7. The Laplace transform treatment in Chapter 5 relies heavily on analytic function theory as does Chapter 8 on Z -transforms. The necessary background on complex variables is provided in Appendix A. This book is intended to...
Linear integral equations and soliton systems
International Nuclear Information System (INIS)
Quispel, G.R.W.
1983-01-01
A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)
Design of CMOS analog integrated fractional-order circuits applications in medicine and biology
Tsirimokou, Georgia; Elwakil, Ahmed
2017-01-01
This book describes the design and realization of analog fractional-order circuits, which are suitable for on-chip implementation, capable of low-voltage operation and electronic adjustment of their characteristics. The authors provide a brief introduction to fractional-order calculus, followed by design issues for fractional-order circuits of various orders and types. The benefits of this approach are demonstrated with current-mode and voltage-mode filter designs. Electronically tunable emulators of fractional-order capacitors and inductors are presented, where the behavior of the corresponding chips fabricated using the AMS 0.35um CMOS process has been experimentally verified. Applications of fractional-order circuits are demonstrated, including a pre-processing stage suitable for the implementation of the Pan-Tompkins algorithm for detecting the QRS complexes of an electrocardiogram (ECG), a fully tunable implementation of the Cole-Cole model used for the modeling of biological tissues, and a simple, non-i...
STABILITY OF LINEAR SYSTEMS WITH MARKOVIAN JUMPS
Directory of Open Access Journals (Sweden)
Jorge Enrique Mayta Guillermo
2016-12-01
Full Text Available In this work we will analyze the stability of linear systems governed by a Markov chain, this family is known in the specialized literature as linear systems with Markov jumps or by its acronyms in English MJLS as it is denoted in [1]. Linear systems governed by a Markov chain are dynamic systems with abrupt changes. We give some denitions of stability for the MJLS system, where these types of stability are equivalent as long as the state space of the Markov chain is nite. Finally we present a theorem that characterizes the stochastic stability by means of an equation of the Lyapunov type. The result is a generalization of a theorem in classical theory.
Owolabi, Kolade M.
2017-03-01
In this paper, some nonlinear space-fractional order reaction-diffusion equations (SFORDE) on a finite but large spatial domain x ∈ [0, L], x = x(x , y , z) and t ∈ [0, T] are considered. Also in this work, the standard reaction-diffusion system with boundary conditions is generalized by replacing the second-order spatial derivatives with Riemann-Liouville space-fractional derivatives of order α, for 0 Fourier spectral method is introduced as a better alternative to existing low order schemes for the integration of fractional in space reaction-diffusion problems in conjunction with an adaptive exponential time differencing method, and solve a range of one-, two- and three-components SFORDE numerically to obtain patterns in one- and two-dimensions with a straight forward extension to three spatial dimensions in a sub-diffusive (0 reaction-diffusion case. With application to models in biology and physics, different spatiotemporal dynamics are observed and displayed.
A robust fractional-order PID controller design based on active queue management for TCP network
Hamidian, Hamideh; Beheshti, Mohammad T. H.
2018-01-01
In this paper, a robust fractional-order controller is designed to control the congestion in transmission control protocol (TCP) networks with time-varying parameters. Fractional controllers can increase the stability and robustness. Regardless of advantages of fractional controllers, they are still not common in congestion control in TCP networks. The network parameters are time-varying, so the robust stability is important in congestion controller design. Therefore, we focused on the robust controller design. The fractional PID controller is developed based on active queue management (AQM). D-partition technique is used. The most important property of designed controller is the robustness to the time-varying parameters of the TCP network. The vertex quasi-polynomials of the closed-loop characteristic equation are obtained, and the stability boundaries are calculated for each vertex quasi-polynomial. The intersection of all stability regions is insensitive to network parameter variations, and results in robust stability of TCP/AQM system. NS-2 simulations show that the proposed algorithm provides a stable queue length. Moreover, simulations show smaller oscillations of the queue length and less packet drop probability for FPID compared to PI and PID controllers. We can conclude from NS-2 simulations that the average packet loss probability variations are negligible when the network parameters change.
Attempt to generalize fractional-order electric elements to complex-order ones
Si, Gangquan; Diao, Lijie; Zhu, Jianwei; Lei, Yuhang; Zhang, Yanbin
2017-06-01
The complex derivative {D}α +/- {{j}β }, with α, β \\in R+ is a generalization of the concept of integer derivative, where α=1, β=0. Fractional-order electric elements and circuits are becoming more and more attractive. In this paper, the complex-order electric elements concept is proposed for the first time, and the complex-order elements are modeled and analyzed. Some interesting phenomena are found that the real part of the order affects the phase of output signal, and the imaginary part affects the amplitude for both the complex-order capacitor and complex-order memristor. More interesting is that the complex-order capacitor can do well at the time of fitting electrochemistry impedance spectra. The complex-order memristor is also analyzed. The area inside the hysteresis loops increases with the increasing of the imaginary part of the order and decreases with the increasing of the real part. Some complex case of complex-order memristors hysteresis loops are analyzed at last, whose loop has touching points beyond the origin of the coordinate system.
Correlated Levy Noise in Linear Dynamical Systems
International Nuclear Information System (INIS)
Srokowski, T.
2011-01-01
Linear dynamical systems, driven by a non-white noise which has the Levy distribution, are analysed. Noise is modelled by a specific stochastic process which is defined by the Langevin equation with a linear force and the Levy distributed symmetric white noise. Correlation properties of the process are discussed. The Fokker-Planck equation driven by that noise is solved. Distributions have the Levy shape and their width, for a given time, is smaller than for processes in the white noise limit. Applicability of the adiabatic approximation in the case of the linear force is discussed. (author)
Introduction to linear systems of differential equations
Adrianova, L Ya
1995-01-01
The theory of linear systems of differential equations is one of the cornerstones of the whole theory of differential equations. At its root is the concept of the Lyapunov characteristic exponent. In this book, Adrianova presents introductory material and further detailed discussions of Lyapunov exponents. She also discusses the structure of the space of solutions of linear systems. Classes of linear systems examined are from the narrowest to widest: 1)�autonomous, 2)�periodic, 3)�reducible to autonomous, 4)�nearly reducible to autonomous, 5)�regular. In addition, Adrianova considers the following: stability of linear systems and the influence of perturbations of the coefficients on the stability the criteria of uniform stability and of uniform asymptotic stability in terms of properties of the solutions several estimates of the growth rate of solutions of a linear system in terms of its coefficients How perturbations of the coefficients change all the elements of the spectrum of the system is defin...
Khater method for nonlinear Sharma Tasso-Olever (STO) equation of fractional order
Bibi, Sadaf; Mohyud-Din, Syed Tauseef; Khan, Umar; Ahmed, Naveed
In this work, we have implemented a direct method, known as Khater method to establish exact solutions of nonlinear partial differential equations of fractional order. Number of solutions provided by this method is greater than other traditional methods. Exact solutions of nonlinear fractional order Sharma Tasso-Olever (STO) equation are expressed in terms of kink, travelling wave, periodic and solitary wave solutions. Modified Riemann-Liouville derivative and Fractional complex transform have been used for compatibility with fractional order sense. Solutions have been graphically simulated for understanding the physical aspects and importance of the method. A comparative discussion between our established results and the results obtained by existing ones is also presented. Our results clearly reveal that the proposed method is an effective, powerful and straightforward technique to work out new solutions of various types of differential equations of non-integer order in the fields of applied sciences and engineering.
Demonstrative fractional order - PID controller based DC motor drive on digital platform.
Khubalkar, Swapnil W; Junghare, Anjali S; Aware, Mohan V; Chopade, Amit S; Das, Shantanu
2017-09-21
In industrial drives applications, fractional order controllers can exhibit phenomenal impact due to realization through digital implementation. Digital fractional order controllers have created wide scope as it possess the inherent advantages like robustness against the plant parameter variation. This paper provides brief design procedure of fractional order proportional-integral-derivative (FO-PID) controller through the indirect approach of approximation using constant phase technique. The new modified dynamic particle swarm optimization (IdPSO) technique is proposed to find controller parameters. The FO-PID controller is implemented using floating point digital signal processor. The building blocks are designed and assembled with all peripheral components for the 1.5kW industrial DC motor drive. The robust operation for parametric variation is ascertained by testing the controller with two separately excited DC motors with the same rating but different parameters. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Bifurcation and chaos of a new discrete fractional-order logistic map
Ji, YuanDong; Lai, Li; Zhong, SuChuan; Zhang, Lu
2018-04-01
The fractional-order discrete maps with chaotic behaviors based on the theory of ;fractional difference; are proposed in recent years. In this paper, instead of using fractional difference, a new fractionalized logistic map is proposed based on the numerical algorithm of fractional differentiation definition. The bifurcation diagrams of this map with various differential orders are given by numerical simulation. The simulation results show that the fractional-order logistic map derived in this manner holds rich dynamical behaviors because of its memory effect. In addition, new types of behaviors of bifurcation and chaos are found, which are different from those of the integer-order and the previous fractional-order logistic maps.
Final Focus Systems in Linear Colliders
International Nuclear Information System (INIS)
Raubenheimer, Tor
1998-01-01
In colliding beam facilities, the ''final focus system'' must demagnify the beams to attain the very small spot sizes required at the interaction points. The first final focus system with local chromatic correction was developed for the Stanford Linear Collider where very large demagnifications were desired. This same conceptual design has been adopted by all the future linear collider designs as well as the SuperConducting Supercollider, the Stanford and KEK B-Factories, and the proposed Muon Collider. In this paper, the over-all layout, physics constraints, and optimization techniques relevant to the design of final focus systems for high-energy electron-positron linear colliders are reviewed. Finally, advanced concepts to avoid some of the limitations of these systems are discussed
Generalized Cross-Gramian for Linear Systems
DEFF Research Database (Denmark)
Shaker, Hamid Reza
2012-01-01
The cross-gramian is a well-known matrix with embedded controllability and observability information. The cross-gramian is related to the Hankel operator and the Hankel singular values of a linear square system and it has several interesting properties. These properties make the cross...... square symmetric systems, the ordinary cross-gramian does not exist. To cope with this problem, a new generalized cross-gramian is introduced in this paper. In contrast to the ordinary cross-gramian, the generalized cross-gramian can be easily obtained for general linear systems and therefore can be used...
Linear dynamic coupling in geared rotor systems
David, J. W.; Mitchell, L. D.
1986-01-01
The effects of high frequency oscillations caused by the gear mesh, on components of a geared system that can be modeled as rigid discs are analyzed using linear dynamic coupling terms. The coupled, nonlinear equations of motion for a disc attached to a rotating shaft are presented. The results of a trial problem analysis show that the inclusion of the linear dynamic coupling terms can produce significant changes in the predicted response of geared rotor systems, and that the produced sideband responses are greater than the unbalanced response. The method is useful in designing gear drives for heavy-lift helicopters, industrial speed reducers, naval propulsion systems, and heavy off-road equipment.
On output regulation for linear systems
Saberi, Ali; Stoorvogel, Antonie Arij; Sannuti, Peddapullaiah
For both continuous- and discrete-time systems, we revisit the output regulation problem for linear systems. We generalize the problem formulation in order • to expand the class of reference or disturbance signals, • to utilize the derivative or feedforward information of reference signals whenever
Linear response theory for quantum open systems
Wei, J. H.; Yan, YiJing
2011-01-01
Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.
When to call a linear system nonnegative
Nieuwenhuis, J.W.
1998-01-01
In this paper we will consider discrete time invariant linear systems that allow for an input-state-output representation with a finite dimensional state space, and that have a finite number of inputs and outputs. The basic issue in this paper is when to call these systems nonnegative. An important
Tikhonov theorem for linear hyperbolic systems
Tang , Ying; Prieur , Christophe; Girard , Antoine
2015-01-01
International audience; A class of linear systems of conservation laws with a small perturbation parameter is introduced. By setting the perturbation parameter to zero, two subsystems, the reduced system standing for the slow dynamics and the boundary-layer system representing the fast dynamics, are computed. It is first proved that the exponential stability of the full system implies the stability of both subsystems. Secondly, a counter example is given to indicate that the converse is not t...
Non-asymptotic fractional order differentiators via an algebraic parametric method
Liu, Dayan
2012-08-01
Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie\\'s modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.
Non-asymptotic fractional order differentiators via an algebraic parametric method
Liu, Dayan; Gibaru, O.; Perruquetti, Wilfrid
2012-01-01
Recently, Mboup, Join and Fliess [27], [28] introduced non-asymptotic integer order differentiators by using an algebraic parametric estimation method [7], [8]. In this paper, in order to obtain non-asymptotic fractional order differentiators we apply this algebraic parametric method to truncated expansions of fractional Taylor series based on the Jumarie's modified Riemann-Liouville derivative [14]. Exact and simple formulae for these differentiators are given where a sliding integration window of a noisy signal involving Jacobi polynomials is used without complex mathematical deduction. The efficiency and the stability with respect to corrupting noises of the proposed fractional order differentiators are shown in numerical simulations. © 2012 IEEE.
Directory of Open Access Journals (Sweden)
Jian-feng Zhao
2017-01-01
Full Text Available This paper presents a three-dimensional autonomous chaotic system with high fraction dimension. It is noted that the nonlinear characteristic of the improper fractional-order chaos is interesting. Based on the continuous chaos and the discrete wavelet function map, an image encryption algorithm is put forward. The key space is formed by the initial state variables, parameters, and orders of the system. Every pixel value is included in secret key, so as to improve antiattack capability of the algorithm. The obtained simulation results and extensive security analyses demonstrate the high level of security of the algorithm and show its robustness against various types of attacks.
Directory of Open Access Journals (Sweden)
Fukang Yin
2013-01-01
Full Text Available A numerical method is presented to obtain the approximate solutions of the fractional partial differential equations (FPDEs. The basic idea of this method is to achieve the approximate solutions in a generalized expansion form of two-dimensional fractional-order Legendre functions (2D-FLFs. The operational matrices of integration and derivative for 2D-FLFs are first derived. Then, by these matrices, a system of algebraic equations is obtained from FPDEs. Hence, by solving this system, the unknown 2D-FLFs coefficients can be computed. Three examples are discussed to demonstrate the validity and applicability of the proposed method.
ITMETH, Iterative Routines for Linear System
International Nuclear Information System (INIS)
Greenbaum, A.
1989-01-01
1 - Description of program or function: ITMETH is a collection of iterative routines for solving large, sparse linear systems. 2 - Method of solution: ITMETH solves general linear systems of the form AX=B using a variety of methods: Jacobi iteration; Gauss-Seidel iteration; incomplete LU decomposition or matrix splitting with iterative refinement; diagonal scaling, matrix splitting, or incomplete LU decomposition with the conjugate gradient method for the problem AA'Y=B, X=A'Y; bi-conjugate gradient method with diagonal scaling, matrix splitting, or incomplete LU decomposition; and ortho-min method with diagonal scaling, matrix splitting, or incomplete LU decomposition. ITMETH also solves symmetric positive definite linear systems AX=B using the conjugate gradient method with diagonal scaling or matrix splitting, or the incomplete Cholesky conjugate gradient method
Conduction cooling systems for linear accelerator cavities
Kephart, Robert
2017-05-02
A conduction cooling system for linear accelerator cavities. The system conducts heat from the cavities to a refrigeration unit using at least one cavity cooler interconnected with a cooling connector. The cavity cooler and cooling connector are both made from solid material having a very high thermal conductivity of approximately 1.times.10.sup.4 W m.sup.-1 K.sup.-1 at temperatures of approximately 4 degrees K. This allows for very simple and effective conduction of waste heat from the linear accelerator cavities to the cavity cooler, along the cooling connector, and thence to the refrigeration unit.
Rf system specifications for a linear accelerator
International Nuclear Information System (INIS)
Young, A.; Eaton, L.E.
1992-01-01
A linear accelerator contains many systems; however, the most complex and costly is the RF system. The goal of an RF system is usually simply stated as maintaining the phase and amplitude of the RF signal within a given tolerance to accelerate the charged particle beam. An RF system that drives a linear accelerator needs a complete system specification, which should contain specifications for all the subsystems (i.e., high-power RF, low-level RF, RF generation/distribution, and automation control). This paper defines a format for the specifications of these subsystems and discusses each RF subsystem independently to provide a comprehensive understanding of the function of each subsystem. This paper concludes with an example of a specification spreadsheet allowing one to input the specifications of a subsystem. Thus, some fundamental parameters (i.e., the cost and size) of the RF system can be determined
Chaos as an intermittently forced linear system.
Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan
2017-05-30
Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.
International Nuclear Information System (INIS)
Dai, Hao; Si, Gangquan; Jia, Lixin; Zhang, Yanbin
2013-01-01
This paper investigates generalized function matrix projective lag synchronization between fractional-order and integer-order complex networks with delayed coupling, non-identical topological structures and different dimensions. Based on Lyapunov stability theory, generalized function matrix projective lag synchronization criteria are derived by using the adaptive control method. In addition, the three-dimensional fractional-order chaotic system and the four-dimensional integer-order hyperchaotic system as the nodes of the drive and the response networks, respectively, are analyzed in detail, and numerical simulation results are presented to illustrate the effectiveness of the theoretical results. (paper)
Final focus systems for linear colliders
International Nuclear Information System (INIS)
Helm, R.; Irwin, J.
1992-08-01
Final focus systems for linear colliders present many exacting challenges in beam optics, component design, and beam quality. Efforts to resolve these problems as they relate to a new generation of linear colliders are under way at several laboratories around the world. We will outline criteria for final focus systems and discuss the current state of understanding and resolution of the outstanding problems. We will discuss tolerances on alignment, field quality and stability for optical elements, and the implications for beam parameters such as emittance, energy spread, bunch length, and stability in position and energy. Beam-based correction procedures, which in principle can alleviate many of the tolerances, will be described. Preliminary results from the Final Focus Test Beam (FFTB) under construction at SLAC will be given. Finally, we mention conclusions from operating experience at the Stanford Linear Collider (SLC)
Final focus systems for linear colliders
International Nuclear Information System (INIS)
Helm, R.; Irwing, J.
1992-01-01
Final focus systems for linear colliders present many exacting challenges in beam optics, component design, and beam quality. Efforts to resolve these problems as they relate to a new generation of linear colliders are under way at several laboratories around the world. We outline criteria for final focus systems and discuss the current state of understanding and resolution of the outstanding problems. We discuss tolerances on alignment, field quality and stability for optical elements, and the implications for beam parameters such as emittance, energy spread , bunch length, and stability in position and energy. Beam-based correction procedures, which in principle can alleviate many of the tolerances, are described. Preliminary results from the Final Focus Test Beam (FFTB) under construction at SLAC are given. Finally, we mention conclusions from operating experience at the Stanford Linear Collider (SLC). (Author) 16 refs., 4 tabs., 6 figs
Dual-range linearized transimpedance amplifier system
Wessendorf, Kurt O.
2010-11-02
A transimpedance amplifier system is disclosed which simultaneously generates a low-gain output signal and a high-gain output signal from an input current signal using a single transimpedance amplifier having two different feedback loops with different amplification factors to generate two different output voltage signals. One of the feedback loops includes a resistor, and the other feedback loop includes another resistor in series with one or more diodes. The transimpedance amplifier system includes a signal linearizer to linearize one or both of the low- and high-gain output signals by scaling and adding the two output voltage signals from the transimpedance amplifier. The signal linearizer can be formed either as an analog device using one or two summing amplifiers, or alternately can be formed as a digital device using two analog-to-digital converters and a digital signal processor (e.g. a microprocessor or a computer).
Directory of Open Access Journals (Sweden)
Jianxin Han
2017-01-01
Full Text Available This paper focuses on chaos suppression strategy of a microresonator actuated by two symmetrical electrodes. Dynamic behavior of this system under the case where the origin is the only stable equilibrium is investigated first. Numerical simulations reveal that system may exhibit chaotic motion under certain excitation conditions. Then, bifurcation diagrams versus amplitude or frequency of AC excitation are drawn to grasp system dynamics nearby its natural frequency. Results show that the vibration is complex and may exhibit period-doubling bifurcation, chaotic motion, or dynamic pull-in instability. For the suppression of chaos, a novel control algorithm, based on an integer-order nonsingular fast terminal sliding mode and a fractional-order switching law, is proposed. Fractional Lyapunov Stability Theorem is used to guarantee the asymptotic stability of the system. Finally, numerical results with both fractional-order and integer-order control laws show that our proposed control law is effective in controlling chaos with system uncertainties and external disturbances.
Consys Linear Control System Design Software Package
International Nuclear Information System (INIS)
Diamantidis, Z.
1987-01-01
This package is created in order to help engineers, researchers, students and all who work on linear control systems. The software includes all time and frequency domain analysises, spectral analysises and networks, active filters and regulators design aids. The programmes are written on Hewlett Packard computer in Basic 4.0
Disturbance Decoupling of Switched Linear Systems
Yurtseven, E.; Heemels, W.P.M.H.; Camlibel, M.K.
2010-01-01
In this paper we consider disturbance decoupling problems for switched linear systems. We will provide necessary and sufficient conditions for three different versions of disturbance decoupling, which differ based on which signals are considered to be the disturbance. In the first version the
Uzawa method for fuzzy linear system
Ke Wang
2013-01-01
An Uzawa method is presented for solving fuzzy linear systems whose coefficient matrix is crisp and the right-hand side column is arbitrary fuzzy number vector. The explicit iterative scheme is given. The convergence is analyzed with convergence theorems and the optimal parameter is obtained. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.
Magin, Richard L.; Li, Weiguo; Velasco, M. Pilar; Trujillo, Juan; Reiter, David A.; Morgenstern, Ashley; Spencer, Richard G.
2011-01-01
We present a fractional-order extension of the Bloch equations to describe anomalous NMR relaxation phenomena (T1 and T2). The model has solutions in the form of Mittag-Leffler and stretched exponential functions that generalize conventional exponential relaxation. Such functions have been shown by others to be useful for describing dielectric and viscoelastic relaxation in complex, heterogeneous materials. Here, we apply these fractional-order T1 and T2 relaxation models to experiments performed at 9.4 and 11.7 Tesla on type I collagen gels, chondroitin sulfate mixtures, and to bovine nasal cartilage (BNC), a largely isotropic and homogeneous form of cartilage. The results show that the fractional-order analysis captures important features of NMR relaxation that are typically described by multi-exponential decay models. We find that the T2 relaxation of BNC can be described in a unique way by a single fractional-order parameter (α), in contrast to the lack of uniqueness of multi-exponential fits in the realistic setting of a finite signal-to-noise ratio. No anomalous behavior of T1 was observed in BNC. In the single-component gels, for T2 measurements, increasing the concentration of the largest components of cartilage matrix, collagen and chondroitin sulfate, results in a decrease in α, reflecting a more restricted aqueous environment. The quality of the curve fits obtained using Mittag-Leffler and stretched exponential functions are in some cases superior to those obtained using mono- and bi-exponential models. In both gels and BNC, α appears to account for microstructural complexity in the setting of an altered distribution of relaxation times. This work suggests the utility of fractional-order models to describe T2 NMR relaxation processes in biological tissues. PMID:21498095
Collimation systems in the next linear collider
International Nuclear Information System (INIS)
Merminga, N.; Irwin, J.; Helm, R.; Ruth, R.D.
1991-02-01
Experience indicates that beam collimation will be an essential element of the next generation e + E - linear colliders. A proposal for using nonlinear lenses to drive beam tails to large amplitudes was presented in a previous paper. Here we study the optimization of such systems including effects of wakefields and optical aberrations. Protection and design of the scrapers in these systems are discussed. 9 refs., 7 figs
Standard diffusive systems are well-posed linear systems
Matignon, Denis; Zwart, Heiko J.
2004-01-01
The class of well-posed linear systems as introduced by Salamon has become a well-understood class of systems, see e.g. the work of Weiss and the book of Staffans. Many partial partial differential equations with boundary control and point observation can be formulated as a well-posed linear system.
Parameter identifiability of linear dynamical systems
Glover, K.; Willems, J. C.
1974-01-01
It is assumed that the system matrices of a stationary linear dynamical system were parametrized by a set of unknown parameters. The question considered here is, when can such a set of unknown parameters be identified from the observed data? Conditions for the local identifiability of a parametrization are derived in three situations: (1) when input/output observations are made, (2) when there exists an unknown feedback matrix in the system and (3) when the system is assumed to be driven by white noise and only output observations are made. Also a sufficient condition for global identifiability is derived.
Stability problems for linear hyperbolic systems
International Nuclear Information System (INIS)
Eckhoff, K.S.
1975-05-01
The stability properties for the trivial solution of a general linear hyperbolic system of partial differential equations of the first order are studied. It is shown that results may be obtained by studying the stability properties of certain systems of ordinary differential equations which can be constructed from the hyperbolic system (the so-called transport equations). In some cases the associated stability problem for the transport equations can in fact be shown to be equivalent to the stability problem for the hyperbolic system, but in general the transport equations will only give the necessary conditions for stability. (Auth.)
Identification of general linear mechanical systems
Sirlin, S. W.; Longman, R. W.; Juang, J. N.
1983-01-01
Previous work in identification theory has been concerned with the general first order time derivative form. Linear mechanical systems, a large and important class, naturally have a second order form. This paper utilizes this additional structural information for the purpose of identification. A realization is obtained from input-output data, and then knowledge of the system input, output, and inertia matrices is used to determine a set of linear equations whereby we identify the remaining unknown system matrices. Necessary and sufficient conditions on the number, type and placement of sensors and actuators are given which guarantee identificability, and less stringent conditions are given which guarantee generic identifiability. Both a priori identifiability and a posteriori identifiability are considered, i.e., identifiability being insured prior to obtaining data, and identifiability being assured with a given data set.
Linear systems optimal and robust control
Sinha, Alok
2007-01-01
Introduction Overview Contents of the Book State Space Description of a Linear System Transfer Function of a Single Input/Single Output (SISO) System State Space Realizations of a SISO System SISO Transfer Function from a State Space Realization Solution of State Space Equations Observability and Controllability of a SISO System Some Important Similarity Transformations Simultaneous Controllability and Observability Multiinput/Multioutput (MIMO) Systems State Space Realizations of a Transfer Function Matrix Controllability and Observability of a MIMO System Matrix-Fraction Description (MFD) MFD of a Transfer Function Matrix for the Minimal Order of a State Space Realization Controller Form Realization from a Right MFD Poles and Zeros of a MIMO Transfer Function Matrix Stability Analysis State Feedback Control and Optimization State Variable Feedback for a Single Input System Computation of State Feedback Gain Matrix for a Multiinput System State Feedback Gain Matrix for a Multi...
Xu, Chang-Jin; Li, Pei-Luan; Pang, Yi-Cheng
2017-02-01
This paper is concerned with fractional-order bidirectional associative memory (BAM) neural networks with time delays. Applying Laplace transform, the generalized Gronwall inequality and estimates of Mittag-Leffler functions, some sufficient conditions which ensure the finite-time stability of fractional-order bidirectional associative memory neural networks with time delays are obtained. Two examples with their simulations are given to illustrate the theoretical findings. Our results are new and complement previously known results. Supported by National Natural Science Foundation of China under Grant Nos.~61673008, 11261010, 11101126, Project of High-Level Innovative Talents of Guizhou Province ([2016]5651), Natural Science and Technology Foundation of Guizhou Province (J[2015]2025 and J[2015]2026), 125 Special Major Science and Technology of Department of Education of Guizhou Province ([2012]011) and Natural Science Foundation of the Education Department of Guizhou Province (KY[2015]482)
Nonlinear Dynamics and Chaos in Fractional-Order Hopfield Neural Networks with Delay
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Xia Huang
2013-01-01
Full Text Available A fractional-order two-neuron Hopfield neural network with delay is proposed based on the classic well-known Hopfield neural networks, and further, the complex dynamical behaviors of such a network are investigated. A great variety of interesting dynamical phenomena, including single-periodic, multiple-periodic, and chaotic motions, are found to exist. The existence of chaotic attractors is verified by the bifurcation diagram and phase portraits as well.
Directory of Open Access Journals (Sweden)
Veyis Turut
2013-01-01
Full Text Available Two tecHniques were implemented, the Adomian decomposition method (ADM and multivariate Padé approximation (MPA, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo sense. First, the fractional differential equation has been solved and converted to power series by Adomian decomposition method (ADM, then power series solution of fractional differential equation was put into multivariate Padé series. Finally, numerical results were compared and presented in tables and figures.
International Nuclear Information System (INIS)
Li Xicheng; Xu Mingyu; Wang Shaowei
2008-01-01
In this paper, we give similarity solutions of partial differential equations of fractional order with a moving boundary condition. The solutions are given in terms of a generalized Wright function. The time-fractional Caputo derivative and two types of space-fractional derivatives are considered. The scale-invariant variable and the form of the solution of the moving boundary are obtained by the Lie group analysis. A comparison between the solutions corresponding to two types of fractional derivative is also given
Couceiro, Micael
2015-01-01
This book examines the bottom-up applicability of swarm intelligence to solving multiple problems, such as curve fitting, image segmentation, and swarm robotics. It compares the capabilities of some of the better-known bio-inspired optimization approaches, especially Particle Swarm Optimization (PSO), Darwinian Particle Swarm Optimization (DPSO) and the recently proposed Fractional Order Darwinian Particle Swarm Optimization (FODPSO), and comprehensively discusses their advantages and disadvantages. Further, it demonstrates the superiority and key advantages of using the FODPSO algorithm, suc
2018-03-14
UNIVERSITY OF TECHNOLOGY Final Report 03/14/2018 DISTRIBUTION A: Distribution approved for public release. AF Office Of Scientific Research (AFOSR...optimal control problems involving fractional-order differential equations Wang, Song Curtin University of Technology Kent Street, Bentley WA6102...Article history : Received 3 October 2016 Accepted 26 March 2017 Available online 29 April 2017 Keywords: Hamilton–Jacobi–Bellman equation Financial
Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate
Directory of Open Access Journals (Sweden)
Adnane Boukhouima
2017-01-01
Full Text Available We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV infection. In the model, the infection transmission process is modeled by a specific functional response. First, we show that the model is mathematically and biologically well posed. Second, the local and global stabilities of the equilibria are investigated. Finally, some numerical simulations are presented in order to illustrate our theoretical results.
Lectures on algebraic system theory: Linear systems over rings
Kamen, E. W.
1978-01-01
The presentation centers on four classes of systems that can be treated as linear systems over a ring. These are: (1) discrete-time systems over a ring of scalars such as the integers; (2) continuous-time systems containing time delays; (3) large-scale discrete-time systems; and (4) time-varying discrete-time systems.
Jumarie, Guy
2013-04-01
By using fractional differences, one recently proposed an alternative to the formulation of fractional differential calculus, of which the main characteristics is a new fractional Taylor series and its companion Rolle's formula which apply to non-differentiable functions. The key is that now we have at hand a differential increment of fractional order which can be manipulated exactly like in the standard Leibniz differential calculus. Briefly the fractional derivative is the quotient of fractional increments. It has been proposed that this calculus can be used to construct a differential geometry on manifold of fractional order. The present paper, on the one hand, refines the framework, and on the other hand, contributes some new results related to arc length of fractional curves, area on fractional differentiable manifold, covariant fractal derivative, Riemann-Christoffel tensor of fractional order, fractional differential equations of fractional geodesic, strip modeling of fractal space time and its relation with Lorentz transformation. The relation with Nottale's fractal space-time theory then appears in quite a natural way.
Fractional order creep model for dam concrete considering degree of hydration
Huang, Yaoying; Xiao, Lei; Bao, Tengfei; Liu, Yu
2018-05-01
Concrete is a material that is an intermediate between an ideal solid and an ideal fluid. The creep of concrete is related not only to the loading age and duration, but also to its temperature and temperature history. Fractional order calculus is a powerful tool for solving physical mechanics modeling problems. Using a software element based on the generalized Kelvin model, a fractional order creep model of concrete considering the loading age and duration is established. Then, the hydration rate of cement is considered in terms of the degree of hydration, and the fractional order creep model of concrete considering the degree of hydration is established. Moreover, uniaxial tensile creep tests of dam concrete under different curing temperatures were conducted, and the results were combined with the creep test data and complex optimization method to optimize the parameters of a new creep model. The results show that the fractional tensile creep model based on hydration degree can better describe the tensile creep properties of concrete, and this model involves fewer parameters than the 8-parameter model.
Adaptive Synchronization of Fractional Order Complex-Variable Dynamical Networks via Pinning Control
Ding, Da-Wei; Yan, Jie; Wang, Nian; Liang, Dong
2017-09-01
In this paper, the synchronization of fractional order complex-variable dynamical networks is studied using an adaptive pinning control strategy based on close center degree. Some effective criteria for global synchronization of fractional order complex-variable dynamical networks are derived based on the Lyapunov stability theory. From the theoretical analysis, one concludes that under appropriate conditions, the complex-variable dynamical networks can realize the global synchronization by using the proper adaptive pinning control method. Meanwhile, we succeed in solving the problem about how much coupling strength should be applied to ensure the synchronization of the fractional order complex networks. Therefore, compared with the existing results, the synchronization method in this paper is more general and convenient. This result extends the synchronization condition of the real-variable dynamical networks to the complex-valued field, which makes our research more practical. Finally, two simulation examples show that the derived theoretical results are valid and the proposed adaptive pinning method is effective. Supported by National Natural Science Foundation of China under Grant No. 61201227, National Natural Science Foundation of China Guangdong Joint Fund under Grant No. U1201255, the Natural Science Foundation of Anhui Province under Grant No. 1208085MF93, 211 Innovation Team of Anhui University under Grant Nos. KJTD007A and KJTD001B, and also supported by Chinese Scholarship Council
Directory of Open Access Journals (Sweden)
Duan Jun-Sheng
2017-12-01
Full Text Available We conduct a detailed study and comparison for the one-degree-of-freedom steady-state vibrations under harmonic driving with a single fractional-order derivative and a distributed-order derivative. For each of the two vibration systems, we consider the stiffness contribution factor and damping contribution factor of the term of fractional derivatives, the amplitude and the phase difference for the response. The effects of driving frequency on these response quantities are discussed. Also the influences of the order α of the fractional derivative and the parameter γ parameterizing the weight function in the distributed-order derivative are analyzed. Two cases display similar response behaviors, but the stiffness contribution factor and damping contribution factor of the distributed-order derivative are almost monotonic change with the parameter γ, not exactly like the case of single fractional-order derivative for the order α. The case of the distributed-order derivative provides us more options for the weight function and parameters.
An injection system for a linear accelerator
International Nuclear Information System (INIS)
Santos, A.C.R.
1978-03-01
An injection system for the Linear Accelerator is developed using the parameters of machines at the Centro Brasileiro de Pesquisas Fisicas and the Instituto Militar de Engenharia. The proposed system consists basically of a prebuncher and a chopper. The pre-buncher is used to improve the energy resolution and also to increase the accelerator target current. The chopper is used to remove from the beam the electrons that have no possibility of attaining the desired energy and that are usually lost in the walls and the cavity tube, thus producing undesirable background. Theoretical development of the chopper is performed in order to obtain its dimensions for future construction. The complete design the pre-buncher and its feed supply system and the experimental verication of its performance are also presented. It is intended to give the necessary information for the design and construction of the complete injection system proposed. (Author) [pt
Operator approach to linear control systems
Cheremensky, A
1996-01-01
Within the framework of the optimization problem for linear control systems with quadratic performance index (LQP), the operator approach allows the construction of a systems theory including a number of particular infinite-dimensional optimization problems with hardly visible concreteness. This approach yields interesting interpretations of these problems and more effective feedback design methods. This book is unique in its emphasis on developing methods for solving a sufficiently general LQP. Although this is complex material, the theory developed here is built on transparent and relatively simple principles, and readers with less experience in the field of operator theory will find enough material to give them a good overview of the current state of LQP theory and its applications. Audience: Graduate students and researchers in the fields of mathematical systems theory, operator theory, cybernetics, and control systems.
Song, Xiao-Na; Song, Shuai; Tejado Balsera, Inés; Liu, Lei-Po
2017-10-01
This paper investigates the mixed H ∞ and passive projective synchronization problem for fractional-order (FO) memristor-based neural networks. Our aim is to design a controller such that, though the unavoidable phenomena of time-delay and parameter uncertainty are fully considered, the resulting closed-loop system is asymptotically stable with a mixed H ∞ and passive performance level. By combining active and adaptive control methods, a novel hybrid control strategy is designed, which can guarantee the robust stability of the closed-loop system and also ensure a mixed H ∞ and passive performance level. Via the application of FO Lyapunov stability theory, the projective synchronization conditions are addressed in terms of linear matrix inequality techniques. Finally, two simulation examples are given to illustrate the effectiveness of the proposed method. Supported by National Natural Science Foundation of China under Grant Nos. U1604146, U1404610, 61473115, 61203047, Science and Technology Research Project in Henan Province under Grant Nos. 152102210273, 162102410024, and Foundation for the University Technological Innovative Talents of Henan Province under Grant No. 18HASTIT019
Directory of Open Access Journals (Sweden)
Yu-xin Zhao
2014-01-01
Full Text Available This paper presents a novel wavelet kernel neural network (WKNN with wavelet kernel function. It is applicable in online learning with adaptive parameters and is applied on parameters tuning of fractional-order PID (FOPID controller, which could handle time delay problem of the complex control system. Combining the wavelet function and the kernel function, the wavelet kernel function is adopted and validated the availability for neural network. Compared to the conservative wavelet neural network, the most innovative character of the WKNN is its rapid convergence and high precision in parameters updating process. Furthermore, the integrated pressurized water reactor (IPWR system is established by RELAP5, and a novel control strategy combining WKNN and fuzzy logic rule is proposed for shortening controlling time and utilizing the experiential knowledge sufficiently. Finally, experiment results verify that the control strategy and controller proposed have the practicability and reliability in actual complicated system.
Iterative solution of large linear systems
Young, David Matheson
1971-01-01
This self-contained treatment offers a systematic development of the theory of iterative methods. Its focal point resides in an analysis of the convergence properties of the successive overrelaxation (SOR) method, as applied to a linear system with a consistently ordered matrix. The text explores the convergence properties of the SOR method and related techniques in terms of the spectral radii of the associated matrices as well as in terms of certain matrix norms. Contents include a review of matrix theory and general properties of iterative methods; SOR method and stationary modified SOR meth
a Continuous-Time Positive Linear System
Directory of Open Access Journals (Sweden)
Kyungsup Kim
2013-01-01
Full Text Available This paper discusses a computational method to construct positive realizations with sparse matrices for continuous-time positive linear systems with multiple complex poles. To construct a positive realization of a continuous-time system, we use a Markov sequence similar to the impulse response sequence that is used in the discrete-time case. The existence of the proposed positive realization can be analyzed with the concept of a polyhedral convex cone. We provide a constructive algorithm to compute positive realizations with sparse matrices of some positive systems under certain conditions. A sufficient condition for the existence of a positive realization, under which the proposed constructive algorithm works well, is analyzed.
International Nuclear Information System (INIS)
Petrila, Iulian; Bodale, Ilie; Rotarescu, Cristian; Stancu, Alexandru
2011-01-01
A comparative analysis between linear and non-linear energy barriers used for modeling statistical thermally-excited ferromagnetic systems is presented. The linear energy barrier is obtained by new symmetry considerations about the anisotropy energy and the link with the non-linear energy barrier is also presented. For a relevant analysis we compare the effects of linear and non-linear energy barriers implemented in two different models: Preisach-Neel and Ising-Metropolis. The differences between energy barriers which are reflected in different coercive field dependence of the temperature are also presented. -- Highlights: → The linear energy barrier is obtained from symmetry considerations. → The linear and non-linear energy barriers are calibrated and implemented in Preisach-Neel and Ising-Metropolis models. → The temperature and time effects of the linear and non-linear energy barriers are analyzed.
New approach to solve symmetric fully fuzzy linear systems
Indian Academy of Sciences (India)
concepts of fuzzy set theory and then define a fully fuzzy linear system of equations. .... To represent the above problem as fully fuzzy linear system, we represent x .... Fully fuzzy linear systems can be solved by Linear programming approach, ...
SLAP, Large Sparse Linear System Solution Package
International Nuclear Information System (INIS)
Greenbaum, A.
1987-01-01
1 - Description of program or function: SLAP is a set of routines for solving large sparse systems of linear equations. One need not store the entire matrix - only the nonzero elements and their row and column numbers. Any nonzero structure is acceptable, so the linear system solver need not be modified when the structure of the matrix changes. Auxiliary storage space is acquired and released within the routines themselves by use of the LRLTRAN POINTER statement. 2 - Method of solution: SLAP contains one direct solver, a band matrix factorization and solution routine, BAND, and several interactive solvers. The iterative routines are as follows: JACOBI, Jacobi iteration; GS, Gauss-Seidel Iteration; ILUIR, incomplete LU decomposition with iterative refinement; DSCG and ICCG, diagonal scaling and incomplete Cholesky decomposition with conjugate gradient iteration (for symmetric positive definite matrices only); DSCGN and ILUGGN, diagonal scaling and incomplete LU decomposition with conjugate gradient interaction on the normal equations; DSBCG and ILUBCG, diagonal scaling and incomplete LU decomposition with bi-conjugate gradient iteration; and DSOMN and ILUOMN, diagonal scaling and incomplete LU decomposition with ORTHOMIN iteration
Freed, Alan; Diethelm, Kai; Luchko, Yury
2002-01-01
This is the first annual report to the U.S. Army Medical Research and Material Command for the three year project "Advanced Soft Tissue Modeling for Telemedicine and Surgical Simulation" supported by grant No. DAMD17-01-1-0673 to The Cleveland Clinic Foundation, to which the NASA Glenn Research Center is a subcontractor through Space Act Agreement SAA 3-445. The objective of this report is to extend popular one-dimensional (1D) fractional-order viscoelastic (FOV) materials models into their three-dimensional (3D) equivalents for finitely deforming continua, and to provide numerical algorithms for their solution.
Experimental verification of on-chip CMOS fractional-order capacitor emulators
Tsirimokou, G.; Psychalinos, C.; Salama, Khaled N.; Elwakil, A.S.
2016-01-01
The experimental results from a fabricated integrated circuit of fractional-order capacitor emulators are reported. The chip contains emulators of capacitors of orders 0.3, 0.4, 0.5, 0.6 and 0.7 with nano-Farad pseudo-capacitances that can be adjusted through a bias current. Two off-chip capacitors are used to set the bandwidth of each emulator independently. The chip was designed in Austria microsystems (AMS) 0.35μ CMOS. © 2016 The Institution of Engineering and Technology.
Dynamic stability analysis of fractional order leaky integrator echo state neural networks
Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Tenreiro Machado, J. A.
2017-06-01
The Leaky integrator echo state neural network (Leaky-ESN) is an improved model of the recurrent neural network (RNN) and adopts an interconnected recurrent grid of processing neurons. This paper presents a new proof for the convergence of a Lyapunov candidate function to zero when time tends to infinity by means of the Caputo fractional derivative with order lying in the range (0, 1). The stability of Fractional-Order Leaky-ESN (FO Leaky-ESN) is then analyzed, and the existence, uniqueness and stability of the equilibrium point are provided. A numerical example demonstrates the feasibility of the proposed method.
Solving Abel’s Type Integral Equation with Mikusinski’s Operator of Fractional Order
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Ming Li
2013-01-01
Full Text Available This paper gives a novel explanation of the integral equation of Abel’s type from the point of view of Mikusinski’s operational calculus. The concept of the inverse of Mikusinski’s operator of fractional order is introduced for constructing a representation of the solution to the integral equation of Abel’s type. The proof of the existence of the inverse of the fractional Mikusinski operator is presented, providing an alternative method of treating the integral equation of Abel’s type.
Experimental verification of on-chip CMOS fractional-order capacitor emulators
Tsirimokou, G.
2016-06-13
The experimental results from a fabricated integrated circuit of fractional-order capacitor emulators are reported. The chip contains emulators of capacitors of orders 0.3, 0.4, 0.5, 0.6 and 0.7 with nano-Farad pseudo-capacitances that can be adjusted through a bias current. Two off-chip capacitors are used to set the bandwidth of each emulator independently. The chip was designed in Austria microsystems (AMS) 0.35μ CMOS. © 2016 The Institution of Engineering and Technology.
ROBUST MPC FOR STABLE LINEAR SYSTEMS
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M.A. Rodrigues
2002-03-01
Full Text Available In this paper, a new model predictive controller (MPC, which is robust for a class of model uncertainties, is developed. Systems with stable dynamics and time-invariant model uncertainty are treated. The development herein proposed is focused on real industrial systems where the controller is part of an on-line optimization scheme and works in the output-tracking mode. In addition, the system has a time-varying number of degrees of freedom since some of the manipulated inputs may become constrained. Moreover, the number of controlled outputs may also vary during system operation. Consequently, the actual system may show operating conditions with a number of controlled outputs larger than the number of available manipulated inputs. The proposed controller uses a state-space model, which is aimed at the representation of the output-predicted trajectory. Based on this model, a cost function is proposed whereby the output error is integrated along an infinite prediction horizon. It is considered the case of multiple operating points, where the controller stabilizes a set of models corresponding to different operating conditions for the system. It is shown that closed-loop stability is guaranteed by the feasibility of a linear matrix optimization problem.
Optimal Control of Switching Linear Systems
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Ali Benmerzouga
2004-06-01
Full Text Available A solution to the control of switching linear systems with input constraints was given in Benmerzouga (1997 for both the conventional enumeration approach and the new approach. The solution given there turned out to be not unique. The main objective in this work is to determine the optimal control sequences {Ui(k , i = 1,..., M ; k = 0, 1, ..., N -1} which transfer the system from a given initial state X0 to a specific target state XT (or to be as close as possible by using the same discrete time solution obtained in Benmerzouga (1997 and minimizing a running cost-to-go function. By using the dynamic programming technique, the optimal solution is found for both approaches given in Benmerzouga (1997. The computational complexity of the modified algorithm is also given.
Well logging system with linearity control
International Nuclear Information System (INIS)
Jones, J.M.
1973-01-01
Apparatus is described for controlling the gain of a nuclear well logging system comprising: (1) means for measuring the energy spectrum of gamma rays produced by earth formation materials surrounding a well borehole; (2) means for measuring the number of counts of a gamma rays having an energy falling within each of at least two predetermined energy band portions of the gamma ray energy spectrum; (3) means for generating a signal proportional to the ratio of the gamma ray counts and for comparing the ratio signal with at least one constant ratio calibration signal; (4) means for generating an error signal representative of the difference of the ratio signal and the constant ratio calibration signal; and (5) means for using the error signal to control the linearity of the well logging system. (author)
Yang, Yongge; Xu, Wei; Yang, Guidong; Jia, Wantao
2016-08-01
The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.
International Nuclear Information System (INIS)
Yang, Yongge; Xu, Wei; Yang, Guidong; Jia, Wantao
2016-01-01
The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.
Energy Technology Data Exchange (ETDEWEB)
Yang, Yongge; Xu, Wei, E-mail: weixu@nwpu.edu.cn; Yang, Guidong; Jia, Wantao [Department of Applied Mathematics, Northwestern Polytechnical University, Xi' an 710072 (China)
2016-08-15
The Poisson white noise, as a typical non-Gaussian excitation, has attracted much attention recently. However, little work was referred to the study of stochastic systems with fractional derivative under Poisson white noise excitation. This paper investigates the stationary response of a class of quasi-linear systems with fractional derivative excited by Poisson white noise. The equivalent stochastic system of the original stochastic system is obtained. Then, approximate stationary solutions are obtained with the help of the perturbation method. Finally, two typical examples are discussed in detail to demonstrate the effectiveness of the proposed method. The analysis also shows that the fractional order and the fractional coefficient significantly affect the responses of the stochastic systems with fractional derivative.
Linear concentration system; Sistema de concentracion lineal
Energy Technology Data Exchange (ETDEWEB)
Gonzalez Lugo, J.I; Leon Rovira, N; Aguayo Tellez, H [Instituto Tecnologico y de Estudios Superiores de Monterrey, Monterrey, Nuevo Leon (Mexico)]. E-mails: a00812662@itesm.mx; noel.leon@itesm.mx; haguayo@itesm.mx
2013-03-15
Solar linear concentration technologies to generate high temperatures are limited to the ranges of 200 to 500 degrees Celsius. While its performance has been tested through prototypes and pilot plants around the world, there are still areas of opportunity that can be exploited to obtain a linear concentration that achieves temperatures above this range in order to have a better use of the available solar energy. Because of this: It is possible to develop a linear concentration system that can track the sun with minimal movement of the absorber-receiver while maintaining temperatures above 850 degrees Celsius sufficient for industrial processes that require that temperature. The methodology consists of a series of stages (conceptual design, simulation, evaluation, development concept, results and validation) through which concepts are generated that allow design and evaluation of solar concentrator configurations with the help of simulation software. We have designed a linear parabolic concentrating system which comprises a set of mirrors segments with different focal lengths that works within the range of 600 degrees Celsius; however, it is advancing in the development of a double concentration to reach 850 degrees Celsius. [Spanish] Las tecnologias de concentracion lineal solar para generar altas temperaturas se ven limitadas a los rangos de 200 a 500 grados centigrados. Si bien su funcionamiento ha sido probado a traves de prototipos y plantas piloto alrededor del mundo, aun existen areas de oportunidad que pueden ser aprovechadas para obtener un sistema de concentracion lineal que permita alcanzar temperaturas mayores a este rango para asi tener un mejor aprovechamiento de la energia solar disponible. Debido a esto: Es posible desarrollar un sistema de concentracion lineal capaz de seguir la trayectoria del Sol con minimo movimiento del absorbedor-recibidor al mismo tiempo que mantiene temperaturas superiores a los 850 grados centigrados suficientes para
Linear Actuator System for the NASA Docking System
Dick, Brandon N.; Oesch, Christopher; Rupp, Timothy W.
2017-01-01
The Linear Actuator System (LAS) is a major sub-system within the NASA Docking System (NDS). The NDS Block 1 will be used on the Boeing Crew Space Transportation (CST-100) system to achieve docking with the International Space Station. Critical functions in the Soft Capture aspect of docking are performed by the LAS. This paper describes the general function of the LAS, the system's key requirements and technical challenges, and the development and qualification approach for the system.
Relative null controllability of linear systems with multiple delays in ...
African Journals Online (AJOL)
varying multiple delays in state and control are developed. If the uncontrolled system is uniformly asymptotically stable, and if the linear system is controllable, then the linear system is null controllable. Journal of the Nigerian Association of ...
Directory of Open Access Journals (Sweden)
Rahmatullah
2018-03-01
Full Text Available We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses. Keywords: Exp-function method, New exact traveling wave solutions, Modified Riemann-Liouville derivative, Fractional complex transformation, Fractional order Boussinesq-like equations, Symbolic computation
Linear optical response of finite systems using multishift linear system solvers
Energy Technology Data Exchange (ETDEWEB)
Hübener, Hannes; Giustino, Feliciano [Department of Materials, University of Oxford, Oxford OX1 3PH (United Kingdom)
2014-07-28
We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.
Control system analysis for the perturbed linear accelerator rf system
Sung Il Kwon
2002-01-01
This paper addresses the modeling problem of the linear accelerator RF system in SNS. Klystrons are modeled as linear parameter varying systems. The effect of the high voltage power supply ripple on the klystron output voltage and the output phase is modeled as an additive disturbance. The cavity is modeled as a linear system and the beam current is modeled as the exogenous disturbance. The output uncertainty of the low level RF system which results from the uncertainties in the RF components and cabling is modeled as multiplicative uncertainty. Also, the feedback loop uncertainty and digital signal processing signal conditioning subsystem uncertainties are lumped together and are modeled as multiplicative uncertainty. Finally, the time delays in the loop are modeled as a lumped time delay. For the perturbed open loop system, the closed loop system performance, and stability are analyzed with the PI feedback controller.
CONTROL SYSTEM ANALYSIS FOR THE PERTURBED LINEAR ACCELERATOR RF SYSTEM
International Nuclear Information System (INIS)
SUNG-IL KWON; AMY H. REGAN
2002-01-01
This paper addresses the modeling problem of the linear accelerator RF system in SNS. Klystrons are modeled as linear parameter varying systems. The effect of the high voltage power supply ripple on the klystron output voltage and the output phase is modeled as an additive disturbance. The cavity is modeled as a linear system and the beam current is modeled as the exogenous disturbance. The output uncertainty of the low level RF system which results from the uncertainties in the RF components and cabling is modeled as multiplicative uncertainty. Also, the feedback loop uncertainty and digital signal processing signal conditioning subsystem uncertainties are lumped together and are modeled as multiplicative uncertainty. Finally, the time delays in the loop are modeled as a lumped time delay. For the perturbed open loop system, the closed loop system performance, and stability are analyzed with the PI feedback controller
Zhang, BiTao; Pi, YouGuo; Luo, Ying
2012-09-01
A fractional order sliding mode control (FROSMC) scheme based on parameters auto-tuning for the velocity control of permanent magnet synchronous motor (PMSM) is proposed in this paper. The control law of the proposed F(R)OSMC scheme is designed according to Lyapunov stability theorem. Based on the property of transferring energy with adjustable type in F(R)OSMC, this paper analyzes the chattering phenomenon in classic sliding mode control (SMC) is attenuated with F(R)OSMC system. A fuzzy logic inference scheme (FLIS) is utilized to obtain the gain of switching control. Simulations and experiments demonstrate that the proposed FROSMC not only achieve better control performance with smaller chatting than that with integer order sliding mode control, but also is robust to external load disturbance and parameter variations. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.
Linear-array systems for aerospace NDE
International Nuclear Information System (INIS)
Smith, Robert A.; Willsher, Stephen J.; Bending, Jamie M.
1999-01-01
Rapid large-area inspection of composite structures for impact damage and multi-layered aluminum skins for corrosion has been a recognized priority for several years in both military and civil aerospace applications. Approaches to this requirement have followed two clearly different routes: the development of novel large-area inspection systems, and the enhancement of current ultrasonic or eddy-current methods to reduce inspection times. Ultrasonic inspection is possible with standard flaw detection equipment but the addition of a linear ultrasonic array could reduce inspection times considerably. In order to investigate their potential, 9-element and 17-element linear ultrasonic arrays for composites, and 64-element arrays for aluminum skins, have been developed to DERA specifications for use with the ANDSCAN area scanning system. A 5 m 2 composite wing surface has been scanned with a scan resolution of approximately 3 mm in 6 hours. With subsequent software and hardware improvements all four composite wing surfaces (top/bottom, left/right) of a military fighter aircraft can potentially be inspected in less than a day. Array technology has been very widely used in the medical ultrasound field although rarely above 10 MHz, whereas lap-joint inspection requires a pulse center-frequency of 12 to 20 MHz in order to resolve the separate interfaces in the lap joint. A 128 mm-long multi-element array of 5 mmx2 mm ultrasonic elements for use with the ANDSCAN scanning software was produced to a DERA specification by an NDT manufacturer with experience in the medical imaging field. This paper analyses the performance of the transducers that have been produced and evaluates their use in scanning systems of different configurations
Model Predictive Control for Linear Complementarity and Extended Linear Complementarity Systems
Directory of Open Access Journals (Sweden)
Bambang Riyanto
2005-11-01
Full Text Available In this paper, we propose model predictive control method for linear complementarity and extended linear complementarity systems by formulating optimization along prediction horizon as mixed integer quadratic program. Such systems contain interaction between continuous dynamics and discrete event systems, and therefore, can be categorized as hybrid systems. As linear complementarity and extended linear complementarity systems finds applications in different research areas, such as impact mechanical systems, traffic control and process control, this work will contribute to the development of control design method for those areas as well, as shown by three given examples.
Non-probabilistic solutions of imprecisely defined fractional-order diffusion equations
International Nuclear Information System (INIS)
Chakraverty, S.; Tapaswini, Smita
2014-01-01
The fractional diffusion equation is one of the most important partial differential equations (PDEs) to model problems in mathematical physics. These PDEs are more practical when those are combined with uncertainties. Accordingly, this paper investigates the numerical solution of a non-probabilistic viz. fuzzy fractional-order diffusion equation subjected to various external forces. A fuzzy diffusion equation having fractional order 0 < α ≤ 1 with fuzzy initial condition is taken into consideration. Fuzziness appearing in the initial conditions is modelled through convex normalized triangular and Gaussian fuzzy numbers. A new computational technique is proposed based on double parametric form of fuzzy numbers to handle the fuzzy fractional diffusion equation. Using the single parametric form of fuzzy numbers, the original fuzzy diffusion equation is converted first into an interval-based fuzzy differential equation. Next, this equation is transformed into crisp form by using the proposed double parametric form of fuzzy numbers. Finally, the same is solved by Adomian decomposition method (ADM) symbolically to obtain the uncertain bounds of the solution. Computed results are depicted in terms of plots. Results obtained by the proposed method are compared with the existing results in special cases. (general)
Thermodynamics of (1-alkanol + linear monoether) systems
International Nuclear Information System (INIS)
Gonzalez, Juan Antonio; Mozo, Ismael; Garcia de la Fuente, Isaias; Cobos, Jose Carlos; Riesco, Nicolas
2008-01-01
Densities, ρ, and speeds of sound, u, of systems formed by 1-heptanol, or 1-octanol, or 1-decanol and dibutylether have been measured at a temperature of (293.15, 298.15, and 303.15) K and atmospheric pressure using a vibrating tube densimeter and sound analyser Anton Paar model DSA-5000. The ρ and u values were used to calculate excess molar volumes, V E , and deviations from the ideal behaviour of the thermal expansion coefficient, Δα p and of the isentropic compressibilities, Δκ S . The available database on molar excess enthalpies, H E , and V E for (1-alkanol + linear monoether) systems was used to investigate interactional and structural effects in such mixtures. The enthalpy of the OH...O bonds is lower for methanol solutions, and for the remainder systems, it is practically independent of the mixture compounds. The V E variation with the chain length of the 1-alkanol points out the existence of structural effects for systems including longer 1-alkanols. The ERAS model is applied to the studied mixtures. ERAS represents quite accurately H E and V E data using parameters which consistently depend on the molecular structure
Identification problems in linear transformation system
International Nuclear Information System (INIS)
Delforge, Jacques.
1975-01-01
An attempt was made to solve the theoretical and numerical difficulties involved in the identification problem relative to the linear part of P. Delattre's theory of transformation systems. The theoretical difficulties are due to the very important problem of the uniqueness of the solution, which must be demonstrated in order to justify the value of the solution found. Simple criteria have been found when measurements are possible on all the equivalence classes, but the problem remains imperfectly solved when certain evolution curves are unknown. The numerical difficulties are of two kinds: a slow convergence of iterative methods and a strong repercussion of numerical and experimental errors on the solution. In the former case a fast convergence was obtained by transformation of the parametric space, while in the latter it was possible, from sensitivity functions, to estimate the errors, to define and measure the conditioning of the identification problem then to minimize this conditioning as a function of the experimental conditions [fr
System theory as applied differential geometry. [linear system
Hermann, R.
1979-01-01
The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.
Normal form of linear systems depending on parameters
International Nuclear Information System (INIS)
Nguyen Huynh Phan.
1995-12-01
In this paper we resolve completely the problem to find normal forms of linear systems depending on parameters for the feedback action that we have studied for the special case of controllable linear systems. (author). 24 refs
PWR control system design using advanced linear and non-linear methodologies
International Nuclear Information System (INIS)
Rabindran, N.; Whitmarsh-Everiss, M.J.
2004-01-01
Consideration is here given to the methodology deployed for non-linear heuristic analysis in the time domain supported by multi-variable linear control system design methods for the purposes of operational dynamics and control system analysis. This methodology is illustrated by the application of structural singular value μ analysis to Pressurised Water Reactor control system design. (author)
Wu, Ailong; Zeng, Zhigang
2016-02-01
We show that the ω-periodic fractional-order fuzzy neural networks cannot generate non-constant ω-periodic signals. In addition, several sufficient conditions are obtained to ascertain the boundedness and global Mittag-Leffler stability of fractional-order fuzzy neural networks. Furthermore, S-asymptotical ω-periodicity and global asymptotical ω-periodicity of fractional-order fuzzy neural networks is also characterized. The obtained criteria improve and extend the existing related results. To illustrate and compare the theoretical criteria, some numerical examples with simulation results are discussed in detail. Crown Copyright © 2015. Published by Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Patino, A; Durand, P-E; Fogret, E; Pellat-Finet, P
2011-01-01
According to a scalar theory of diffraction, light propagation can be expressed by two-dimensional fractional order Fourier transforms. Since the fractional Fourier transform of a chirp function is a Dirac distribution, focusing a light beam is optically achieved by using a diffractive screen whose transmission function is a two-dimensional chirp function. This property is applied to designing Fresnel microlenses, and the orders of the involved Fourier fractional transforms depend on diffraction distances as well as on emitter and receiver radii of curvature. If the emitter is astigmatic (with two principal radii of curvature), the diffraction phenomenon involves two one-dimensional fractional Fourier transforms whose orders are different. This degree of freedom allows us to design microlenses that can focus astigmatic Gaussian beams, as produced by a line-shaped laser diode source.
Directory of Open Access Journals (Sweden)
Qiguang Zhu
2014-05-01
Full Text Available To resolve the difficulty in establishing accurate priori noise model for the extended Kalman filtering algorithm, propose the fractional-order Darwinian particle swarm optimization (PSO algorithm has been proposed and introduced into the fuzzy adaptive extended Kalman filtering algorithm. The natural selection method has been adopted to improve the standard particle swarm optimization algorithm, which enhanced the diversity of particles and avoided the premature. In addition, the fractional calculus has been used to improve the evolution speed of particles. The PSO algorithm after improved has been applied to train fuzzy adaptive extended Kalman filter and achieve the simultaneous localization and mapping. The simulation results have shown that compared with the geese particle swarm optimization training of fuzzy adaptive extended Kalman filter localization and mapping algorithm, has been greatly improved in terms of localization and mapping.
Directory of Open Access Journals (Sweden)
Omar Abu Arqub
2014-01-01
Full Text Available The purpose of this paper is to present a new kind of analytical method, the so-called residual power series, to predict and represent the multiplicity of solutions to nonlinear boundary value problems of fractional order. The present method is capable of calculating all branches of solutions simultaneously, even if these multiple solutions are very close and thus rather difficult to distinguish even by numerical techniques. To verify the computational efficiency of the designed proposed technique, two nonlinear models are performed, one of them arises in mixed convection flows and the other one arises in heat transfer, which both admit multiple solutions. The results reveal that the method is very effective, straightforward, and powerful for formulating these multiple solutions.
The Study of Fractional Order Controller with SLAM in the Humanoid Robot
Directory of Open Access Journals (Sweden)
Shuhuan Wen
2014-01-01
Full Text Available We present a fractional order PI controller (FOPI with SLAM method, and the proposed method is used in the simulation of navigation of NAO humanoid robot from Aldebaran. We can discretize the transfer function by the Al-Alaoui generating function and then get the FOPI controller by Power Series Expansion (PSE. FOPI can be used as a correction part to reduce the accumulated error of SLAM. In the FOPI controller, the parameters (Kp,Ki, and α need to be tuned to obtain the best performance. Finally, we compare the results of position without controller and with PI controller, FOPI controller. The simulations show that the FOPI controller can reduce the error between the real position and estimated position. The proposed method is efficient and reliable for NAO navigation.
Optimal Trajectory Tracking Control for a Wheeled Mobile Robot Using Fractional Order PID Controller
Directory of Open Access Journals (Sweden)
Ameer L. Saleh
2018-02-01
Full Text Available This paper present an optimal Fractional Order PID (FOPID controller based on Particle Swarm Optimization (PSO for controlling the trajectory tracking of Wheeled Mobile Robot(WMR.The issue of trajectory tracking with given a desired reference velocity is minimized to get the distance and deviation angle equal to zero, to realize the objective of trajectory tracking a two FOPID controllers are used for velocity control and azimuth control to implement the trajectory tracking control. A path planning and path tracking methodologies are used to give different desired tracking trajectories. PSO algorithm is using to find the optimal parameters of FOPID controllers. The kinematic and dynamic models of wheeled mobile robot for desired trajectory tracking with PSO algorithm are simulated in Simulink-Matlab. Simulation results show that the optimal FOPID controllers are more effective and has better dynamic performance than the conventional methods.
Directory of Open Access Journals (Sweden)
Hai Zhang
2017-01-01
Full Text Available This paper investigates the existence and globally asymptotic stability of equilibrium solution for Riemann-Liouville fractional-order hybrid BAM neural networks with distributed delays and impulses. The factors of such network systems including the distributed delays, impulsive effects, and two different fractional-order derivatives between the U-layer and V-layer are taken into account synchronously. Based on the contraction mapping principle, the sufficient conditions are derived to ensure the existence and uniqueness of the equilibrium solution for such network systems. By constructing a novel Lyapunov functional composed of fractional integral and definite integral terms, the globally asymptotic stability criteria of the equilibrium solution are obtained, which are dependent on the order of fractional derivative and network parameters. The advantage of our constructed method is that one may directly calculate integer-order derivative of the Lyapunov functional. A numerical example is also presented to show the validity and feasibility of the theoretical results.
Peng, Xiao; Wu, Huaiqin; Song, Ka; Shi, Jiaxin
2017-10-01
This paper is concerned with the global Mittag-Leffler synchronization and the synchronization in finite time for fractional-order neural networks (FNNs) with discontinuous activations and time delays. Firstly, the properties with respect to Mittag-Leffler convergence and convergence in finite time, which play a critical role in the investigation of the global synchronization of FNNs, are developed, respectively. Secondly, the novel state-feedback controller, which includes time delays and discontinuous factors, is designed to realize the synchronization goal. By applying the fractional differential inclusion theory, inequality analysis technique and the proposed convergence properties, the sufficient conditions to achieve the global Mittag-Leffler synchronization and the synchronization in finite time are addressed in terms of linear matrix inequalities (LMIs). In addition, the upper bound of the setting time of the global synchronization in finite time is explicitly evaluated. Finally, two examples are given to demonstrate the validity of the proposed design method and theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved.
Superconducting linear accelerator system for NSC
Indian Academy of Sciences (India)
This paper reports the construction of a superconducting linear accelerator as a booster to the 15 UD Pelletron accelerator at Nuclear Science Centre, New Delhi. The LINAC will use superconducting niobium quarter wave resonators as the accelerating element. Construction of the linear accelerator has progressed ...
Directory of Open Access Journals (Sweden)
Zeng Cheng
2014-12-01
Full Text Available Remarkable improvements in the stability properties of discrete system zeros may be achieved by using a new design of the fractional-order hold (FROH circuit. This paper first analyzes asymptotic behaviors of the limiting zeros, as the sampling period T tends to zero, of the sampled-data models on the basis of the normal form representation for continuous-time systems with a new hold proposed. Further, we also give the approximate expression of limiting zeros of the resulting sampled-data system as power series with respect to a sampling period up to the third order term when the relative degree of the continuous-time system is equal to three, and the corresponding stability of the discretization zeros is discussed for fast sampling rates. Of particular interest are the stability conditions of sampling zeros in the case of a new FROH even though the relative degree of a continuous-time system is greater than two, whereas the conventional FROH fails to do so. An insightful interpretation of the obtained sampled-data model can be made in terms of minimal intersample ripple by design, where multirate sampled systems have a poor intersample behavior. Our results provide a more accurate approximation for asymptotic zeros, and certain known results on asymptotic behavior of limiting zeros are shown to be particular cases of the ideas presented here.
Ahmed M. A. El-Sayed; Ebtisam O. Bin-Taher
2011-01-01
In this article, we prove the existence of positive nondecreasing solutions for a multi-term fractional-order functional differential equations. We consider Cauchy boundary problems with: nonlocal conditions, two-point boundary conditions, integral conditions, and deviated arguments.
Rahmatullah; Ellahi, Rahmat; Mohyud-Din, Syed Tauseef; Khan, Umar
2018-03-01
We have computed new exact traveling wave solutions, including complex solutions of fractional order Boussinesq-Like equations, occurring in physical sciences and engineering, by applying Exp-function method. The method is blended with fractional complex transformation and modified Riemann-Liouville fractional order operator. Our obtained solutions are verified by substituting back into their corresponding equations. To the best of our knowledge, no other technique has been reported to cope with the said fractional order nonlinear problems combined with variety of exact solutions. Graphically, fractional order solution curves are shown to be strongly related to each other and most importantly, tend to fixate on their integer order solution curve. Our solutions comprise high frequencies and very small amplitude of the wave responses.
Symmetric linear systems - An application of algebraic systems theory
Hazewinkel, M.; Martin, C.
1983-01-01
Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.
Directory of Open Access Journals (Sweden)
Kai Liu
2018-06-01
Full Text Available The significant task for control performance assessment (CPA is to review and evaluate the performance of the control system. The control system in the semiconductor industry exhibits a complex dynamic behavior, which is hard to analyze. This paper investigates the interesting crossover properties of Hurst exponent estimations and proposes a novel method for feature extraction of the nonlinear multi-input multi-output (MIMO systems. At first, coupled data from real industry are analyzed by multifractal detrended fluctuation analysis (MFDFA and the resultant multifractal spectrum is obtained. Secondly, the crossover points with spline fit in the scale-law curve are located and then employed to segment the entire scale-law curve into several different scaling regions, in which a single Hurst exponent can be estimated. Thirdly, to further ascertain the origin of the multifractality of control signals, the generalized Hurst exponents of the original series are compared with shuffled data. At last, non-Gaussian statistical properties, multifractal properties and Hurst exponents of the process control variables are derived and compared with different sets of tuning parameters. The results have shown that CPA of the MIMO system can be better employed with the help of fractional order signal processing (FOSP.
A study on switched linear system identification using game ...
African Journals Online (AJOL)
A study on switched linear system identification using game-theoretic strategies and neural computing. ... This study deals with application of game-theoretic strategies and neural computing to switched linear ... AJOL African Journals Online.
Reduction of Linear Functional Systems using Fuhrmann's Equivalence
Directory of Open Access Journals (Sweden)
Mohamed S. Boudellioua
2016-11-01
Full Text Available Functional systems arise in the treatment of systems of partial differential equations, delay-differential equations, multidimensional equations, etc. The problem of reducing a linear functional system to a system containing fewer equations and unknowns was first studied by Serre. Finding an equivalent presentation of a linear functional system containing fewer equations and fewer unknowns can generally simplify both the study of the structural properties of the linear functional system and of different numerical analysis issues, and it can sometimes help in solving the linear functional system. In this paper, Fuhrmann's equivalence is used to present a constructive result on the reduction of under-determined linear functional systems to a single equation involving a single unknown. This equivalence transformation has been studied by a number of authors and has been shown to play an important role in the theory of linear functional systems.
Fractional order integration and fuzzy logic based filter for denoising of echocardiographic image.
Saadia, Ayesha; Rashdi, Adnan
2016-12-01
Ultrasound is widely used for imaging due to its cost effectiveness and safety feature. However, ultrasound images are inherently corrupted with speckle noise which severely affects the quality of these images and create difficulty for physicians in diagnosis. To get maximum benefit from ultrasound imaging, image denoising is an essential requirement. To perform image denoising, a two stage methodology using fuzzy weighted mean and fractional integration filter has been proposed in this research work. In stage-1, image pixels are processed by applying a 3 × 3 window around each pixel and fuzzy logic is used to assign weights to the pixels in each window, replacing central pixel of the window with weighted mean of all neighboring pixels present in the same window. Noise suppression is achieved by assigning weights to the pixels while preserving edges and other important features of an image. In stage-2, the resultant image is further improved by fractional order integration filter. Effectiveness of the proposed methodology has been analyzed for standard test images artificially corrupted with speckle noise and real ultrasound B-mode images. Results of the proposed technique have been compared with different state-of-the-art techniques including Lsmv, Wiener, Geometric filter, Bilateral, Non-local means, Wavelet, Perona et al., Total variation (TV), Global Adaptive Fractional Integral Algorithm (GAFIA) and Improved Fractional Order Differential (IFD) model. Comparison has been done on quantitative and qualitative basis. For quantitative analysis different metrics like Peak Signal to Noise Ratio (PSNR), Speckle Suppression Index (SSI), Structural Similarity (SSIM), Edge Preservation Index (β) and Correlation Coefficient (ρ) have been used. Simulations have been done using Matlab. Simulation results of artificially corrupted standard test images and two real Echocardiographic images reveal that the proposed method outperforms existing image denoising techniques
Zamani, Abbasali; Barakati, S Masoud; Yousofi-Darmian, Saeed
2016-09-01
Load-frequency control is one of the most important issues in power system operation. In this paper, a Fractional Order PID (FOPID) controller based on Gases Brownian Motion Optimization (GBMO) is used in order to mitigate frequency and exchanged power deviation in two-area power system with considering governor saturation limit. In a FOPID controller derivative and integrator parts have non-integer orders which should be determined by designer. FOPID controller has more flexibility than PID controller. The GBMO algorithm is a recently introduced search method that has suitable accuracy and convergence rate. Thus, this paper uses the advantages of FOPID controller as well as GBMO algorithm to solve load-frequency control. However, computational load will higher than conventional controllers due to more complexity of design procedure. Also, a GBMO based fuzzy controller is designed and analyzed in detail. The performance of the proposed controller in time domain and its robustness are verified according to comparison with other controllers like GBMO based fuzzy controller and PI controller that used for load-frequency control system in confronting with model parameters variations. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
Sharma, Richa; Gaur, Prerna; Mittal, A P
2015-09-01
The robotic manipulators are multi-input multi-output (MIMO), coupled and highly nonlinear systems. The presence of external disturbances and time-varying parameters adversely affects the performance of these systems. Therefore, the controller designed for these systems should effectively deal with such complexities, and it is an intriguing task for control engineers. This paper presents two-degree of freedom fractional order proportional-integral-derivative (2-DOF FOPID) controller scheme for a two-link planar rigid robotic manipulator with payload for trajectory tracking task. The tuning of all controller parameters is done using cuckoo search algorithm (CSA). The performance of proposed 2-DOF FOPID controllers is compared with those of their integer order designs, i.e., 2-DOF PID controllers, and with the traditional PID controllers. In order to show effectiveness of proposed scheme, the robustness testing is carried out for model uncertainties, payload variations with time, external disturbance and random noise. Numerical simulation results indicate that the 2-DOF FOPID controllers are superior to their integer order counterparts and the traditional PID controllers. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.
Qiao, Wenjun; Tang, Xiaoqi; Zheng, Shiqi; Xie, Yuanlong; Song, Bao
2016-09-01
In this paper, an adaptive two-degree-of-freedom (2Dof) proportional-integral (PI) controller is proposed for the speed control of permanent magnet synchronous motor (PMSM). Firstly, an enhanced just-in-time learning technique consisting of two novel searching engines is presented to identify the model of the speed control system in a real-time manner. Secondly, a general formula is given to predict the future speed reference which is unavailable at the interval of two bus-communication cycles. Thirdly, the fractional order generalized predictive control (FOGPC) is introduced to improve the control performance of the servo drive system. Based on the identified model parameters and predicted speed reference, the optimal control law of FOGPC is derived. Finally, the designed 2Dof PI controller is auto-tuned by matching with the optimal control law. Simulations and real-time experimental results on the servo drive system of PMSM are provided to illustrate the effectiveness of the proposed strategy. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
High density linear systems for fusion power
International Nuclear Information System (INIS)
Ellis, W.R.; Krakowski, R.A.
1975-01-01
The physics and technological limitations and uncertainties associated with the linear theta pinch are discussed in terms of a generalized energy balance, which has as its basis the ratio (Q/sub E/) of total electrical energy generated to net electrical energy consumed. Included in this total is the virtual energy of bred fissile fuel, if a hybrid blanket is used, as well as the actual of real energy deposited in the blanket by the fusion neutron. The advantages and disadvantages of the pulsed operation demanded by the linear theta pinch are also discussed
Zhang, Bitao; Pi, YouGuo
2013-07-01
The traditional integer order proportional-integral-differential (IO-PID) controller is sensitive to the parameter variation or/and external load disturbance of permanent magnet synchronous motor (PMSM). And the fractional order proportional-integral-differential (FO-PID) control scheme based on robustness tuning method is proposed to enhance the robustness. But the robustness focuses on the open-loop gain variation of controlled plant. In this paper, an enhanced robust fractional order proportional-plus-integral (ERFOPI) controller based on neural network is proposed. The control law of the ERFOPI controller is acted on a fractional order implement function (FOIF) of tracking error but not tracking error directly, which, according to theory analysis, can enhance the robust performance of system. Tuning rules and approaches, based on phase margin, crossover frequency specification and robustness rejecting gain variation, are introduced to obtain the parameters of ERFOPI controller. And the neural network algorithm is used to adjust the parameter of FOIF. Simulation and experimental results show that the method proposed in this paper not only achieve favorable tracking performance, but also is robust with regard to external load disturbance and parameter variation. Crown Copyright © 2013. Published by Elsevier Ltd. All rights reserved.
Xu, Xuefang; Qiao, Zijian; Lei, Yaguo
2018-03-01
The presence of repetitive transients in vibration signals is a typical symptom of local faults of rotating machinery. Infogram was developed to extract the repetitive transients from vibration signals based on Shannon entropy. Unfortunately, the Shannon entropy is maximized for random processes and unable to quantify the repetitive transients buried in heavy random noise. In addition, the vibration signals always contain multiple intrinsic oscillatory modes due to interaction and coupling effects between machine components. Under this circumstance, high values of Shannon entropy appear in several frequency bands or high value of Shannon entropy doesn't appear in the optimal frequency band, and the infogram becomes difficult to interpret. Thus, it also becomes difficult to select the optimal frequency band for extracting the repetitive transients from the whole frequency bands. To solve these problems, multiscale fractional order entropy (MSFE) infogram is proposed in this paper. With the help of MSFE infogram, the complexity and nonlinear signatures of the vibration signals can be evaluated by quantifying spectral entropy over a range of scales in fractional domain. Moreover, the similarity tolerance of MSFE infogram is helpful for assessing the regularity of signals. A simulation and two experiments concerning a locomotive bearing and a wind turbine gear are used to validate the MSFE infogram. The results demonstrate that the MSFE infogram is more robust to the heavy noise than infogram and the high value is able to only appear in the optimal frequency band for the repetitive transient extraction.
Laser beam pointing and stabilization by fractional-order PID control: Tuning rule and experiments
Al-Alwan, Asem Ibrahim Alwan
2017-10-24
This paper studies the problem of high-precision positioning of laser beams by using a robust Fractional-Order Proportional-Integral-Derivative (FOPID) controller. The control problem addressed in laser beams aims to maintain the position of the laser beam on a Position Sensing Device (PSD) despite the effects of noise and active disturbances. The FOPID controller is well known for its simplicity with better tuning flexibility along with robustness to noise and output disturbance rejections. Thus, a control strategy based on FOPID to achieve the control objectives has been proposed. The FOPID gains and differentiation orders are optimally tuned in order to fulfill the robustness design specifications by solving a nonlinear optimization problem. A comparison to the conventional Proportional-Integral-Derivative (PID) and robust PID is also provided from simulation and experiment set-up. Due to sensor noise, practical PID controllers that filter the position signal before taking the derivative have been also proposed. Experimental results show that the requirements are totally met for the laser beam platform to be stabilized.
Closed-loop step response for tuning PID-fractional-order-filter controllers.
Amoura, Karima; Mansouri, Rachid; Bettayeb, Maâmar; Al-Saggaf, Ubaid M
2016-09-01
Analytical methods are usually applied for tuning fractional controllers. The present paper proposes an empirical method for tuning a new type of fractional controller known as PID-Fractional-Order-Filter (FOF-PID). Indeed, the setpoint overshoot method, initially introduced by Shamsuzzoha and Skogestad, has been adapted for tuning FOF-PID controller. Based on simulations for a range of first order with time delay processes, correlations have been derived to obtain PID-FOF controller parameters similar to those obtained by the Internal Model Control (IMC) tuning rule. The setpoint overshoot method requires only one closed-loop step response experiment using a proportional controller (P-controller). To highlight the potential of this method, simulation results have been compared with those obtained with the IMC method as well as other pertinent techniques. Various case studies have also been considered. The comparison has revealed that the proposed tuning method performs as good as the IMC. Moreover, it might offer a number of advantages over the IMC tuning rule. For instance, the parameters of the fractional controller are directly obtained from the setpoint closed-loop response data without the need of any model of the plant to be controlled. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.
All-optical temporal fractional order differentiator using an in-fiber ellipsoidal air-microcavity
Zhang, Lihong; Sun, Shuqian; Li, Ming; Zhu, Ninghua
2017-12-01
An all-optical temporal fractional order differentiator with ultrabroad bandwidth (~1.6 THz) and extremely simple fabrication is proposed and experimentally demonstrated based on an in-fiber ellipsoidal air-microcavity. The ellipsoidal air-microcavity is fabricated by splicing a single mode fiber (SMF) and a photonic crystal fiber (PCF) together using a simple arc-discharging technology. By changing the arc-discharging times, the propagation loss can be adjusted and then the differentiation order is tuned. A nearly Gaussian-like optical pulse with 3 dB bandwidth of 8 nm is launched into the differentiator and a 0.65 order differentiation of the input pulse is achieved with a processing error of 2.55%. Project supported by the the National Natural Science Foundation of China (Nos. 61522509, 61377002, 61535012), the National High-Tech Research & Development Program of China (No. SS2015AA011002), and the Beijing Natural Science Foundation (No. 4152052). Ming Li was supported in part by the Thousand Young Talent Program.
Laser beam pointing and stabilization by fractional-order PID control: Tuning rule and experiments
Al-Alwan, Asem Ibrahim Alwan; Guo, Xingang; Ndoye, Ibrahima; Laleg-Kirati, Taous-Meriem
2017-01-01
This paper studies the problem of high-precision positioning of laser beams by using a robust Fractional-Order Proportional-Integral-Derivative (FOPID) controller. The control problem addressed in laser beams aims to maintain the position of the laser beam on a Position Sensing Device (PSD) despite the effects of noise and active disturbances. The FOPID controller is well known for its simplicity with better tuning flexibility along with robustness to noise and output disturbance rejections. Thus, a control strategy based on FOPID to achieve the control objectives has been proposed. The FOPID gains and differentiation orders are optimally tuned in order to fulfill the robustness design specifications by solving a nonlinear optimization problem. A comparison to the conventional Proportional-Integral-Derivative (PID) and robust PID is also provided from simulation and experiment set-up. Due to sensor noise, practical PID controllers that filter the position signal before taking the derivative have been also proposed. Experimental results show that the requirements are totally met for the laser beam platform to be stabilized.
Directory of Open Access Journals (Sweden)
Sunita Deswal
2013-01-01
Full Text Available The aim of this paper is to study magneto-thermoelastic interactions in an initially stressed isotropic homogeneous half-space in the context of fractional order theory of generalized thermoelasticity. State space formulation with the Laplace transform technique is used to obtain the general solution, and the resulting formulation is applied to the ramp type increase in thermal load and zero stress. Solutions of the problem in the physical domain are obtained by using a numerical method of the Laplace inverse transform based on the Fourier expansion technique, and the expressions for the displacement, temperature, and stress inside the half-space are obtained. Numerical computations are carried out for a particular material for illustrating the results. Results obtained for the field variables are displayed graphically. Some comparisons have been shown in figures to present the effect of fractional parameter, ramp parameter, magnetic field, and initial stress on the field variables. Some particular cases of special interest have been deduced from the present investigation.
ℋ∞ Adaptive observer for nonlinear fractional-order systems
Ndoye, Ibrahima; Laleg-Kirati, Taous-Meriem; Darouach, Mohamed; Voos, Holger
2016-01-01
inequalities (LMIs) by using an indirect Lyapunov method.The proposed ℋ∞ adaptive observer is also robust against Lipschitz additive nonlinear uncertainty. The performance of the observer is illustrated through some examples including the chaotic Lorenz and Lü
Q-S synchronization of the fractional-order unified system
Indian Academy of Sciences (India)
2013-03-03
Mar 3, 2013 ... of memory and hereditary properties of various materials and processes. ... engineering application and information science, in particular in secure ... has received a great deal of attention and a series of works on Q-S ...
Analysis of Linear Hybrid Systems in CLP
DEFF Research Database (Denmark)
Banda, Gourinath; Gallagher, John Patrick
2009-01-01
In this paper we present a procedure for representing the semantics of linear hybrid automata (LHAs) as constraint logic programs (CLP); flexible and accurate analysis and verification of LHAs can then be performed using generic CLP analysis and transformation tools. LHAs provide an expressive...
Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel
El-Gebeily, M.; Yushau, B.
2008-01-01
In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…
A SYSTEMIC VISION OF BIOLOGY: OVERCOMING LINEARITY
Directory of Open Access Journals (Sweden)
M. Mayer
2005-07-01
were used to build a hipermedia material. This technology permit overcomes a linear communication, improving the comprehension of the network perspective. The teachers speeches revealed their conceptual con- structions along the course, showed the development of the competences in identify interconnection points in the flow and chemical cycling of energy, compatible with a systemic view of life.
Solving Fully Fuzzy Linear System of Equations in General Form
Directory of Open Access Journals (Sweden)
A. Yousefzadeh
2012-06-01
Full Text Available In this work, we propose an approach for computing the positive solution of a fully fuzzy linear system where the coefficient matrix is a fuzzy $nimes n$ matrix. To do this, we use arithmetic operations on fuzzy numbers that introduced by Kaffman in and convert the fully fuzzy linear system into two $nimes n$ and $2nimes 2n$ crisp linear systems. If the solutions of these linear systems don't satisfy in positive fuzzy solution condition, we introduce the constrained least squares problem to obtain optimal fuzzy vector solution by applying the ranking function in given fully fuzzy linear system. Using our proposed method, the fully fuzzy linear system of equations always has a solution. Finally, we illustrate the efficiency of proposed method by solving some numerical examples.
Dynamics of unsymmetric piecewise-linear/non-linear systems using finite elements in time
Wang, Yu
1995-08-01
The dynamic response and stability of a single-degree-of-freedom system with unsymmetric piecewise-linear/non-linear stiffness are analyzed using the finite element method in the time domain. Based on a Hamilton's weak principle, this method provides a simple and efficient approach for predicting all possible fundamental and sub-periodic responses. The stability of the steady state response is determined by using Floquet's theory without any special effort for calculating transition matrices. This method is applied to a number of examples, demonstrating its effectiveness even for a strongly non-linear problem involving both clearance and continuous stiffness non-linearities. Close agreement is found between available published findings and the predictions of the finite element in time approach, which appears to be an efficient and reliable alternative technique for non-linear dynamic response and stability analysis of periodic systems.
Reliability modelling and simulation of switched linear system ...
African Journals Online (AJOL)
Reliability modelling and simulation of switched linear system control using temporal databases. ... design of fault-tolerant real-time switching systems control and modelling embedded micro-schedulers for complex systems maintenance.
Sayevand, K.; Pichaghchi, K.
2018-04-01
In this paper, we were concerned with the description of the singularly perturbed boundary value problems in the scope of fractional calculus. We should mention that, one of the main methods used to solve these problems in classical calculus is the so-called matched asymptotic expansion method. However we shall note that, this was not achievable via the existing classical definitions of fractional derivative, because they do not obey the chain rule which one of the key elements of the matched asymptotic expansion method. In order to accommodate this method to fractional derivative, we employ a relatively new derivative so-called the local fractional derivative. Using the properties of local fractional derivative, we extend the matched asymptotic expansion method to the scope of fractional calculus and introduce a reliable new algorithm to develop approximate solutions of the singularly perturbed boundary value problems of fractional order. In the new method, the original problem is partitioned into inner and outer solution equations. The reduced equation is solved with suitable boundary conditions which provide the terminal boundary conditions for the boundary layer correction. The inner solution problem is next solved as a solvable boundary value problem. The width of the boundary layer is approximated using appropriate resemblance function. Some theoretical results are established and proved. Some illustrating examples are solved and the results are compared with those of matched asymptotic expansion method and homotopy analysis method to demonstrate the accuracy and efficiency of the method. It can be observed that, the proposed method approximates the exact solution very well not only in the boundary layer, but also away from the layer.
Directory of Open Access Journals (Sweden)
Tianhu He
2014-01-01
Full Text Available The dynamic response of a one-dimensional problem for a thermoelastic rod with finite length is investigated in the context of the fractional order theory of thermoelasticity in the present work. The rod is fixed at both ends and subjected to a moving heat source. The fractional order thermoelastic coupled governing equations for the rod are formulated. Laplace transform as well as its numerical inversion is applied to solving the governing equations. The variations of the considered temperature, displacement, and stress in the rod are obtained and demonstrated graphically. The effects of time, velocity of the moving heat source, and fractional order parameter on the distributions of the considered variables are of concern and discussed in detail.
Energy balance in a system with quasispherical linear compression
International Nuclear Information System (INIS)
Es'kov, A.G.; Kozlov, N.P.; Kurtmullaev, R.K.; Semenov, V.N.; Khvesyuk, V.I.; Yaminskii, A.V.
1983-01-01
This letter reports the resists of some experimental studies and a numerical simulation of the Tor-linear fusion system, 1 in which a heavy plasma shell with a closed magnetic structure is compressed in a quasispherical manner. The parameters of the Tor-Linear, at the Kurchatov Institute of Atomic Energy in Moscow are as follows: The energy stored in the system which accelerates the linear is E = 0.5 MJ; the linear mass is m = 0.2 kg; the working volume of the linear module is 1.5 x 10 -3 m 3 ; the linear velocity is approx.10 3 m/s; the guiding field in the toriod in the linear is 1--10 x 10 21 m -3 ; and the intial volume of the plasma in the linear chamber is 2.5 x 10 -4 m 3 . In this series of experiments, new solutions were developed for all the systems of the plasma--linear complex of the Tor-Linear: to produce a plasma toroid, to transport it, and to trap it in the linear cavity
A Proposed Method for Solving Fuzzy System of Linear Equations
Directory of Open Access Journals (Sweden)
Reza Kargar
2014-01-01
Full Text Available This paper proposes a new method for solving fuzzy system of linear equations with crisp coefficients matrix and fuzzy or interval right hand side. Some conditions for the existence of a fuzzy or interval solution of m×n linear system are derived and also a practical algorithm is introduced in detail. The method is based on linear programming problem. Finally the applicability of the proposed method is illustrated by some numerical examples.
Singh, Brajesh K; Srivastava, Vineet K
2015-04-01
The main goal of this paper is to present a new approximate series solution of the multi-dimensional (heat-like) diffusion equation with time-fractional derivative in Caputo form using a semi-analytical approach: fractional-order reduced differential transform method (FRDTM). The efficiency of FRDTM is confirmed by considering four test problems of the multi-dimensional time fractional-order diffusion equation. FRDTM is a very efficient, effective and powerful mathematical tool which provides exact or very close approximate solutions for a wide range of real-world problems arising in engineering and natural sciences, modelled in terms of differential equations.
Directory of Open Access Journals (Sweden)
Min Jia
2012-01-01
Full Text Available We study a model arising from porous media, electromagnetic, and signal processing of wireless communication system -tαx(t=f(t,x(t,x'(t,x”(t,…,x(n-2(t, 0
Pilkey, W. D.; Chen, Y. H.
1974-01-01
An indirect synthesis method is used in the efficient optimal design of multi-degree of freedom, multi-design element, nonlinear, transient systems. A limiting performance analysis which requires linear programming for a kinematically linear system is presented. The system is selected using system identification methods such that the designed system responds as closely as possible to the limiting performance. The efficiency is a result of the method avoiding the repetitive systems analyses accompanying other numerical optimization methods.
Minimal solution of general dual fuzzy linear systems
International Nuclear Information System (INIS)
Abbasbandy, S.; Otadi, M.; Mosleh, M.
2008-01-01
Fuzzy linear systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of general dual fuzzy linear equation systems. Two necessary and sufficient conditions for the minimal solution existence are given. Also, some examples in engineering and economic are considered
Partial Linearization of Mechanical Systems with Application to Observer Design
Sarras, Ioannis; Venkatraman, Aneesh; Ortega, Romeo; Schaft, Arjan van der
2008-01-01
We consider general mechanical systems and establish a necessary and sufficient condition for the existence of a suitable change in the generalized momentum coordinates such that the new dynamics become linear in the transformed momenta. The class of systems which can be (partially) linearized by
Simultaneous Balancing and Model Reduction of Switched Linear Systems
Monshizadeh, Nima; Trentelman, Hendrikus; Camlibel, M.K.
2011-01-01
In this paper, first, balanced truncation of linear systems is revisited. Then, simultaneous balancing of multiple linear systems is investigated. Necessary and sufficient conditions are introduced to identify the case where simultaneous balancing is possible. The validity of these conditions is not
Linear System Control Using Stochastic Learning Automata
Ziyad, Nigel; Cox, E. Lucien; Chouikha, Mohamed F.
1998-01-01
This paper explains the use of a Stochastic Learning Automata (SLA) to control switching between three systems to produce the desired output response. The SLA learns the optimal choice of the damping ratio for each system to achieve a desired result. We show that the SLA can learn these states for the control of an unknown system with the proper choice of the error criteria. The results of using a single automaton are compared to using multiple automata.
Useful tools for non-linear systems: Several non-linear integral inequalities
Czech Academy of Sciences Publication Activity Database
Agahi, H.; Mohammadpour, A.; Mesiar, Radko; Vaezpour, M. S.
2013-01-01
Roč. 49, č. 1 (2013), s. 73-80 ISSN 0950-7051 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : Monotone measure * Comonotone functions * Integral inequalities * Universal integral Subject RIV: BA - General Mathematics Impact factor: 3.058, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-useful tools for non-linear systems several non-linear integral inequalities.pdf
Decentralized linear quadratic power system stabilizers for multi ...
Indian Academy of Sciences (India)
Introduction. Modern excitation systems considerably enhance the overall transient stability of power systems ..... to the local bus rather than the angle δ measured with respect to the remote bus. ... With this in view, the linear and nonlinear per-.
A new active absorption system and its performance to linear and non-linear waves
DEFF Research Database (Denmark)
Andersen, Thomas Lykke; Clavero, M.; Frigaard, Peter Bak
2016-01-01
Highlights •An active absorption system for wavemakers has been developed. •The theory for flush mounted gauges has been extended to cover also small gaps. •The new system has been validated in a wave flume with wavemakers in both ends. •A generation and absorption procedure for highly non-linear...
Directory of Open Access Journals (Sweden)
Bashir Ahmad
2013-02-01
Full Text Available In this article, we discuss the existence of solutions for a boundary-value problem of integro-differential equations of fractional order with nonlocal fractional boundary conditions by means of some standard tools of fixed point theory. Our problem describes a more general form of fractional stochastic dynamic model for financial asset. An illustrative example is also presented.
Directory of Open Access Journals (Sweden)
Ahmed M. A. El-Sayed
2011-12-01
Full Text Available In this article, we prove the existence of positive nondecreasing solutions for a multi-term fractional-order functional differential equations. We consider Cauchy boundary problems with: nonlocal conditions, two-point boundary conditions, integral conditions, and deviated arguments.
On Optimal Feedback Control for Stationary Linear Systems
International Nuclear Information System (INIS)
Russell, David L.
2010-01-01
We study linear-quadratic optimal control problems for finite dimensional stationary linear systems AX+BU=Z with output Y=CX+DU from the viewpoint of linear feedback solution. We interpret solutions in relation to system robustness with respect to disturbances Z and relate them to nonlinear matrix equations of Riccati type and eigenvalue-eigenvector problems for the corresponding Hamiltonian system. Examples are included along with an indication of extensions to continuous, i.e., infinite dimensional, systems, primarily of elliptic type.
Virtual Estimator for Piecewise Linear Systems Based on Observability Analysis
Morales-Morales, Cornelio; Adam-Medina, Manuel; Cervantes, Ilse; Vela-Valdés and, Luis G.; García Beltrán, Carlos Daniel
2013-01-01
This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results. PMID:23447007
Gradient remediability in linear distributed parabolic systems ...
African Journals Online (AJOL)
The aim of this paper is the introduction of a new concept that concerned the analysis of a large class of distributed parabolic systems. It is the general concept of gradient remediability. More precisely, we study with respect to the gradient observation, the existence of an input operator (gradient efficient actuators) ensuring ...
Linearization of Nonautonomous Impulsive System with Nonuniform Exponential Dichotomy
Directory of Open Access Journals (Sweden)
Yongfei Gao
2014-01-01
Full Text Available This paper gives a version of Hartman-Grobman theorem for the impulsive differential equations. We assume that the linear impulsive system has a nonuniform exponential dichotomy. Under some suitable conditions, we proved that the nonlinear impulsive system is topologically conjugated to its linear system. Indeed, we do construct the topologically equivalent function (the transformation. Moreover, the method to prove the topological conjugacy is quite different from those in previous works (e.g., see Barreira and Valls, 2006.
On the discretization of linear fractional representations of LPV systems
Toth, R.; Lovera, M.; Heuberger, P.S.C.; Corno, M.; Hof, Van den P.M.J.
2012-01-01
Commonly, controllers for linear parameter-varying (LPV) systems are designed in continuous time using a linear fractional representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a
Automatic frequency control system for driving a linear accelerator
International Nuclear Information System (INIS)
Helgesson, A.L.
1976-01-01
An automatic frequency control system is described for maintaining the drive frequency applied to a linear accelerator to produce maximum particle output from the accelerator. The particle output amplitude is measured and the frequency of the radio frequency source powering the linear accelerator is adjusted to maximize particle output amplitude
Application of Nearly Linear Solvers to Electric Power System Computation
Grant, Lisa L.
To meet the future needs of the electric power system, improvements need to be made in the areas of power system algorithms, simulation, and modeling, specifically to achieve a time frame that is useful to industry. If power system time-domain simulations could run in real-time, then system operators would have situational awareness to implement online control and avoid cascading failures, significantly improving power system reliability. Several power system applications rely on the solution of a very large linear system. As the demands on power systems continue to grow, there is a greater computational complexity involved in solving these large linear systems within reasonable time. This project expands on the current work in fast linear solvers, developed for solving symmetric and diagonally dominant linear systems, in order to produce power system specific methods that can be solved in nearly-linear run times. The work explores a new theoretical method that is based on ideas in graph theory and combinatorics. The technique builds a chain of progressively smaller approximate systems with preconditioners based on the system's low stretch spanning tree. The method is compared to traditional linear solvers and shown to reduce the time and iterations required for an accurate solution, especially as the system size increases. A simulation validation is performed, comparing the solution capabilities of the chain method to LU factorization, which is the standard linear solver for power flow. The chain method was successfully demonstrated to produce accurate solutions for power flow simulation on a number of IEEE test cases, and a discussion on how to further improve the method's speed and accuracy is included.
Feedback linearizing control of a MIMO power system
Ilyes, Laszlo
Prior research has demonstrated that either the mechanical or electrical subsystem of a synchronous electric generator may be controlled using single-input single-output (SISO) nonlinear feedback linearization. This research suggests a new approach which applies nonlinear feedback linearization to a multi-input multi-output (MIMO) model of the synchronous electric generator connected to an infinite bus load model. In this way, the electrical and mechanical subsystems may be linearized and simultaneously decoupled through the introduction of a pair of auxiliary inputs. This allows well known, linear, SISO control methods to be effectively applied to the resulting systems. The derivation of the feedback linearizing control law is presented in detail, including a discussion on the use of symbolic math processing as a development tool. The linearizing and decoupling properties of the control law are validated through simulation. And finally, the robustness of the control law is demonstrated.
Li, Shuliang; Meng, Wei; Xie, Yufeng
2017-12-23
With the rapid development of the Yangtze River economic belt, the amount of waste-sewage water discharged into the Yangtze River basin increases sharply year by year, which has impeded the sustainable development of the Yangtze River basin. The water security along the Yangtze River basin is very important for China, It is something aboutwater security of roughly one-third of China's population and the sustainable development of the 19 provinces, municipalities and autonomous regions among the Yangtze River basin. Therefore, a scientific prediction of the amount of waste-sewage water discharged into Yangtze River basin has a positive significance on sustainable development of industry belt along with Yangtze River basin. This paper builds the fractional DWSGM(1,1)(DWSGM(1,1) model is short for Discharge amount of Waste Sewage Grey Model for one order equation and one variable) model based on the fractional accumulating generation operator and fractional reducing operator, and calculates the optimal order of "r" by using particle swarm optimization(PSO)algorithm for solving the minimum average relative simulation error. Meanwhile, the simulation performance of DWSGM(1,1)model with the optimal fractional order is tested by comparing the simulation results of grey prediction models with different orders. Finally, the optimal fractional order DWSGM(1,1)grey model is applied to predict the amount of waste-sewage water discharged into the Yangtze River basin, and corresponding countermeasures and suggestions are put forward through analyzing and comparing the prediction results. This paper has positive significance on enriching the fractional order modeling method of the grey system.
Portable, x-band, linear accelerator systems
International Nuclear Information System (INIS)
Schonberg, R.G.; Deruyter, H.; Fowkes, W.R.; Johnson, W.A.; Miller, R.H.; Potter, J.M.; Weaver, J.N.
1985-01-01
Three light-weight, x-band, electron accelerators have been developed to provide a series of highly portable sources of x-rays and neutrons for nondestructive testing. The 1.5 MeV x-ray unit has a 200 kW magnetron for an RF source and an air-cooled, traveling wave accelerating structure to minimize its weight. The 4 and 6 MeV units share the same drive system which contains a 1.2 MW magnetron. The 4 MeV unit uses a traveling-wave guide to produce x-rays and the 6MeV unit uses a standing-wave guide to produce x-rays or neutrons. The choice of 9.3 GHz was dictated by the availability of a high power coaxial magnetron and by the obvious dimensional and weight advantages of a higher frequency over the more common S-band frequencies around 3 GHz
Structure Learning in Stochastic Non-linear Dynamical Systems
Morris, R. D.; Smelyanskiy, V. N.; Luchinsky, D. G.
2005-12-01
A great many systems can be modeled in the non-linear dynamical systems framework, as x˙ = f(x) + ξ(t), where f(x) is the potential function for the system, and ξ(t) is the driving noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications, for example in predator-prey systems, where the very structure of the coupling between predator-prey pairs can have great ecological significance.
Portable, x-band, linear accelerator systems
International Nuclear Information System (INIS)
Schonberg, R.G.; Deruyter, H.; Fowkes, W.R.; Johnson, W.A.; Miller, R.H.; Potter, J.M.; Weaver, J.N.
1985-01-01
Three light-weight, x-band, electron accelerators have been developed to provide a series of highly portable sources of x-rays and neutrons for non-destructive testing. The 1.5 MeV x-ray unit has a 200 kW magnetron for an RF source and an air-cooled, traveling wave accelerating structure to minimize its weight. The 4 and 6 MeV units share the same drive system which contains a 1.2 MW magnetron. The 4 MeV unit uses a traveling-wave guide to produce x-rays and the 6MeV unit uses a standing-wave guide to produce x-rays or neutrons. The choice of 9.3 GHz was dictated by the availability of a high power coaxial magnetron and by the obvious dimensional and weight advantages of a higher frequency over the more common S-band frequencies around 3 GHz
Linear quadratic Gaussian balancing for discrete-time infinite-dimensional linear systems
Opmeer, MR; Curtain, RF
2004-01-01
In this paper, we study the existence of linear quadratic Gaussian (LQG)-balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show
Sparse Linear Solver for Power System Analysis Using FPGA
National Research Council Canada - National Science Library
Johnson, J. R; Nagvajara, P; Nwankpa, C
2005-01-01
.... Numerical solution to load flow equations are typically computed using Newton-Raphson iteration, and the most time consuming component of the computation is the solution of a sparse linear system...
Perfect commuting-operator strategies for linear system games
Cleve, Richard; Liu, Li; Slofstra, William
2017-01-01
Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely presented group associated with the linear system which arises from the non-commutative equations.
A conceptual design of Final Focus Systems for linear colliders
International Nuclear Information System (INIS)
Brown, K.L.
1987-06-01
Linear colliders are a relatively recent development in the evolution of particle accelerators. This report discusses some of the approaches that have been considered for the design of Final Focus Systems to demagnify the beam exiting from a linac to the small size suitable for collisions at the interaction point. The system receiving the most attention is the one adopted for the SLAC Linear Collider. However, the theory and optical techniques discussed should be applicable to the design efforts for future machines
ON THE STABILIZATION OF THE LINEAR HYBRID SYSTEM STRUCTURE
Directory of Open Access Journals (Sweden)
Kirillov
2014-11-01
Full Text Available The linear control hybrid system, consisting of a fi- nite set of subsystems (modes having different dimensions, is considered. The moments of reset time are determined by some complementary function – evolutionary time. This function satisfies the special complementary ordinary differential equation. The mode stabilization problem is solved for some class of piecewise linear controls. The method of stabilization relies on the set of invariant planes, the existence of which is due to the special form of the hybrid system.
Iterative algorithms for large sparse linear systems on parallel computers
Adams, L. M.
1982-01-01
Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.
Simultaneous Balancing and Model Reduction of Switched Linear Systems
Monshizadeh, Nima; Trentelman, Hendrikus; Camlibel, M.K.
2011-01-01
In this paper, first, balanced truncation of linear systems is revisited. Then, simultaneous balancing of multiple linear systems is investigated. Necessary and sufficient conditions are introduced to identify the case where simultaneous balancing is possible. The validity of these conditions is not limited to a certain type of balancing, and they are applicable for different types of balancing corresponding to different equations, like Lyapunov or Riccati equations. The results obtained are ...
Solar photovoltaic water pumping system using a new linear actuator
Andrada Gascón, Pedro; Castro, Javier
2007-01-01
In this paper a photovoltaic solar pumping system using a new linear actuator is presented. This linear actuator is a double-sided flat two-phase variable-reluctance linear stepper motor that moves a piston-type water pump with the help of a rope, a pulley and a counterweight. The entire actuator pump ensemble is controlled by a simple electronic unit that manages the electric power generated by a photovoltaic array. The proposed system is suitable for rural communities in developing...
Phase and amplitude detection system for the Stanford Linear Accelerator
International Nuclear Information System (INIS)
Fox, J.D.; Schwarz, H.D.
1983-01-01
A computer controlled phase and amplitude detection system to measure and stabilize the rf power sources in the Stanford Linear Accelerator is described. This system measures the instantaneous phase and amplitude of a 1 microsecond 2856 MHz rf pulse and will be used for phase feedback control and for amplitude and phase jitter detection. This paper discusses the measurement system performance requirements for the operation of the Stanford Linear Collider, and the design and implementation of the phase and amplitude detection system. The fundamental software algorithms used in the measurement are described, as is the performance of the prototype phase and amplitude detector system
International Nuclear Information System (INIS)
Chen, H.-H.; Chen, C.-S.; Lee, C.-I
2009-01-01
This paper investigates the synchronization of unidirectional and bidirectional coupled unified chaotic systems. A balanced coupling coefficient control method is presented for global asymptotic synchronization using the Lyapunov stability theorem and a minimum scheme with no constraints/constraints. By using the result of the above analysis, the balanced coupling coefficients are then designed to achieve the chaos synchronization of linearly coupled unified chaotic systems. The feasibility and effectiveness of the proposed chaos synchronization scheme are verified via numerical simulations.
International Nuclear Information System (INIS)
Deswal, Sunita; Kalkal, Kapil Kumar; Sheoran, Sandeep Singh
2016-01-01
A mathematical model of fractional order two-temperature generalized thermoelasticity with diffusion and initial stress is proposed to analyze the transient wave phenomenon in an infinite thermoelastic half-space. The governing equations are derived in cylindrical coordinates for a two dimensional axi-symmetric problem. The analytical solution is procured by employing the Laplace and Hankel transforms for time and space variables respectively. The solutions are investigated in detail for a time dependent heat source. By using numerical inversion method of integral transforms, we obtain the solutions for displacement, stress, temperature and diffusion fields in physical domain. Computations are carried out for copper material and displayed graphically. The effect of fractional order parameter, two-temperature parameter, diffusion, initial stress and time on the different thermoelastic and diffusion fields is analyzed on the basis of analytical and numerical results. Some special cases have also been deduced from the present investigation.
International Nuclear Information System (INIS)
Ezzat, M.A.; El-Bary, A.A.
2016-01-01
In this study, the constitutive relation for the heat flux vector is derived to be the Fourier's law of heat conduction with a variable thermal conductivity and time-fractional order. The Stokes' flow of unsteady incompressible thermoelectric fluid due to a moving plate in the presence of a transverse magnetic field is molded. Stokes' first problem is solved by applying Laplace transform with respect to time variable and evaluating the inverse transform integrals by using a numerical approach. Numerical results for the temperature and the velocity distributions are given and illustrated graphically for given problem. The results indicate that the thermal conductivity and time-fractional order play a major role in the temperature and velocity distributions. (authors)
Solution of generalized shifted linear systems with complex symmetric matrices
International Nuclear Information System (INIS)
Sogabe, Tomohiro; Hoshi, Takeo; Zhang, Shao-Liang; Fujiwara, Takeo
2012-01-01
We develop the shifted COCG method [R. Takayama, T. Hoshi, T. Sogabe, S.-L. Zhang, T. Fujiwara, Linear algebraic calculation of Green’s function for large-scale electronic structure theory, Phys. Rev. B 73 (165108) (2006) 1–9] and the shifted WQMR method [T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, On a weighted quasi-residual minimization strategy of the QMR method for solving complex symmetric shifted linear systems, Electron. Trans. Numer. Anal. 31 (2008) 126–140] for solving generalized shifted linear systems with complex symmetric matrices that arise from the electronic structure theory. The complex symmetric Lanczos process with a suitable bilinear form plays an important role in the development of the methods. The numerical examples indicate that the methods are highly attractive when the inner linear systems can efficiently be solved.
Economic MPC for a linear stochastic system of energy units
DEFF Research Database (Denmark)
Jørgensen, John Bagterp; Sokoler, Leo Emil; Standardi, Laura
2016-01-01
This paper summarizes comprehensively the work in four recent PhD theses from the Technical University of Denmark related to Economic MPC of future power systems. Future power systems will consist of a large number of decentralized power producers and a large number of controllable power consumers...... in addition to stochastic power producers such as wind turbines and solar power plants. Control of such large scale systems requires new control algorithms. In this paper, we formulate the control of such a system as an Economic Model Predictive Control (MPC) problem. When the power producers and controllable...... power consumers have linear dynamics, the Economic MPC may be expressed as a linear program. We provide linear models for a number of energy units in an energy system, formulate an Economic MPC for coordination of such a system. We indicate how advances in computational MPC makes the solutions...
Stability analysis of switched linear systems defined by graphs
Athanasopoulos, N.; Lazar, M.
2014-01-01
We present necessary and sufficient conditions for global exponential stability for switched discrete-time linear systems, under arbitrary switching, which is constrained within a set of admissible transitions. The class of systems studied includes the family of systems under arbitrary switching,
Euclidean null controllability of linear systems with delays in state ...
African Journals Online (AJOL)
Sufficient conditions are developed for the Euclidean controllability of linear systems with delay in state and in control. Namely, if the uncontrolled system is uniformly asymptotically stable and the control equation proper, then the control system is Euclidean null controllable. Journal of the Nigerian Association of ...
Incremental Closed-loop Identification of Linear Parameter Varying Systems
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon; Trangbæk, Klaus
2011-01-01
, closed-loop system identification is more difficult than open-loop identification. In this paper we prove that the so-called Hansen Scheme, a technique known from linear time-invariant systems theory for transforming closed-loop system identification problems into open-loop-like problems, can be extended...
Stability and response bounds of non-conservative linear systems
DEFF Research Database (Denmark)
Pommer, Christian
2003-01-01
For a linear system of second order differential equations the stability is studied by Lyapunov's direct method. The Lyapunov matrix equation is solved and a sufficient condition for stability is expressed by the system matrices. For a system which satisfies the condition for stability the Lyapunov...
Linear Optimization of Frequency Spectrum Assignments Across System
2016-03-01
selection tools, frequency allocation, transmission optimization, electromagnetic maneuver warfare, electronic protection, assignment model 15. NUMBER ...Characteristics Modeled ...............................................................29 Table 10. Antenna Systems Modeled , Number of Systems and...surveillance EW early warning GAMS general algebraic modeling system GHz gigahertz IDE integrated development environment ILP integer linear program
Fractional-order leaky integrate-and-fire model with long-term memory and power law dynamics.
Teka, Wondimu W; Upadhyay, Ranjit Kumar; Mondal, Argha
2017-09-01
Pyramidal neurons produce different spiking patterns to process information, communicate with each other and transform information. These spiking patterns have complex and multiple time scale dynamics that have been described with the fractional-order leaky integrate-and-Fire (FLIF) model. Models with fractional (non-integer) order differentiation that generalize power law dynamics can be used to describe complex temporal voltage dynamics. The main characteristic of FLIF model is that it depends on all past values of the voltage that causes long-term memory. The model produces spikes with high interspike interval variability and displays several spiking properties such as upward spike-frequency adaptation and long spike latency in response to a constant stimulus. We show that the subthreshold voltage and the firing rate of the fractional-order model make transitions from exponential to power law dynamics when the fractional order α decreases from 1 to smaller values. The firing rate displays different types of spike timing adaptation caused by changes on initial values. We also show that the voltage-memory trace and fractional coefficient are the causes of these different types of spiking properties. The voltage-memory trace that represents the long-term memory has a feedback regulatory mechanism and affects spiking activity. The results suggest that fractional-order models might be appropriate for understanding multiple time scale neuronal dynamics. Overall, a neuron with fractional dynamics displays history dependent activities that might be very useful and powerful for effective information processing. Copyright © 2017 Elsevier Ltd. All rights reserved.
Energy Technology Data Exchange (ETDEWEB)
Ezzat, Magdy A., E-mail: maezzat2000@yahoo.com [Department of Mathematics, Faculty of Sciences and Letters in Al Bukayriyyah, Al-Qassim University, Al-Qassim (Saudi Arabia); El-Karamany, Ahmed S., E-mail: qaramani@gmail.com [Department of Mathematical and Physical Sciences, Nizwa University, P.O. Box 1357, Nizwa 611 (Oman); Ezzat, Shereen M. [Department of Mathematics, Faculty of Sciences and Letters in Al Bukayriyyah, Al-Qassim University, Al-Qassim (Saudi Arabia)
2012-11-15
Highlights: Black-Right-Pointing-Pointer We model fractional order dual-phase-lag heat conduction law. Black-Right-Pointing-Pointer We applied the model on a perfect conducting half-space of elastic material. Black-Right-Pointing-Pointer Some theories of generalized thermoelasticity follow as limit cases. Black-Right-Pointing-Pointer State space approach is adopted for the solution of one-dimensional problems. Black-Right-Pointing-Pointer The model will improve the efficiency of thermoelectric material. - Abstract: A new mathematical model of two-temperature magneto-thermoelasticity is constructed where the fractional order dual-phase-lag heat conduction law is considered. The state space approach developed in Ezzat (2008) is adopted for the solution of one-dimensional application for a perfect conducting half-space of elastic material, which is thermally shocked in the presence of a transverse magnetic field. The Laplace transform technique is used. A numerical method is employed for the inversion of the Laplace transforms. According to the numerical results and its graphs, conclusion about the new theory has been constructed. Some theories of generalized thermoelasticity follow as limit cases. Some comparisons have been shown in figures to estimate effects of temperature discrepancy and fractional order parameter on all the studied fields.
Stability analysis of switched linear systems defined by graphs
Athanasopoulos, Nikolaos; Lazar, Mircea
2015-01-01
We present necessary and sufficient conditions for global exponential stability for switched discrete-time linear systems, under arbitrary switching, which is constrained within a set of admissible transitions. The class of systems studied includes the family of systems under arbitrary switching, periodic systems, and systems with minimum and maximum dwell time specifications. To reach the result, we describe the set of rules that define the admissible transitions with a weighted directed gra...
Modeling and analysis of linear hyperbolic systems of balance laws
Bartecki, Krzysztof
2016-01-01
This monograph focuses on the mathematical modeling of distributed parameter systems in which mass/energy transport or wave propagation phenomena occur and which are described by partial differential equations of hyperbolic type. The case of linear (or linearized) 2 x 2 hyperbolic systems of balance laws is considered, i.e., systems described by two coupled linear partial differential equations with two variables representing physical quantities, depending on both time and one-dimensional spatial variable. Based on practical examples of a double-pipe heat exchanger and a transportation pipeline, two typical configurations of boundary input signals are analyzed: collocated, wherein both signals affect the system at the same spatial point, and anti-collocated, in which the input signals are applied to the two different end points of the system. The results of this book emerge from the practical experience of the author gained during his studies conducted in the experimental installation of a heat exchange cente...
A convex optimization approach for solving large scale linear systems
Directory of Open Access Journals (Sweden)
Debora Cores
2017-01-01
Full Text Available The well-known Conjugate Gradient (CG method minimizes a strictly convex quadratic function for solving large-scale linear system of equations when the coefficient matrix is symmetric and positive definite. In this work we present and analyze a non-quadratic convex function for solving any large-scale linear system of equations regardless of the characteristics of the coefficient matrix. For finding the global minimizers, of this new convex function, any low-cost iterative optimization technique could be applied. In particular, we propose to use the low-cost globally convergent Spectral Projected Gradient (SPG method, which allow us to extend this optimization approach for solving consistent square and rectangular linear system, as well as linear feasibility problem, with and without convex constraints and with and without preconditioning strategies. Our numerical results indicate that the new scheme outperforms state-of-the-art iterative techniques for solving linear systems when the symmetric part of the coefficient matrix is indefinite, and also for solving linear feasibility problems.
Error Estimates for a Semidiscrete Finite Element Method for Fractional Order Parabolic Equations
Jin, Bangti
2013-01-01
We consider the initial boundary value problem for a homogeneous time-fractional diffusion equation with an initial condition ν(x) and a homogeneous Dirichlet boundary condition in a bounded convex polygonal domain Ω. We study two semidiscrete approximation schemes, i.e., the Galerkin finite element method (FEM) and lumped mass Galerkin FEM, using piecewise linear functions. We establish almost optimal with respect to the data regularity error estimates, including the cases of smooth and nonsmooth initial data, i.e., ν ∈ H2(Ω) ∩ H0 1(Ω) and ν ∈ L2(Ω). For the lumped mass method, the optimal L2-norm error estimate is valid only under an additional assumption on the mesh, which in two dimensions is known to be satisfied for symmetric meshes. Finally, we present some numerical results that give insight into the reliability of the theoretical study. © 2013 Society for Industrial and Applied Mathematics.
A comparison between linear and toroidal Extrap systems
International Nuclear Information System (INIS)
Lehnert, B.
1988-09-01
The Extrap scheme consists of a Z-pinch immersed in an octupole field generated by currents in a set of external conductors. A comparison between linear and toroidal Extrap geometry is made in this paper. As compared to toroidal systems, linear geometry has the advantages of relative simplicity and of a current drive by means of electrodes. Linear devices are convenient for basic studies of Extrap, at moderately high pinch currents and plasma temperatures. Within the parameter ranges of experiments at high pinch currents and plasma temperatures, linear systems have on the other hand some substantial disadvantages, on account of the plasma interaction with the end regions. This results in a limitation of the energy confinement time, and leads in the case of an ohmically heated plasma to excessively high plasma densities and small pinch radii which also complicate the introduction of the external conductors. (author)
Linear local stability of electrostatic drift modes in helical systems
International Nuclear Information System (INIS)
Yamagishi, O.; Nakajima, N.; Sugama, H.; Nakamura, Y.
2003-01-01
We investigate the stability of the drift wave in helical systems. For this purpose, we solve the linear local gyrokinetic-Poisson equation, in the electrostatic regime. As a model of helical plasmas, Large helical Device (LHD) is considered. The equation we apply is rather exact in the framework of linear gyrokinetic theory, where only the approximation is the ballooning representation. In this paper, we consider only collisionless cases. All the frequency regime can be naturally reated without any assumptions, and in such cases, ion temperature gradient modes (ITG), trapped electron modes (TEM), and electron temperature gradient modes (ETG) are expected to become unstable linearly independently. (orig.)
H 2 guaranteed cost control of discrete linear systems
Directory of Open Access Journals (Sweden)
Colmenares W.
2000-01-01
Full Text Available This paper presents necessary and sufficient conditions for the existence of a quadratically stabilizing output feedback controller which also assures H 2 guaranteed cost performance on a discrete linear uncertain system where the uncertainty is of the norm bounded type. The conditions are presented as a collection of linear matrix inequalities.The solution, however requires a search over a scalar parameter space.
Structured Control of Affine Linear Parameter Varying Systems
DEFF Research Database (Denmark)
Adegas, Fabiano Daher; Stoustrup, Jakob
2011-01-01
This paper presents a new procedure to design structured controllers for discrete-time afﬁne linear parametervarying systems (A LPV). The class of control structures includes decentralized of any order, ﬁxed order output feedback, simultaneous plant-control design, among others. A parametervarying...... non-convex condition for an upper bound on the induced L2-norm performance is solved by an iterative linear matrix inequalities (LMI) optimization algorithm. Numerical examples demostrate the effectiveness of the proposed approach....
On the stability of non-linear systems
International Nuclear Information System (INIS)
Guelman, M.
1968-09-01
A study is made of the absolute stability of nonlinear systems, using Liapounov's second method and taking into account the results obtained from V.M. Popov's work. The results already established are first presented, in particular concerning the frequency domain criterions for absolute stability of automatic control systems containing one single non linearity. The results have been extended to show the existence of a limiting parabola. New use is then made of the methods studied for deriving absolute stability criterions for a system containing a different type of non linearity. Finally, the results obtained are considered from the point of view of Aizerman's conjecture. (author) [fr
Applications of equivalent linearization approaches to nonlinear piping systems
International Nuclear Information System (INIS)
Park, Y.; Hofmayer, C.; Chokshi, N.
1997-01-01
The piping systems in nuclear power plants, even with conventional snubber supports, are highly complex nonlinear structures under severe earthquake loadings mainly due to various mechanical gaps in support structures. Some type of nonlinear analysis is necessary to accurately predict the piping responses under earthquake loadings. The application of equivalent linearization approaches (ELA) to seismic analyses of nonlinear piping systems is presented. Two types of ELA's are studied; i.e., one based on the response spectrum method and the other based on the linear random vibration theory. The test results of main steam and feedwater piping systems supported by snubbers and energy absorbers are used to evaluate the numerical accuracy and limitations
State space and input-output linear systems
Delchamps, David F
1988-01-01
It is difficult for me to forget the mild sense of betrayal I felt some ten years ago when I discovered, with considerable dismay, that my two favorite books on linear system theory - Desoer's Notes for a Second Course on Linear Systems and Brockett's Finite Dimensional Linear Systems - were both out of print. Since that time, of course, linear system theory has undergone a transformation of the sort which always attends the maturation of a theory whose range of applicability is expanding in a fashion governed by technological developments and by the rate at which such advances become a part of engineering practice. The growth of the field has inspired the publication of some excellent books; the encyclopedic treatises by Kailath and Chen, in particular, come immediately to mind. Nonetheless, I was inspired to write this book primarily by my practical needs as a teacher and researcher in the field. For the past five years, I have taught a one semester first year gradu ate level linear system theory course i...
Unification of three linear models for the transient visual system
Brinker, den A.C.
1989-01-01
Three different linear filters are considered as a model describing the experimentally determined triphasic impulse responses of discs. These impulse responses arc associated with the transient visual system. Each model reveals a different feature of the system. Unification of the models is
Punctuated equilibrium in a non-linear system of action
J.S. Timmermans (Jos)
2008-01-01
textabstractColeman's equilibrium model of social development, the Linear System of Action, is extended to cover the dynamics of societal transitions. The model implemented has the characteristics of a dissipative system. A variation and selection algorithm favoring the retention of relatively
Lag synchronization of chaotic systems with time-delayed linear
Indian Academy of Sciences (India)
In this paper, the lag synchronization of chaotic systems with time-delayed linear terms via impulsive control is investigated. Based on the stability theory of impulsive delayed differential equations, some sufficient conditions are obtained guaranteeing the synchronized behaviours between two delayed chaotic systems.
INPUT-OUTPUT STRUCTURE OF LINEAR-DIFFERENTIAL ALGEBRAIC SYSTEMS
KUIJPER, M; SCHUMACHER, JM
Systems of linear differential and algebraic equations occur in various ways, for instance, as a result of automated modeling procedures and in problems involving algebraic constraints, such as zero dynamics and exact model matching. Differential/algebraic systems may represent an input-output
Frequency Interval Cross Gramians for Linear and Bilinear Systems
DEFF Research Database (Denmark)
Jazlan, Ahmad; Sreeram, Victor; Shaker, Hamid Reza
2017-01-01
In many control engineering problems, it is desired to analyze the systems at particular frequency intervals of interest. This paper focuses on the development of frequency interval cross gramians for both linear and bilinear systems. New generalized Sylvester equations for calculating the freque...
Switching control of linear systems for generating chaos
International Nuclear Information System (INIS)
Liu Xinzhi; Teo, Kok-Lay; Zhang Hongtao; Chen Guanrong
2006-01-01
In this paper, a new switching method is developed, which can be applied to generating different types of chaos or chaos-like dynamics from two or more linear systems. A numerical simulation is given to illustrate the generated chaotic dynamic behavior of the systems with some variable parameters. Finally, a circuit is built to realize various chaotic dynamical behaviors
New approach to solve symmetric fully fuzzy linear systems
Indian Academy of Sciences (India)
In this paper, we present a method to solve fully fuzzy linear systems with symmetric coefﬁcient matrix. The symmetric coefﬁcient matrix is decomposed into two systems of equations by using Cholesky method and then a solution can be obtained. Numerical examples are given to illustrate our method.
Criteria for stability of linear dynamical systems with multiple delays ...
African Journals Online (AJOL)
In this study we considered a linear Dynamical system with multiple delays and find suitable conditions on the systems parameters such that for a given initial function, we can define a mapping in a carefully chosen complete metric space on which the mapping has a unique fixed point. An asymptotic stability theory for the ...
A data-acquisition system for high speed linear CCD
International Nuclear Information System (INIS)
Liu Zhiyan; Chen Xiangcai; Jiang Xiaoshan; Zhang Hongyu; Liang Zhongwang; Xiang Haisheng; Hu Jun
2010-01-01
A data-acquisition system for high speed linear CCD (Charge Coupled device) is mainly introduced. The optical fiber transmission technology is used. The data is sent to PC through USB or PCI interface. The construction of the system, the design of the PCI interface hardware, software design and the design of the control program running on host computer are also introduced. (authors)
Partial Synchronization Manifolds for Linearly Time-Delay Coupled Systems
Steur, Erik; van Leeuwen, Cees; Michiels, Wim
2014-01-01
Sometimes a network of dynamical systems shows a form of incomplete synchronization characterized by synchronization of some but not all of its systems. This type of incomplete synchronization is called partial synchronization. Partial synchronization is associated with the existence of partial synchronization manifolds, which are linear invariant subspaces of C, the state space of the network of systems. We focus on partial synchronization manifolds in networks of system...
The linear sizes tolerances and fits system modernization
Glukhov, V. I.; Grinevich, V. A.; Shalay, V. V.
2018-04-01
The study is carried out on the urgent topic for technical products quality providing in the tolerancing process of the component parts. The aim of the paper is to develop alternatives for improving the system linear sizes tolerances and dimensional fits in the international standard ISO 286-1. The tasks of the work are, firstly, to classify as linear sizes the elements additionally linear coordinating sizes that determine the detail elements location and, secondly, to justify the basic deviation of the tolerance interval for the element's linear size. The geometrical modeling method of real details elements, the analytical and experimental methods are used in the research. It is shown that the linear coordinates are the dimensional basis of the elements linear sizes. To standardize the accuracy of linear coordinating sizes in all accuracy classes, it is sufficient to select in the standardized tolerance system only one tolerance interval with symmetrical deviations: Js for internal dimensional elements (holes) and js for external elements (shafts). The main deviation of this coordinating tolerance is the average zero deviation, which coincides with the nominal value of the coordinating size. Other intervals of the tolerance system are remained for normalizing the accuracy of the elements linear sizes with a fundamental change in the basic deviation of all tolerance intervals is the maximum deviation corresponding to the limit of the element material: EI is the lower tolerance for the of the internal elements (holes) sizes and es is the upper tolerance deviation for the outer elements (shafts) sizes. It is the sizes of the material maximum that are involved in the of the dimensional elements mating of the shafts and holes and determine the fits type.
Damped oscillations of linear systems a mathematical introduction
Veselić, Krešimir
2011-01-01
The theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike. This theory plays a central role in explaining the stability of mechanical structures in civil engineering, but it also has applications in other fields such as electrical network systems and quantum mechanics. This volume gives an introduction to linear finite dimensional damped systems as they are viewed by an applied mathematician. After a short overview of the physical principles leading to the linear system model, a largely self-contained mathematical theory for this model is presented. This includes the geometry of the underlying indefinite metric space, spectral theory of J-symmetric matrices and the associated quadratic eigenvalue problem. Particular attention is paid to the sensitivity issues which influence numerical computations. Finally, several recent research developments are included, e.g. Lyapunov stability and ...