Applying the Nernst equation to simulate redox potential variations for biological nitrification and denitrification processes.

Science.gov (United States)

Chang, Cheng-Nan; Cheng, Hong-Bang; Chao, Allen C

2004-03-15

In this paper, various forms of Nernst equations have been developed based on the real stoichiometric relationship of biological nitrification and denitrification reactions. Instead of using the Nernst equation based on a one-to-one stoichiometric relation for the oxidizing and the reducing species, the basic Nernst equation is modified into slightly different forms. Each is suitable for simulating the redox potential (ORP) variation of a specific biological nitrification or denitrification process. Using the data published in the literature, the validity of these developed Nernst equations has been verified by close fits of the measured ORP data with the calculated ORP curve. The simulation results also indicate that if the biological process is simulated using an incorrect form of Nernst equation, the calculated ORP curve will not fit the measured data. Using these Nernst equations, the ORP value that corresponds to a predetermined degree of completion for the biochemical reaction can be calculated. Thus, these Nernst equations will enable a more efficient on-line control of the biological process.

Optimal control of compressible Navier-Stokes equations

International Nuclear Information System (INIS)

Ito, K.; Ravindran, S.S.

1994-01-01

Optimal control for the viscous incompressible flows, which are governed by incompressible Navier-Stokes equations, has been the subject of extensive study in recent years, see, e.g., [AT], [GHS], [IR], and [S]. In this paper we consider the optimal control of compressible isentropic Navier-Stokes equations. We develop the weak variational formulation and discuss the existence and necessary optimality condition characterizing the optimal control. A numerical method based on the mixed-finite element method is also discussed to compute the control and numerical results are presented

Semilinear Kolmogorov Equations and Applications to Stochastic Optimal Control

International Nuclear Information System (INIS)

Masiero, Federica

2005-01-01

Semilinear parabolic differential equations are solved in a mild sense in an infinite-dimensional Hilbert space. Applications to stochastic optimal control problems are studied by solving the associated Hamilton-Jacobi-Bellman equation. These results are applied to some controlled stochastic partial differential equations

Null controllability of the viscous Camassa–Holm equation with ...

Indian Academy of Sciences (India)

In this paper, we study the null controllability of the viscous Camassa–. Holm equation on the one-dimensional torus. By using a moving distributed control, we obtain that the system is null controllable for a given data with certain regularity. Keywords. Viscous Camassa–Holm equation; null controllability; moving control;.

Euler's fluid equations: Optimal control vs optimization

Energy Technology Data Exchange (ETDEWEB)

Holm, Darryl D., E-mail: d.holm@ic.ac.u [Department of Mathematics, Imperial College London, SW7 2AZ (United Kingdom)

2009-11-23

An optimization method used in image-processing (metamorphosis) is found to imply Euler's equations for incompressible flow of an inviscid fluid, without requiring that the Lagrangian particle labels exactly follow the flow lines of the Eulerian velocity vector field. Thus, an optimal control problem and an optimization problem for incompressible ideal fluid flow both yield the same Euler fluid equations, although their Lagrangian parcel dynamics are different. This is a result of the gauge freedom in the definition of the fluid pressure for an incompressible flow, in combination with the symmetry of fluid dynamics under relabeling of their Lagrangian coordinates. Similar ideas are also illustrated for SO(N) rigid body motion.

Constrained Optimization and Optimal Control for Partial Differential Equations

CERN Document Server

Leugering, Günter; Griewank, Andreas

2012-01-01

This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The cont

Boundary Shape Control of the Navier-Stokes Equations and Applications

Institute of Scientific and Technical Information of China (English)

Kaitai LI; Jian SU; Aixiang HUANG

2010-01-01

In this paper,the geometrical design for the blade's surface(s)in an impeller or for the profile of an aircraft,is modeled from the mathematical point of view by a boundary shape control problem for the Navier-Stokes equations.The objective function is the sum of a global dissipative function and the power of the fluid.The control variables are the geometry of the boundary and the state equations are the Navier-Stokes equations.The Euler-Lagrange equations of the optimal control problem are derived,which are an elliptic boundary value system of fourth order,coupled with the Navier-Stokes equations.The authors also prove the existence of the solution of the optimal control problem,the existence of the solution of the Navier-Stokes equations with mixed boundary conditions,the weak continuity of the solution of the Navier-Stokes equations with respect to the geometry shape of the blade's surface and the existence of solutions of the equations for the G(a)teaux derivative of the solution of the Navier-Stokes equations with respect to the geometry of the boundary.

Multiplicity Control in Structural Equation Modeling

Science.gov (United States)

Cribbie, Robert A.

2007-01-01

Researchers conducting structural equation modeling analyses rarely, if ever, control for the inflated probability of Type I errors when evaluating the statistical significance of multiple parameters in a model. In this study, the Type I error control, power and true model rates of famsilywise and false discovery rate controlling procedures were…

Study on the instrumentation and control of the fermentaion process

Energy Technology Data Exchange (ETDEWEB)

Nanba, Akira

1988-03-25

An attempt was made to create models representing various fermentation processes, and these models were applied to a computer-controlled bread yeast culture plant. First, batch ethanol fermentation processes using yeast were analyzed in the light of reaction rate theory, and various model equations were presented. Using these models, analysis was made at various fermentation temperatures. As a result, it was found that the model equations are applicable to ethanol production and that the reaction rate equation is useful for analyzing high-concentration ethanol fermentation processes. Next, heat involved in ethanol fermentation was measured with a calorimeter. In combination with the above models, automatic montitoring based on microcomputer control, data processing, and display on a screen was attempted, with good results. Using the above findings, the ethanol generation reaction in the bread yeast culture was analyzed qualitatively. Culture control was performed with ethanol growth patterns as signals. The above technique has proved to be applicable to industrial bread yeast production. (17 figs, 3 tabs, 29 refs)

Control functions in nonseparable simultaneous equations models

OpenAIRE

Blundell, R.; Matzkin, R. L.

2014-01-01

The control function approach (Heckman and Robb (1985)) in a system of linear simultaneous equations provides a convenient procedure to estimate one of the functions in the system using reduced form residuals from the other functions as additional regressors. The conditions on the structural system under which this procedure can be used in nonlinear and nonparametric simultaneous equations has thus far been unknown. In this paper, we define a new property of functions called control function ...

Optimal control problem for the extended Fisher–Kolmogorov equation

Indian Academy of Sciences (India)

by methods of optimal control, such as chemical engineering and vehicle ... ern optimal control theories and applied models are not only represented by .... Obviously, equation (2.5) is an ordinary differential equation and according to ODE.

Validation of the mortality prediction equation for damage control ...

African Journals Online (AJOL)

, preoperative lowest pH and lowest core body temperature to derive an equation for the purpose of predicting mortality in damage control surgery. It was shown to reliably predict death despite damage control surgery. The equation derivation ...

Optimal control problem for the extended Fisher–Kolmogorov equation

Indian Academy of Sciences (India)

In this paper, the optimal control problem for the extended Fisher–Kolmogorov equation is studied. The optimal control under boundary condition is given, the existence of optimal solution to the equation is proved and the optimality system is established.

Controllability of the moments for Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation

OpenAIRE

Rozanova-Pierrat , Anna

2006-01-01

Recalling the proprieties of the Khokhlov-Zabolotskaya-Kuznetsov(KZK) equation, we prove the controllability of moments result for the linear part of KZK equation. Then we prove the local controllability result for the full KZK equation applying a known method of perturbation for the nonlinear inverse problem.

Nonlinear fluctuations-induced rate equations for linear birth-death processes

Science.gov (United States)

Honkonen, J.

2008-05-01

The Fock-space approach to the solution of master equations for one-step Markov processes is reconsidered. It is shown that in birth-death processes with an absorbing state at the bottom of the occupation-number spectrum and occupation-number independent annihilation probability of occupation-number fluctuations give rise to rate equations drastically different from the polynomial form typical of birth-death processes. The fluctuation-induced rate equations with the characteristic exponential terms are derived for Mikhailov’s ecological model and Lanchester’s model of modern warfare.

Nonlinear fluctuation-induced rate equations for linear birth-death processes

International Nuclear Information System (INIS)

Honkonen, J.

2008-01-01

The Fock-space approach to the solution of master equations for the one-step Markov processes is reconsidered. It is shown that in birth-death processes with an absorbing state at the bottom of the occupation-number spectrum and occupation-number independent annihilation probability occupation-number fluctuations give rise to rate equations drastically different from the polynomial form typical of birth-death processes. The fluctuation-induced rate equations with the characteristic exponential terms are derived for Mikhailov's ecological model and Lanchester's model of modern warfare

The monitoring and control of TRUEX processes

International Nuclear Information System (INIS)

Regalbuto, M.C.; Misra, B.; Chamberlain, D.B.; Leonard, R.A.; Vandegrift, G.F.

1992-04-01

The Generic TRUEX Model (GTM) was used to design a flowsheet for the TRUEX solvent extraction process that would be used to determine its instrumentation and control requirements. Sensitivity analyses of the key process variables, namely, the aqueous and organic flow rates, feed compositions, and the number of contactor stages, were carried out to assess their impact on the operation of the TRUEX process. Results of these analyses provide a basis for the selection of an instrument and control system and the eventual implementation of a control algorithm. Volume Two of this report is an evaluation of the instruments available for measuring many of the physical parameters. Equations that model the dynamic behavior of the TRUEX process have been generated. These equations can be used to describe the transient or dynamic behavior of the process for a given flowsheet in accordance with the TRUEX model. Further work will be done with the dynamic model to determine how and how quickly the system responds to various perturbations. The use of perturbation analysis early in the design stage will lead to a robust flowsheet, namely, one that will meet all process goals and allow for wide control bounds. The process time delay, that is, the speed with which the system reaches a new steady state, is an important parameter in monitoring and controlling a process. In the future, instrument selection and point-of-variable measurement, now done using the steady-state results reported here, will be reviewed and modified as necessary based on this dynamic method of analysis

Null controllability of a cascade system of Schrodinger equations

Directory of Open Access Journals (Sweden)

Marcos Lopez-Garcia

2016-03-01

Full Text Available This article presents a control problem for a cascade system of two linear N-dimensional Schrodinger equations. We address the problem of null controllability by means of a control supported in a region not satisfying the classical geometrical control condition. The proof is based on the application of a Carleman estimate with degenerate weights to each one of the equations and a careful analysis of the system in order to prove null controllability with only one control force.

Kinematic equations for resolved-rate control of an industrial robot arm

Science.gov (United States)

Barker, L. K.

1983-01-01

An operator can use kinematic, resolved-rate equations to dynamically control a robot arm by watching its response to commanded inputs. Known resolved-rate equations for the control of a particular six-degree-of-freedom industrial robot arm and proceeds to simplify the equations for faster computations are derived. Methods for controlling the robot arm in regions which normally cause mathematical singularities in the resolved-rate equations are discussed.

Nonlinear H-infinity control, Hamiltonian systems and Hamilton-Jacobi equations

CERN Document Server

Aliyu, MDS

2011-01-01

A comprehensive overview of nonlinear Haeu control theory for both continuous-time and discrete-time systems, Nonlinear Haeu-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear Haeu-control, nonlinear Haeu -filtering, mixed H2/ Haeu-nonlinear control and filtering, nonlinear Haeu-almost-disturbance-decoupling, and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter

Langevin equation with multiplicative white noise: Transformation of diffusion processes into the Wiener process in different prescriptions

International Nuclear Information System (INIS)

Kwok, Sau Fa

2012-01-01

A Langevin equation with multiplicative white noise and its corresponding Fokker–Planck equation are considered in this work. From the Fokker–Planck equation a transformation into the Wiener process is provided for different orders of prescription in discretization rule for the stochastic integrals. A few applications are also discussed. - Highlights: ► Fokker–Planck equation corresponding to the Langevin equation with mul- tiplicative white noise is presented. ► Transformation of diffusion processes into the Wiener process in different prescriptions is provided. ► The prescription parameter is associated with the growth rate for a Gompertz-type model.

Optimal Control of Beer Fermentation Process Using Differential ...

African Journals Online (AJOL)

Optimal Control of Beer Fermentation Process Using Differential Transform Method. ... Journal of Applied Sciences and Environmental Management ... The method of differential transform was used to obtain the solution governing the fermentation process; the system of equation was transformed using the differential ...

approximate controllability of a non-autonomous differential equation

Indian Academy of Sciences (India)

53

for a non-autonomous functional differential equation using the theory of linear ... approximate controllability of various functional differential equations in abstract ...... the operator A(t) and into the requirement that x(t) ∈ D(A) for all t ≥ 0.

State Space Reduction of Linear Processes using Control Flow Reconstruction

NARCIS (Netherlands)

van de Pol, Jan Cornelis; Timmer, Mark

2009-01-01

We present a new method for fighting the state space explosion of process algebraic specifications, by performing static analysis on an intermediate format: linear process equations (LPEs). Our method consists of two steps: (1) we reconstruct the LPE's control flow, detecting control flow parameters

State Space Reduction of Linear Processes Using Control Flow Reconstruction

NARCIS (Netherlands)

van de Pol, Jan Cornelis; Timmer, Mark; Liu, Zhiming; Ravn, Anders P.

2009-01-01

We present a new method for fighting the state space explosion of process algebraic specifications, by performing static analysis on an intermediate format: linear process equations (LPEs). Our method consists of two steps: (1) we reconstruct the LPE's control flow, detecting control flow parameters

Ambit processes and stochastic partial differential equations

DEFF Research Database (Denmark)

Barndorff-Nielsen, Ole; Benth, Fred Espen; Veraart, Almut

Ambit processes are general stochastic processes based on stochastic integrals with respect to Lévy bases. Due to their flexible structure, they have great potential for providing realistic models for various applications such as in turbulence and finance. This papers studies the connection betwe...... ambit processes and solutions to stochastic partial differential equations. We investigate this relationship from two angles: from the Walsh theory of martingale measures and from the viewpoint of the Lévy noise analysis....

Numerical approximation of null controls for the heat equation: Ill-posedness and remedies

International Nuclear Information System (INIS)

Münch, Arnaud; Zuazua, Enrique

2010-01-01

minimal L 2 -norm exhibit a singular highly oscillatory behavior near the final controllability time, which cannot be captured numerically. Standard techniques, such as Tychonoff's regularization or quasi-reversibility methods, allow a slight smoothing of the singularities but significantly reduce the quality of the approximation. In this paper we develop some more involved and less-standard approaches which turn out to be more efficient. We first discuss the advantages of using controls with compact support with respect to the time variable or the effect of adding numerical dissipative singular terms. We also develop the numerical version of the so-called transmutation method that allows writing the control of a heat process in terms of the corresponding control of the associated wave process, by means of a 'time convolution' with a one-dimensional controlled fundamental heat solution. This method, although it can be proved to converge, is also subtle in its computational implementation. Indeed, it requires using convergent numerical schemes for the control of the wave equation, a problem that, as mentioned above, is delicate in itself. But we also need to compute an accurate approximation of a controlled fundamental heat solution, an issue that requires its own analysis and significant numerical and computational new developments. These methods are thoroughly illustrated and discussed in the paper, accompanied by some numerical experiments in one space dimension that show the subtlety of the issue. These experiments allow one to compare the efficiency of the various methods. This is done in the case where the control is distributed in some subdomain of the domain where the heat process evolves but similar results and numerical experiments could be derived for other cases, such as the one in which the control acts on the boundary. The techniques we employ here can also be adapted to the multi-dimensional case

Feynman-Kac equations for reaction and diffusion processes

Science.gov (United States)

Hou, Ru; Deng, Weihua

2018-04-01

This paper provides a theoretical framework for deriving the forward and backward Feynman-Kac equations for the distribution of functionals of the path of a particle undergoing both diffusion and reaction processes. Once given the diffusion type and reaction rate, a specific forward or backward Feynman-Kac equation can be obtained. The results in this paper include those for normal/anomalous diffusions and reactions with linear/nonlinear rates. Using the derived equations, we apply our findings to compute some physical (experimentally measurable) statistics, including the occupation time in half-space, the first passage time, and the occupation time in half-interval with an absorbing or reflecting boundary, for the physical system with anomalous diffusion and spontaneous evanescence.

State-dependent differential Riccati equation to track control of time-varying systems with state and control nonlinearities.

Science.gov (United States)

Korayem, M H; Nekoo, S R

2015-07-01

This work studies an optimal control problem using the state-dependent Riccati equation (SDRE) in differential form to track for time-varying systems with state and control nonlinearities. The trajectory tracking structure provides two nonlinear differential equations: the state-dependent differential Riccati equation (SDDRE) and the feed-forward differential equation. The independence of the governing equations and stability of the controller are proven along the trajectory using the Lyapunov approach. Backward integration (BI) is capable of solving the equations as a numerical solution; however, the forward solution methods require the closed-form solution to fulfill the task. A closed-form solution is introduced for SDDRE, but the feed-forward differential equation has not yet been obtained. Different ways of solving the problem are expressed and analyzed. These include BI, closed-form solution with corrective assumption, approximate solution, and forward integration. Application of the tracking problem is investigated to control robotic manipulators possessing rigid or flexible joints. The intention is to release a general program for automatic implementation of an SDDRE controller for any manipulator that obeys the Denavit-Hartenberg (D-H) principle when only D-H parameters are received as input data. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Controllability and Stabilization of Bilinear and Semilinear Partial Differential Equations

DEFF Research Database (Denmark)

Krishnaswamy, Vijayaraghavan

The topic of the thesis is the investigation of the question of controllability of weakly nonlinear partial differntial equations. The method is based on the Hilbert Uniqueness Method.......The topic of the thesis is the investigation of the question of controllability of weakly nonlinear partial differntial equations. The method is based on the Hilbert Uniqueness Method....

The establishment of in-process plutonium mass equation in Rokkasho Reprocessing Plant

International Nuclear Information System (INIS)

Yamaya, Kosuke; Ebata, Takashi; Yamazaki, Yoshihiro; Kawai, Akio; Iwamoto, Tomonori

2008-01-01

At Rokkasho Reprocessing Plant (RRP), Active Test (AT) using actual spent fuels for the final confirmation of the equipment and the system has been performed toward the commercial operation. From the safeguards viewpoint, performance of material accountancy equipment is confirmed and data for evaluating parameters of the inspection equipment is obtained by making use of the AT period. RRP is applied to Near Real Time material Accountancy (NRTA). Under the NRTA scheme, the inventory at a cut-off time during process operation needs to be accounted for. There are some un-measurable inventories of plutonium in the process, which will be calculated from inventory estimation equations. The amount of these plutonium inventories calculated from the equations is so large that it is essential to improve the inventory estimation equations to be quite accurate. Therefore, correctness of the inventory estimation equations is evaluated by using process operation data obtained during AT. This paper describes the results of evaluating the inventory estimation equations by using the process operation data and the NRTA procedure under continuous operating condition as well. (author)

Global dynamics and control of a comprehensive nonlinear beam equation

International Nuclear Information System (INIS)

You Yuncheng; Taboada, M.

1994-01-01

A nonlinear hinged extensible elastic beam equation with the structural damping and Balakrishnan-Taylor damping of full exponent is studied as a general model for large space structures. It is proved that there exists an absorbing set in the energy space and that there exist inertial manifolds whose exponential attracting rates however are nonuniform. The control spillover problem associated with the stabilization of this equation is resolved by constructing a linear finite-dimensional feedback control based on the existence of inertial manifolds of the uncontrolled equation. Moreover, the results obtained are robust with respect to uncertainty in the structural parameters. (author). 5 refs

Model Predictive Control of Mineral Column Flotation Process

Directory of Open Access Journals (Sweden)

Yahui Tian

2018-06-01

Full Text Available Column flotation is an efficient method commonly used in the mineral industry to separate useful minerals from ores of low grade and complex mineral composition. Its main purpose is to achieve maximum recovery while ensuring desired product grade. This work addresses a model predictive control design for a mineral column flotation process modeled by a set of nonlinear coupled heterodirectional hyperbolic partial differential equations (PDEs and ordinary differential equations (ODEs, which accounts for the interconnection of well-stirred regions represented by continuous stirred tank reactors (CSTRs and transport systems given by heterodirectional hyperbolic PDEs, with these two regions combined through the PDEs’ boundaries. The model predictive control considers both optimality of the process operations and naturally present input and state/output constraints. For the discrete controller design, spatially varying steady-state profiles are obtained by linearizing the coupled ODE–PDE model, and then the discrete system is obtained by using the Cayley–Tustin time discretization transformation without any spatial discretization and/or without model reduction. The model predictive controller is designed by solving an optimization problem with input and state/output constraints as well as input disturbance to minimize the objective function, which leads to an online-solvable finite constrained quadratic regulator problem. Finally, the controller performance to keep the output at the steady state within the constraint range is demonstrated by simulation studies, and it is concluded that the optimal control scheme presented in this work makes this flotation process more efficient.

River water quality model no. 1 (RWQM1): II. Biochemical process equations

DEFF Research Database (Denmark)

Reichert, P.; Borchardt, D.; Henze, Mogens

2001-01-01

In this paper, biochemical process equations are presented as a basis for water quality modelling in rivers under aerobic and anoxic conditions. These equations are not new, but they summarise parts of the development over the past 75 years. The primary goals of the presentation are to stimulate...... transformation processes. This paper is part of a series of three papers. In the first paper, the general modelling approach is described; in the present paper, the biochemical process equations of a complex model are presented; and in the third paper, recommendations are given for the selection of a reasonable...

Optimal control penalty finite elements - Applications to integrodifferential equations

Science.gov (United States)

Chung, T. J.

The application of the optimal-control/penalty finite-element method to the solution of integrodifferential equations in radiative-heat-transfer problems (Chung et al.; Chung and Kim, 1982) is discussed and illustrated. The nonself-adjointness of the convective terms in the governing equations is treated by utilizing optimal-control cost functions and employing penalty functions to constrain auxiliary equations which permit the reduction of second-order derivatives to first order. The OCPFE method is applied to combined-mode heat transfer by conduction, convection, and radiation, both without and with scattering and viscous dissipation; the results are presented graphically and compared to those obtained by other methods. The OCPFE method is shown to give good results in cases where standard Galerkin FE fail, and to facilitate the investigation of scattering and dissipation effects.

Stepless control system for reciprocating compressors: energy savings + process control improvement

Energy Technology Data Exchange (ETDEWEB)

Grande, Alvaro; Wenisch, Markus [Hoerbiger Ventilwerke GmbH and Co KG, Wien (Austria); Jacobs, Denis [HOERBIGER do Brasil Industria de Equipamentos, Cajamar, SP (Brazil)

2012-07-01

In the past, the capacity of reciprocating compressors was typically controlled by on/off unloaders (step-control) and recycle valves. But due to the fact that the power ratings of new reciprocating compressors for the oil and gas industry increase significantly, advanced control systems are required to reduce power costs and save energy. On top of that, multi-stage compressors are frequently integrated into complex process plants that demand precise control and operational flexibility. There are several solutions for this equation, but maybe the most successful is the use of the reverse flow principle applied to an electronically controlled and hydraulically actuated suction valve unloaders system. (author)

Optimal Wentzell Boundary Control of Parabolic Equations

International Nuclear Information System (INIS)

Luo, Yousong

2017-01-01

This paper deals with a class of optimal control problems governed by an initial-boundary value problem of a parabolic equation. The case of semi-linear boundary control is studied where the control is applied to the system via the Wentzell boundary condition. The differentiability of the state variable with respect to the control is established and hence a necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained convex problems. A second order condition is also derived.

Optimal Wentzell Boundary Control of Parabolic Equations

Energy Technology Data Exchange (ETDEWEB)

Luo, Yousong, E-mail: yousong.luo@rmit.edu.au [RMIT University, School of Mathematical and Geospatial Sciences (Australia)

2017-04-15

This paper deals with a class of optimal control problems governed by an initial-boundary value problem of a parabolic equation. The case of semi-linear boundary control is studied where the control is applied to the system via the Wentzell boundary condition. The differentiability of the state variable with respect to the control is established and hence a necessary condition is derived for the optimal solution in the case of both unconstrained and constrained problems. The condition is also sufficient for the unconstrained convex problems. A second order condition is also derived.

Integration Processes of Delay Differential Equation Based on Modified Laguerre Functions

Directory of Open Access Journals (Sweden)

Yeguo Sun

2012-01-01

Full Text Available We propose long-time convergent numerical integration processes for delay differential equations. We first construct an integration process based on modified Laguerre functions. Then we establish its global convergence in certain weighted Sobolev space. The proposed numerical integration processes can also be used for systems of delay differential equations. We also developed a technique for refinement of modified Laguerre-Radau interpolations. Lastly, numerical results demonstrate the spectral accuracy of the proposed method and coincide well with analysis.

Reduced equations of motion for quantum systems driven by diffusive Markov processes.

Science.gov (United States)

Sarovar, Mohan; Grace, Matthew D

2012-09-28

The expansion of a stochastic Liouville equation for the coupled evolution of a quantum system and an Ornstein-Uhlenbeck process into a hierarchy of coupled differential equations is a useful technique that simplifies the simulation of stochastically driven quantum systems. We expand the applicability of this technique by completely characterizing the class of diffusive Markov processes for which a useful hierarchy of equations can be derived. The expansion of this technique enables the examination of quantum systems driven by non-Gaussian stochastic processes with bounded range. We present an application of this extended technique by simulating Stark-tuned Förster resonance transfer in Rydberg atoms with nonperturbative position fluctuations.

A dynamic uranium-leaching model for process-control studies

International Nuclear Information System (INIS)

Vetter, D.A.; Barker, I.J.; Turner, G.A.

1989-01-01

The modelling of the uranium-leaching process, and the logging of data from a plant for the evaluation of the model, are reported. A phenomenological approach was adopted in the development of the model. A set of eight chemical reactions was chosen to represent the complex chemistry of the process, and kinetic expressions for these reactions were incorporated in differential equations representing mass and energy balances. These equations were coded in FORTRAN to form a program that simulated the process, and that allowed averaged and continuous data from the plant to be compared with the model. This allowed the model to be 'tuned', and to reveal a number of minor problems with the control infrastructure on the plant. 7 figs., 21 refs

Optimal Control for the Degenerate Elliptic Logistic Equation

International Nuclear Information System (INIS)

Delgado, M.; Montero, J.A.; Suarez, A.

2002-01-01

We consider the optimal control of harvesting the diffusive degenerate elliptic logistic equation. Under certain assumptions, we prove the existence and uniqueness of an optimal control. Moreover, the optimality system and a characterization of the optimal control are also derived. The sub-supersolution method, the singular eigenvalue problem and differentiability with respect to the positive cone are the techniques used to obtain our results

Tap density equations of granular powders based on the rate process theory and the free volume concept.

Science.gov (United States)

Hao, Tian

2015-02-28

The tap density of a granular powder is often linked to the flowability via the Carr index that measures how tight a powder can be packed, under an assumption that more easily packed powders usually flow poorly. Understanding how particles are packed is important for revealing why a powder flows better than others. There are two types of empirical equations that were proposed to fit the experimental data of packing fractions vs. numbers of taps in the literature: the inverse logarithmic and the stretched exponential. Using the rate process theory and the free volume concept under the assumption that particles will obey similar thermodynamic laws during the tapping process if the "granular temperature" is defined in a different way, we obtain the tap density equations, and they are reducible to the two empirical equations currently widely used in literature. Our equations could potentially fit experimental data better with an additional adjustable parameter. The tapping amplitude and frequency, the weight of the granular materials, and the environmental temperature are grouped into this parameter that weighs the pace of the packing process. The current results, in conjunction with our previous findings, may imply that both "dry" (granular) and "wet" (colloidal and polymeric) particle systems are governed by the same physical mechanisms in term of the role of the free volume and how particles behave (a rate controlled process).

Stochastic optimal control in infinite dimension dynamic programming and HJB equations

CERN Document Server

Fabbri, Giorgio; Święch, Andrzej

2017-01-01

Providing an introduction to stochastic optimal control in infinite dimension, this book gives a complete account of the theory of second-order HJB equations in infinite-dimensional Hilbert spaces, focusing on its applicability to associated stochastic optimal control problems. It features a general introduction to optimal stochastic control, including basic results (e.g. the dynamic programming principle) with proofs, and provides examples of applications. A complete and up-to-date exposition of the existing theory of viscosity solutions and regular solutions of second-order HJB equations in Hilbert spaces is given, together with an extensive survey of other methods, with a full bibliography. In particular, Chapter 6, written by M. Fuhrman and G. Tessitore, surveys the theory of regular solutions of HJB equations arising in infinite-dimensional stochastic control, via BSDEs. The book is of interest to both pure and applied researchers working in the control theory of stochastic PDEs, and in PDEs in infinite ...

Perturbation theory for continuous stochastic equations

International Nuclear Information System (INIS)

Chechetkin, V.R.; Lutovinov, V.S.

1987-01-01

The various general perturbational schemes for continuous stochastic equations are considered. These schemes have many analogous features with the iterational solution of Schwinger equation for S-matrix. The following problems are discussed: continuous stochastic evolution equations for probability distribution functionals, evolution equations for equal time correlators, perturbation theory for Gaussian and Poissonian additive noise, perturbation theory for birth and death processes, stochastic properties of systems with multiplicative noise. The general results are illustrated by diffusion-controlled reactions, fluctuations in closed systems with chemical processes, propagation of waves in random media in parabolic equation approximation, and non-equilibrium phase transitions in systems with Poissonian breeding centers. The rate of irreversible reaction X + X → A (Smoluchowski process) is calculated with the use of general theory based on continuous stochastic equations for birth and death processes. The threshold criterion and range of fluctuational region for synergetic phase transition in system with Poissonian breeding centers are also considered. (author)

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

International Nuclear Information System (INIS)

Granita; Bahar, A.

2015-01-01

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found

Stochastic differential equation model for linear growth birth and death processes with immigration and emigration

Energy Technology Data Exchange (ETDEWEB)

Granita, E-mail: granitafc@gmail.com [Dept. Mathematical Education, State Islamic University of Sultan Syarif Kasim Riau, 28293 Indonesia and Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor (Malaysia); Bahar, A. [Dept. of Mathematical Science, Universiti Teknologi Malaysia, 81310,Johor Malaysia and UTM Center for Industrial and Applied Mathematics (UTM-CIAM) (Malaysia)

2015-03-09

This paper discusses on linear birth and death with immigration and emigration (BIDE) process to stochastic differential equation (SDE) model. Forward Kolmogorov equation in continuous time Markov chain (CTMC) with a central-difference approximation was used to find Fokker-Planckequation corresponding to a diffusion process having the stochastic differential equation of BIDE process. The exact solution, mean and variance function of BIDE process was found.

Optimal control of the process of cultivation in the conditions of infection

Directory of Open Access Journals (Sweden)

N. V. Sukhanova

2016-01-01

Full Text Available The article presents a way of solving of the optimal control problem of antibiotic feeding under condition of infection, consisting in the selection of the optimal control in the field of admissible control, with the aim of achieving a compromise between the losses in production due to the presence of foreign microflora, and the cost of its suppression due to the application of antibiotic. The presence of other microorganisms in the finished product, in particular of the “wild“ ones, considerably impairs the quality indicators of the final product (in particular, it reduces the storage time. In peculiar conditions of production it is possible to improve the quality of target product due to elimination of infection, including, when used antibiotics in the process of cultivation, but due to the lack of efficient algorithms and control systems of their supply the question is still open. We use the system of Lotka-Volterra adapted for microbiological process as a mathematical model adequately describing the situation of competitive interaction of two populations of microorganisms (useful and “wild“ ones due to the consumption of one resource. The aim is to find a control law U(t belonging to the field of admissible control. The control that affords minimum to the optimization criterion in accordance with the principle of maximum is defined by the condition of the maximum of Hamilton function and the resulting canonical system of equations. The modified conjugated system of equations in matrix form is obtained. The solution of system of differential-different equations in the analytical form is found using the method of coordinate transformation. As a result an optimal control law is found (with regard to the selected criterion. This is the control law of application of the antibiotic, allowing to control the concentration of foreign microflora in the process of cultivation of microorganisms and accounting for the specific

A stochastic model of multiple scattering of charged particles: process, transport equation and solutions

International Nuclear Information System (INIS)

Papiez, L.; Moskvin, V.; Tulovsky, V.

2001-01-01

The process of angular-spatial evolution of multiple scattering of charged particles can be described by a special case of Boltzmann integro-differential equation called Lewis equation. The underlying stochastic process for this evolution is the compound Poisson process on the surface of the unit sphere. The significant portion of events that constitute compound Poisson process that describes multiple scattering have diffusional character. This property allows to analyze the process of angular-spatial evolution of multiple scattering of charged particles as combination of soft and hard collision processes and compute appropriately its transition densities. These computations provide a method of the approximate solution to the Lewis equation. (orig.)

Existence of the Optimal Control for Stochastic Boundary Control Problems Governed by Semilinear Parabolic Equations

Directory of Open Access Journals (Sweden)

Weifeng Wang

2014-01-01

Full Text Available We study an optimal control problem governed by a semilinear parabolic equation, whose control variable is contained only in the boundary condition. An existence theorem for the optimal control is obtained.

Selection of site specific vibration equation by using analytic hierarchy process in a quarry

Energy Technology Data Exchange (ETDEWEB)

Kalayci, Ulku, E-mail: ukalayci@istanbul.edu.tr; Ozer, Umit, E-mail: uozer@istanbul.edu.tr

2016-01-15

This paper presents a new approach for the selection of the most accurate SSVA (Site Specific Vibration Attenuation) equation for blasting processes in a quarry located near settlements in Istanbul, Turkey. In this context, the SSVA equations obtained from the same study area in the literature were considered in terms of distance between the shot points and buildings and the amount of explosive charge. In this purpose, 11 different SSVA equations obtained from the study area in the past 12 years, forecasting capabilities according to designated new conditions, using 102 vibration records as test data obtained from the study area was investigated. In this study, AHP (Analytic Hierarchy Process) was selected as an analysis method in order to determine the most accurate equation among 11 SSAV equations, and the parameters such as year, distance, charge, and r{sup 2} of the equations were used as criteria for AHP. Finally, the most appropriate equation was selected among the existing ones, and the process of selecting according to different target criteria was presented. Furthermore, it was noted that the forecasting results of the selected equation is more accurate than that formed using the test results. - Highlights: • The optimum Site Specific Vibration Attenuation equation for blasting in a quarry located near settlements was determined. • It is indicated that SSVA equations changing over the years don’t give always accurate estimates at changing conditions. • Selection of the blast induced SSVA equation was made using AHP. • Equation selection method was highlighted based on parameters such as charge, distance, and quarry geometry changes (year).

Selection of site specific vibration equation by using analytic hierarchy process in a quarry

International Nuclear Information System (INIS)

Kalayci, Ulku; Ozer, Umit

2016-01-01

This paper presents a new approach for the selection of the most accurate SSVA (Site Specific Vibration Attenuation) equation for blasting processes in a quarry located near settlements in Istanbul, Turkey. In this context, the SSVA equations obtained from the same study area in the literature were considered in terms of distance between the shot points and buildings and the amount of explosive charge. In this purpose, 11 different SSVA equations obtained from the study area in the past 12 years, forecasting capabilities according to designated new conditions, using 102 vibration records as test data obtained from the study area was investigated. In this study, AHP (Analytic Hierarchy Process) was selected as an analysis method in order to determine the most accurate equation among 11 SSAV equations, and the parameters such as year, distance, charge, and r"2 of the equations were used as criteria for AHP. Finally, the most appropriate equation was selected among the existing ones, and the process of selecting according to different target criteria was presented. Furthermore, it was noted that the forecasting results of the selected equation is more accurate than that formed using the test results. - Highlights: • The optimum Site Specific Vibration Attenuation equation for blasting in a quarry located near settlements was determined. • It is indicated that SSVA equations changing over the years don’t give always accurate estimates at changing conditions. • Selection of the blast induced SSVA equation was made using AHP. • Equation selection method was highlighted based on parameters such as charge, distance, and quarry geometry changes (year).

Control Operator for the Two-Dimensional Energized Wave Equation

Directory of Open Access Journals (Sweden)

Sunday Augustus REJU

2006-07-01

Full Text Available This paper studies the analytical model for the construction of the two-dimensional Energized wave equation. The control operator is given in term of space and time t independent variables. The integral quadratic objective cost functional is subject to the constraint of two-dimensional Energized diffusion, Heat and a source. The operator that shall be obtained extends the Conjugate Gradient method (ECGM as developed by Hestenes et al (1952, [1]. The new operator enables the computation of the penalty cost, optimal controls and state trajectories of the two-dimensional energized wave equation when apply to the Conjugate Gradient methods in (Waziri & Reju, LEJPT & LJS, Issues 9, 2006, [2-4] to appear in this series.

Solution of generalized control system equations at steady state

International Nuclear Information System (INIS)

Vilim, R.B.

1987-01-01

Although a number of reactor systems codes feature generalized control system models, none of the models offer a steady-state solution finder. Indeed, if a transient is to begin from steady-state conditions, the user must provide estimates for the control system initial conditions and run a null transient until the plant converges to steady state. Several such transients may have to be run before values for control system demand signals are found that produce the desired plant steady state. The intent of this paper is (a) to present the control system equations assumed in the SASSYS reactor systems code and to identify the appropriate set of initial conditions, (b) to describe the generalized block diagram approach used to represent these equations, and (c) to describe a solution method and algorithm for computing these initial conditions from the block diagram. The algorithm has been installed in the SASSYS code for use with the code's generalized control system model. The solution finder greatly enhances the effectiveness of the code and the efficiency of the user in running it

40 CFR 63.496 - Back-end process provisions-procedures to determine compliance using control or recovery devices.

Science.gov (United States)

2010-07-01

... boiler or process heater. (iii) The control efficiency of the boiler or process heater shall be calculated using Equation 29. ER05SE96.027 where: R=Control efficiency of boiler or process heater, percent..., the control efficiency of the boiler or process heater shall be determined using the procedures in...

Controllability for a Wave Equation with Moving Boundary

Directory of Open Access Journals (Sweden)

Lizhi Cui

2014-01-01

Full Text Available We investigate the controllability for a one-dimensional wave equation in domains with moving boundary. This model characterizes small vibrations of a stretched elastic string when one of the two endpoints varies. When the speed of the moving endpoint is less than 1-1/e, by Hilbert uniqueness method, sidewise energy estimates method, and multiplier method, we get partial Dirichlet boundary controllability. Moreover, we will give a sharper estimate on controllability time that only depends on the speed of the moving endpoint.

NONLINEAR MODEL PREDICTIVE CONTROL OF CHEMICAL PROCESSES

Directory of Open Access Journals (Sweden)

SILVA R. G.

1999-01-01

Full Text Available A new algorithm for model predictive control is presented. The algorithm utilizes a simultaneous solution and optimization strategy to solve the model's differential equations. The equations are discretized by equidistant collocation, and along with the algebraic model equations are included as constraints in a nonlinear programming (NLP problem. This algorithm is compared with the algorithm that uses orthogonal collocation on finite elements. The equidistant collocation algorithm results in simpler equations, providing a decrease in computation time for the control moves. Simulation results are presented and show a satisfactory performance of this algorithm.

Population density equations for stochastic processes with memory kernels

Science.gov (United States)

Lai, Yi Ming; de Kamps, Marc

2017-06-01

We present a method for solving population density equations (PDEs)-a mean-field technique describing homogeneous populations of uncoupled neurons—where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. The method combines recent developments in two different disciplines that traditionally have had limited interaction: computational neuroscience and the theory of random networks. The method uses a geometric binning scheme, based on the method of characteristics, to capture the deterministic neurodynamics of the population, separating the deterministic and stochastic process cleanly. We can independently vary the choice of the deterministic model and the model for the stochastic process, leading to a highly modular numerical solution strategy. We demonstrate this by replacing the master equation implicit in many formulations of the PDE formalism by a generalization called the generalized Montroll-Weiss equation—a recent result from random network theory—describing a random walker subject to transitions realized by a non-Markovian process. We demonstrate the method for leaky- and quadratic-integrate and fire neurons subject to spike trains with Poisson and gamma-distributed interspike intervals. We are able to model jump responses for both models accurately to both excitatory and inhibitory input under the assumption that all inputs are generated by one renewal process.

Mobile point sensors and actuators in the controllability theory of partial differential equations

CERN Document Server

Khapalov, Alexander Y

2017-01-01

This book presents a concise study of controllability theory of partial differential equations when they are equipped with actuators and/or sensors that are finite dimensional at every moment of time. Based on the author’s extensive research in the area of controllability theory, this monograph specifically focuses on the issues of controllability, observability, and stabilizability for parabolic and hyperbolic partial differential equations. The topics in this book also cover related applied questions such as the problem of localization of unknown pollution sources based on information obtained from point sensors that arise in environmental monitoring. Researchers and graduate students interested in controllability theory of partial differential equations and its applications will find this book to be an invaluable resource to their studies.

On the controllability of the semilinear heat equation with hysteresis

International Nuclear Information System (INIS)

Bagagiolo, Fabio

2012-01-01

We study the null controllability problem for a semilinear parabolic equation, with hysteresis entering in the semilinearity. Under suitable hypotheses, we prove the controllability result and explicitly treat the cases where the hysteresis relationship is given by a Play or a Preisach operator.

Process control of a gaseous diffusion cascade for isotopic separation of uranium

International Nuclear Information System (INIS)

Bilous, Olegh; Doneddu, F.

1986-01-01

Various aspects of dynamics and process control of a gaseous diffusion cascade are described. The cascade enriches uranium hexafluoride gas (HEX) in the light isotope of uranium in a countercurrent flow. The linearized equations describing the equipment models are derived. One can then write the mass balances on the high and low pressure sides of a stage and the overall heat balance of a stage. These heat and mass balances are linear difference equations on the stage number with time derivatives which are then replaced by jω factors to examine the effects of cyclic perturbations. The mass balances are first treated for a cascade section of 12 stages with temperatures assumed constant. The effect of a perturbation of pressure on one of the stages is described first for ω=0 (that is for steady state). Then Nyquist diagrams are obtained. The effect of transport change is also studied. Then temperature is introduced, assuming pressures to be constant. The cases of a section of 12 stages and a cascade of 120 stages are examined. Again Nyquist diagrams of temperature frequency response to a perturbation on one stage are calculated. Process control of the heat exchangers is introduced. The method used to solve the difference equations may be applied to other types of perturbations and to the complete scheme of process control. (author)

Dissolution process analysis using model-free Noyes-Whitney integral equation.

Science.gov (United States)

Hattori, Yusuke; Haruna, Yoshimasa; Otsuka, Makoto

2013-02-01

Drug dissolution process of solid dosages is theoretically described by Noyes-Whitney-Nernst equation. However, the analysis of the process is demonstrated assuming some models. Normally, the model-dependent methods are idealized and require some limitations. In this study, Noyes-Whitney integral equation was proposed and applied to represent the drug dissolution profiles of a solid formulation via the non-linear least squares (NLLS) method. The integral equation is a model-free formula involving the dissolution rate constant as a parameter. In the present study, several solid formulations were prepared via changing the blending time of magnesium stearate (MgSt) with theophylline monohydrate, α-lactose monohydrate, and crystalline cellulose. The formula could excellently represent the dissolution profile, and thereby the rate constant and specific surface area could be obtained by NLLS method. Since the long time blending coated the particle surface with MgSt, it was found that the water permeation was disturbed by its layer dissociating into disintegrant particles. In the end, the solid formulations were not disintegrated; however, the specific surface area gradually increased during the process of dissolution. The X-ray CT observation supported this result and demonstrated that the rough surface was dominant as compared to dissolution, and thus, specific surface area of the solid formulation gradually increased. Copyright © 2012 Elsevier B.V. All rights reserved.

Nonparametric estimation of stochastic differential equations with sparse Gaussian processes.

Science.gov (United States)

García, Constantino A; Otero, Abraham; Félix, Paulo; Presedo, Jesús; Márquez, David G

2017-08-01

The application of stochastic differential equations (SDEs) to the analysis of temporal data has attracted increasing attention, due to their ability to describe complex dynamics with physically interpretable equations. In this paper, we introduce a nonparametric method for estimating the drift and diffusion terms of SDEs from a densely observed discrete time series. The use of Gaussian processes as priors permits working directly in a function-space view and thus the inference takes place directly in this space. To cope with the computational complexity that requires the use of Gaussian processes, a sparse Gaussian process approximation is provided. This approximation permits the efficient computation of predictions for the drift and diffusion terms by using a distribution over a small subset of pseudosamples. The proposed method has been validated using both simulated data and real data from economy and paleoclimatology. The application of the method to real data demonstrates its ability to capture the behavior of complex systems.

EQUATIONS FOR GAS RELEASING PROCESS FROM PRESSURIZED VESSELS IN ODH EVALUATION

International Nuclear Information System (INIS)

JIA, L.X.; WANG, L.

2001-01-01

IN THE EVALUATION OF ODH, THE CALCULATION OF THE SPILL RATE FROM THE PRESSURIZED VESSEL IS THE CENTRAL TASK. THE ACCURACY OF THE ENGINEERING ESTIMATION BECOMES ONE OF THE SAFETY DESIGN ISSUES. THIS PAPER SUMMARIZES THE EQUATIONS FOR THE OXYGEN CONCENTRATION CALCULATION IN DIFFERENT CASES, AND DISCUSSES THE EQUATIONS FOR THE GAS RELEASE PROCESS CALCULATION BOTH FOR THE HIGH-PRESSURE GAS TANK AND THE LOW-TEMPERATURE LIQUID CONTAINER

Solving Algebraic Riccati Equation Real Time for Integrated Vehicle Dynamics Control

NARCIS (Netherlands)

Kunnappillil Madhusudhanan, A; Corno, M.; Bonsen, B.; Holweg, E.

2012-01-01

In this paper we present a comparison study of different computational methods to implement State Dependent Riccati Equation (SDRE) based control in real time for a vehicle dynamics control application. Vehicles are mechatronic systems with nonlinear dynamics. One of the promising nonlinear control

From stochastic processes to numerical methods: A new scheme for solving reaction subdiffusion fractional partial differential equations

Energy Technology Data Exchange (ETDEWEB)

Angstmann, C.N.; Donnelly, I.C. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Henry, B.I., E-mail: B.Henry@unsw.edu.au [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia); Jacobs, B.A. [School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050 (South Africa); DST–NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) (South Africa); Langlands, T.A.M. [Department of Mathematics and Computing, University of Southern Queensland, Toowoomba QLD 4350 (Australia); Nichols, J.A. [School of Mathematics and Statistics, UNSW Australia, Sydney NSW 2052 (Australia)

2016-02-15

We have introduced a new explicit numerical method, based on a discrete stochastic process, for solving a class of fractional partial differential equations that model reaction subdiffusion. The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks. We show that the diffusion limit of the master equations recovers the fractional partial differential equation of interest. This limiting procedure guarantees the consistency of the numerical scheme. The positivity of the solution and stability results are simply obtained, provided that the underlying process is well posed. We also show that the method can be applied to standard reaction–diffusion equations. This work highlights the broader applicability of using discrete stochastic processes to provide numerical schemes for partial differential equations, including fractional partial differential equations.

Tuning of Controller for Type 1 Diabetes Treatment with Stochastic Differential Equations

DEFF Research Database (Denmark)

Duun-Henriksen, Anne Katrine; Boiroux, Dimitri; Schmidt, Signe

2012-01-01

due to the noise corrupted observations from the CGM. In this paper we present a method to estimate the optimal Kalman gain in the controller based on stochastic differential equation modeling. With this model type we could estimate the process noise and observation noise separately based on data from......People with type 1 diabetes need several insulin injections every day to keep their blood glucose level in the normal range and thereby avoiding the acute and long term complications of diabetes. One of the recent treatments consists of a pump injecting insulin into the subcutaneous layer combined...

On the Controllability of a Differential Equation with Delayed and Advanced Arguments

Directory of Open Access Journals (Sweden)

Raúl Manzanilla

2010-01-01

Full Text Available A semigroup theory for a differential equation with delayed and advanced arguments is developed, with a detailed description of the infinitesimal generator. This in turn allows to study the exact controllability of the equation, by rewriting it as a classical Cauchy problem.

Conditions for the existence of control functions in nonseparable simultaneous equations models

OpenAIRE

Blundell, Richard; Matzkin, Rosa L.

2010-01-01

The control function approach (Heckman and Robb (1985)) in a system of linear simultaneous equations provides a convenient procedure to estimate one of the functions in the system using reduced form residuals from the other functions as additional regressors. The conditions on the structural system under which this procedure can be used in nonlinear and nonparametric simultaneous equations has thus far been unknown. In this note, we define a new property of functions called control function s...

Direct Yaw Control of Vehicle using State Dependent Riccati Equation with Integral Terms

Directory of Open Access Journals (Sweden)

SANDHU, F.

2016-05-01

Full Text Available Direct yaw control of four-wheel vehicles using optimal controllers such as the linear quadratic regulator (LQR and the sliding mode controller (SMC either considers only certain parameters constant in the nonlinear equations of vehicle model or totally neglect their effects to obtain simplified models, resulting in loss of states for the system. In this paper, a modified state-dependent Ricatti equation method obtained by the simplification of the vehicle model is proposed. This method overcomes the problem of the lost states by including state integrals. The results of the proposed system are compared with the sliding mode slip controller and state-dependent Ricatti equation method using high fidelity vehicle model in the vehicle simulation software package, Carsim. Results show 38% reduction in the lateral velocity, 34% reduction in roll and 16% reduction in excessive yaw by only increasing the fuel consumption by 6.07%.

Integrated vehicle dynamics control using State Dependent Riccati Equations

NARCIS (Netherlands)

Bonsen, B.; Mansvelders, R.; Vermeer, E.

2010-01-01

In this paper we discuss a State Dependent Riccati Equations (SDRE) solution for Integrated Vehicle Dynamics Control (IVDC). The SDRE approach is a nonlinear variant of the well known Linear Quadratic Regulator (LQR) and implements a quadratic cost function optimization. A modified version of this

Numerical simulation of the control of the three-dimensional transition process in boundary layers

Science.gov (United States)

Kral, L. D.; Fasel, H. F.

1990-01-01

Surface heating techniques to control the three-dimensional laminar-turbulent transition process are numerically investigated for a water boundary layer. The Navier-Stokes and energy equations are solved using a fully implicit finite difference/spectral method. The spatially evolving boundary layer is simulated. Results of both passive and active methods of control are shown for small amplitude two-dimensional and three-dimensional disturbance waves. Control is also applied to the early stages of the secondary instability process using passive or active control techniques.

Management of Industrial Processes with Programmable Logic Controller

Directory of Open Access Journals (Sweden)

Marius Tufoi

2009-10-01

Full Text Available In a modern economy, automation (the control is primarily to raise the competitiveness of a product, either directly through price or quality, or indirectly through the improvement of working conditions of staff productive. The control of industrial processes involves the management of dynamic systems that have continuous states. These systems are described by differential equations and, in general, analog inputs and outputs. Management of these systems is achieved, in general, with classical automation, by automation or with analog computers which contains modules with input / output analog performance. If states, inputs and outputs of a system can be modeled using binary variables, then these systems can be driven with Programmable Logic Controller.

ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

KAUST Repository

Calatroni, Luca

2013-08-01

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.

ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

KAUST Repository

Calatroni, Luca; Dü ring, Bertram; Schö nlieb, Carola-Bibiane

2013-01-01

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H -1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation.

Control and Stabilization of the Benjamin-Ono Equation in {L^2({{T})}}

Science.gov (United States)

Laurent, Camille; Linares, Felipe; Rosier, Lionel

2015-12-01

We study the control and stabilization of the Benjamin-Ono equation in {L^2({T})}, the lowest regularity where the initial value problem is well-posed. This problem was already initiated in Linares and Rosier (Trans Am Math Soc 367:4595-4626, 2015) where a stronger stabilization term was used (that makes the equation of parabolic type in the control zone). Here we employ a more natural stabilization term related to the L 2-norm. Moreover, by proving a theorem of controllability in L 2, we manage to prove the global controllability in large time. Our analysis relies strongly on the bilinear estimates proved in Molinet and Pilod (Anal PDE 5:365-395, 2012) and some new extension of these estimates established here.

On the control of the chaotic attractors of the 2-d Navier-Stokes equations.

Science.gov (United States)

Smaoui, Nejib; Zribi, Mohamed

2017-03-01

The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, R e . Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.

Stochastic modeling of stock price process induced from the conjugate heat equation

Science.gov (United States)

Paeng, Seong-Hun

2015-02-01

Currency can be considered as a ruler for values of commodities. Then the price is the measured value by the ruler. We can suppose that inflation and variation of exchange rate are caused by variation of the scale of the ruler. In geometry, variation of the scale means that the metric is time-dependent. The conjugate heat equation is the modified heat equation which satisfies the heat conservation law for the time-dependent metric space. We propose a new model of stock prices by using the stochastic process whose transition probability is determined by the kernel of the conjugate heat equation. Our model of stock prices shows how the volatility term is affected by inflation and exchange rate. This model modifies the Black-Scholes equation in light of inflation and exchange rate.

Lumping of degree-based mean-field and pair-approximation equations for multistate contact processes

Science.gov (United States)

Kyriakopoulos, Charalampos; Grossmann, Gerrit; Wolf, Verena; Bortolussi, Luca

2018-01-01

Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information-spreading networks. While devising stochastic models of such processes is relatively easy, analyzing them is very challenging from a computational point of view, particularly for large networks appearing in real applications. One strategy to reduce the complexity of their analysis is to rely on approximations, often in terms of a set of differential equations capturing the evolution of a random node, distinguishing nodes with different topological contexts (i.e., different degrees of different neighborhoods), such as degree-based mean-field (DBMF), approximate-master-equation (AME), or pair-approximation (PA) approaches. The number of differential equations so obtained is typically proportional to the maximum degree kmax of the network, which is much smaller than the size of the master equation of the underlying stochastic model, yet numerically solving these equations can still be problematic for large kmax. In this paper, we consider AME and PA, extended to cope with multiple local states, and we provide an aggregation procedure that clusters together nodes having similar degrees, treating those in the same cluster as indistinguishable, thus reducing the number of equations while preserving an accurate description of global observables of interest. We also provide an automatic way to build such equations and to identify a small number of degree clusters that give accurate results. The method is tested on several case studies, where it shows a high level of compression and a reduction of computational time of several orders of magnitude for large networks, with minimal loss in accuracy.

Fast engineering optimization: A novel highly effective control parameterization approach for industrial dynamic processes.

Science.gov (United States)

Liu, Ping; Li, Guodong; Liu, Xinggao

2015-09-01

Control vector parameterization (CVP) is an important approach of the engineering optimization for the industrial dynamic processes. However, its major defect, the low optimization efficiency caused by calculating the relevant differential equations in the generated nonlinear programming (NLP) problem repeatedly, limits its wide application in the engineering optimization for the industrial dynamic processes. A novel highly effective control parameterization approach, fast-CVP, is first proposed to improve the optimization efficiency for industrial dynamic processes, where the costate gradient formulae is employed and a fast approximate scheme is presented to solve the differential equations in dynamic process simulation. Three well-known engineering optimization benchmark problems of the industrial dynamic processes are demonstrated as illustration. The research results show that the proposed fast approach achieves a fine performance that at least 90% of the computation time can be saved in contrast to the traditional CVP method, which reveals the effectiveness of the proposed fast engineering optimization approach for the industrial dynamic processes. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Dissipative Structures of the Kuramoto–Sivashinsky Equation

Directory of Open Access Journals (Sweden)

N. A. Kudryashov

2015-01-01

Full Text Available In the present work, we study the features of dissipative structures formation described by the periodic boundary value problem for the Kuramoto-Sivashinsky equation. The numerical algorithm which is based on the pseudospectral method is presented. We prove the efficiency and accuracy of the proposed numerical method on the exact solution of the equation considered. Using this approach, we performed the numerical simulation of dissipative structure formations described by the Kuramoto–Sivashinsky equation. The influence of the problem parameters on these processes are studied. The quantitative and qualitative characteristics of dissipative structure formations are described. We have shown that there is a value of the control parameter at which the processes of dissipative structure formation are observed. In particular, using the cyclic convolution we define the average value of this parameter. Also, we find the dependence of the amplitude of the structures on the value of control parameter.

Novel Numerical Methods for Optimal Control Problems Involving Fractional-Order Differential Equations

Science.gov (United States)

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

Finite difference approximation of control via the potential in a 1-D Schrodinger equation

Directory of Open Access Journals (Sweden)

K. Kime

2000-04-01

Full Text Available We consider the problem of steering given initial data to given terminal data via a time-dependent potential, the control, in a 1-D Schrodinger equation. We determine a condition for existence of a transferring potential within our approximation. Using Maple, we give equations for the control and also examples in which the potential is restricted to be centralized and to be a step potential.

Control of Stochastic Master Equation Models of Genetic Regulatory Networks by Approximating Their Average Behavior

Science.gov (United States)

Umut Caglar, Mehmet; Pal, Ranadip

2010-10-01

The central dogma of molecular biology states that ``information cannot be transferred back from protein to either protein or nucleic acid.'' However, this assumption is not exactly correct in most of the cases. There are a lot of feedback loops and interactions between different levels of systems. These types of interactions are hard to analyze due to the lack of data in the cellular level and probabilistic nature of interactions. Probabilistic models like Stochastic Master Equation (SME) or deterministic models like differential equations (DE) can be used to analyze these types of interactions. SME models based on chemical master equation (CME) can provide detailed representation of genetic regulatory system, but their use is restricted by the large data requirements and computational costs of calculations. The differential equations models on the other hand, have low calculation costs and much more adequate to generate control procedures on the system; but they are not adequate to investigate the probabilistic nature of interactions. In this work the success of the mapping between SME and DE is analyzed, and the success of a control policy generated by DE model with respect to SME model is examined. Index Terms--- Stochastic Master Equation models, Differential Equation Models, Control Policy Design, Systems biology

A New Control Paradigm for Stochastic Differential Equations

Science.gov (United States)

Schmid, Matthias J. A.

This study presents a novel comprehensive approach to the control of dynamic systems under uncertainty governed by stochastic differential equations (SDEs). Large Deviations (LD) techniques are employed to arrive at a control law for a large class of nonlinear systems minimizing sample path deviations. Thereby, a paradigm shift is suggested from point-in-time to sample path statistics on function spaces. A suitable formal control framework which leverages embedded Freidlin-Wentzell theory is proposed and described in detail. This includes the precise definition of the control objective and comprises an accurate discussion of the adaptation of the Freidlin-Wentzell theorem to the particular situation. The new control design is enabled by the transformation of an ill-posed control objective into a well-conditioned sequential optimization problem. A direct numerical solution process is presented using quadratic programming, but the emphasis is on the development of a closed-form expression reflecting the asymptotic deviation probability of a particular nominal path. This is identified as the key factor in the success of the new paradigm. An approach employing the second variation and the differential curvature of the effective action is suggested for small deviation channels leading to the Jacobi field of the rate function and the subsequently introduced Jacobi field performance measure. This closed-form solution is utilized in combination with the supplied parametrization of the objective space. For the first time, this allows for an LD based control design applicable to a large class of nonlinear systems. Thus, Minimum Large Deviations (MLD) control is effectively established in a comprehensive structured framework. The construction of the new paradigm is completed by an optimality proof for the Jacobi field performance measure, an interpretive discussion, and a suggestion for efficient implementation. The potential of the new approach is exhibited by its extension

Blowup with vorticity control for a 2D model of the Boussinesq equations

Science.gov (United States)

Hoang, V.; Orcan-Ekmekci, B.; Radosz, M.; Yang, H.

2018-06-01

We propose a system of equations with nonlocal flux in two space dimensions which is closely modeled after the 2D Boussinesq equations in a hyperbolic flow scenario. Our equations involve a vorticity stretching term and a non-local Biot-Savart law and provide insight into the underlying intrinsic mechanisms of singularity formation. We prove stable, controlled finite time blowup involving upper and lower bounds on the vorticity up to the time of blowup for a wide class of initial data.

Infinite Horizon Discrete Time Control Problems for Bounded Processes

Directory of Open Access Journals (Sweden)

2009-03-01

Full Text Available We establish Pontryagin Maximum Principles in the strong form for infinite horizon optimal control problems for bounded processes, for systems governed by difference equations. Results due to Ioffe and Tihomirov are among the tools used to prove our theorems. We write necessary conditions with weakened hypotheses of concavity and without invertibility, and we provide new results on the adjoint variable. We show links between bounded problems and nonbounded ones. We also give sufficient conditions of optimality.

Mathematical and physical aspects of controlling the exact solutions of the 3D Gross-Pitaevskii equation

International Nuclear Information System (INIS)

Fedele, Renato; Jovanovic, Dusan; De Nicola, Sergio; Eliasson, Bengt; Shukla, Padma K.

2010-01-01

The possibility of the decomposition of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) into a pair of coupled Schroedinger-type equations, is investigated. It is shown that, under suitable mathematical conditions, it is possible to construct the exact controlled solutions of the 3D GPE from the solutions of a linear 2D Schroedinger equation coupled with a 1D nonlinear Schroedinger equation (the transverse and longitudinal components of the GPE, respectively). The coupling between these two equations is the functional of the transverse and the longitudinal profiles. The applied method of nonlinear decomposition, called the controlling potential method (CPM), yields the full 3D solution in the form of the product of the solutions of the transverse and longitudinal components of the GPE. It is shown that the CPM constitutes a variational principle and sets up a condition on the controlling potential well. Its physical interpretation is given in terms of the minimization of the (energy) effects introduced by the control. The method is applied to the case of a parabolic external potential to construct analytically an exact BEC state in the form of a bright soliton, for which the quantitative comparison between the external and controlling potentials is presented.

On the solution of Stein's equation and Fisher information matrix of an ARMAX process

NARCIS (Netherlands)

Klein, A.; Spreij, P.

2004-01-01

The main goal of this paper consists in expressing the solution of a Stein equation in terms of the Fisher information matrix (FIM) of a scalar ARMAX process. A condition for expressing the FIM in terms of a solution to a Stein equation is also set forth. Such interconnections can be derived when a

An application of neural networks to process and materials control

International Nuclear Information System (INIS)

Howell, J.A.; Whiteson, R.

1991-01-01

Process control consists of two basic elements: a model of the process and knowledge of the desired control algorithm. In some cases the level of the control algorithm is merely supervisory, as in an alarm-reporting or anomaly-detection system. If the model of the process is known, then a set of equations may often be solved explicitly to provide the control algorithm. Otherwise, the model has to be discovered through empirical studies. Neural networks have properties that make them useful in this application. They can learn (make internal models from experience or observations). The problem of anomaly detection in materials control systems fits well into this general control framework. To successfully model a process with a neutral network, a good set of observables must be chosen. These observables must in some sense adequately span the space of representable events, so that a signature metric can be built for normal operation. In this way, a non-normal event, one that does not fit within the signature, can be detected. In this paper, we discuss the issues involved in applying a neural network model to anomaly detection in materials control systems. These issues include data selection and representation, network architecture, prediction of events, the use of simulated data, and software tools. 10 refs., 4 figs., 1 tab

Optimal Control Strategies in a Two Dimensional Differential Game Using Linear Equation under a Perturbed System

Directory of Open Access Journals (Sweden)

Musa Danjuma SHEHU

2008-06-01

Full Text Available This paper lays emphasis on formulation of two dimensional differential games via optimal control theory and consideration of control systems whose dynamics is described by a system of Ordinary Differential equation in the form of linear equation under the influence of two controls U(. and V(.. Base on this, strategies were constructed. Hence we determine the optimal strategy for a control say U(. under a perturbation generated by the second control V(. within a given manifold M.

A stochastic version of the Price equation reveals the interplay of deterministic and stochastic processes in evolution

Directory of Open Access Journals (Sweden)

Rice Sean H

2008-09-01

Full Text Available Abstract Background Evolution involves both deterministic and random processes, both of which are known to contribute to directional evolutionary change. A number of studies have shown that when fitness is treated as a random variable, meaning that each individual has a distribution of possible fitness values, then both the mean and variance of individual fitness distributions contribute to directional evolution. Unfortunately the most general mathematical description of evolution that we have, the Price equation, is derived under the assumption that both fitness and offspring phenotype are fixed values that are known exactly. The Price equation is thus poorly equipped to study an important class of evolutionary processes. Results I present a general equation for directional evolutionary change that incorporates both deterministic and stochastic processes and applies to any evolving system. This is essentially a stochastic version of the Price equation, but it is derived independently and contains terms with no analog in Price's formulation. This equation shows that the effects of selection are actually amplified by random variation in fitness. It also generalizes the known tendency of populations to be pulled towards phenotypes with minimum variance in fitness, and shows that this is matched by a tendency to be pulled towards phenotypes with maximum positive asymmetry in fitness. This equation also contains a term, having no analog in the Price equation, that captures cases in which the fitness of parents has a direct effect on the phenotype of their offspring. Conclusion Directional evolution is influenced by the entire distribution of individual fitness, not just the mean and variance. Though all moments of individuals' fitness distributions contribute to evolutionary change, the ways that they do so follow some general rules. These rules are invisible to the Price equation because it describes evolution retrospectively. An equally general

Analysis of buffering process of control rod hydraulic absorber

International Nuclear Information System (INIS)

Bao Jishi; Qin Benke; Bo Hanliang

2011-01-01

Control Rod Hydraulic Drive Mechanism(CRHDM) is a newly invented build-in control rod drive mechanism. Hydraulic absorber is the key part of this mechanism, and is used to cushion the control rod when the rod scrams. Thus, it prevents the control rod from being deformed and damaged. In this paper dynamics program ANSYS CFX is used to calculate all kinds of flow conditions in hydraulic absorber to obtain its hydraulic characteristics. Based on the flow resistance coefficients obtained from the simulation results, fluid mass and momentum equations were developed to get the trend of pressure change in the hydraulic cylinder and the displacement of the piston rod during the buffering process of the control rod. The results obtained in this paper indicate that the hydraulic absorber meets the design requirement. The work in this paper will be helpful for the design and optimization of the control rod hydraulic absorber. (author)

Poisson Stochastic Process and Basic Schauder and Sobolev Estimates in the Theory of Parabolic Equations

Science.gov (United States)

Krylov, N. V.; Priola, E.

2017-09-01

We show, among other things, how knowing Schauder or Sobolev-space estimates for the one-dimensional heat equation allows one to derive their multidimensional analogs for equations with coefficients depending only on the time variable with the same constants as in the case of the one-dimensional heat equation. The method is quite general and is based on using the Poisson stochastic process. It also applies to equations involving non-local operators. It looks like no other methods are available at this time and it is a very challenging problem to find a purely analytical approach to proving such results.

Controlling chaos in a pendulum equation with ultra-subharmonic resonances

International Nuclear Information System (INIS)

Yang Jianping; Jing Zhujun

2009-01-01

Analytical and numerical results concerning control of chaos in a pendulum equation with parametric and external excitations are given by using Melnikov methods. We give the necessary conditions of chaos control with ultra-subharmonic resonances (i.e. Ω/ω=p/q,q>1,p,q are prime), where homoclinic chaos or heteroclinic chaos can be inhibited. Numerical simulations show that chaotic behavior can be converted to period-nq (n element of Z + ) orbits by adjusting amplitude and phase-difference of parametric excitation, and the distribution of maximum Lyapunov exponents in parameter-plane (Ψ,β) gives the regions in which chaos can be controlled.

Robust fast controller design via nonlinear fractional differential equations.

Science.gov (United States)

Zhou, Xi; Wei, Yiheng; Liang, Shu; Wang, Yong

2017-07-01

A new method for linear system controller design is proposed whereby the closed-loop system achieves both robustness and fast response. The robustness performance considered here means the damping ratio of closed-loop system can keep its desired value under system parameter perturbation, while the fast response, represented by rise time of system output, can be improved by tuning the controller parameter. We exploit techniques from both the nonlinear systems control and the fractional order systems control to derive a novel nonlinear fractional order controller. For theoretical analysis of the closed-loop system performance, two comparison theorems are developed for a class of fractional differential equations. Moreover, the rise time of the closed-loop system can be estimated, which facilitates our controller design to satisfy the fast response performance and maintain the robustness. Finally, numerical examples are given to illustrate the effectiveness of our methods. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

FMTLxLyLz DIMENSIONAL EQUAT DIMENSIONAL EQUATION ...

African Journals Online (AJOL)

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plant made of 12mm thick steel plate was used in de steel plate ... water treatment plant. ... ameters affecting filtration processes were used to derive an equation usin ..... system. However, in deriving the equation onl terms are incorporated.

Macroscopic transport equations in many-body systems from microscopic exclusion processes in disordered media: a review

Directory of Open Access Journals (Sweden)

Marta Galanti

2016-08-01

Full Text Available Describing particle transport at the macroscopic or mesoscopic level in non-ideal environments poses fundamental theoretical challenges in domains ranging from inter and intra-cellular transport in biology to diffusion in porous media. Yet, often the nature of the constraints coming from many-body interactions or reflecting a complex and confining environment are better understood and modeled at the microscopic level.In this paper we review the subtle link between microscopic exclusion processes and the mean-field equations that ensue from them in the continuum limit. We show that in an inhomogeneous medium, i.e. when jumps are controlled by site-dependent hopping rates, one can obtain three different nonlinear advection-diffusion equations in the continuum limit, suitable for describing transport in the presence of quenched disorder and external fields, depending on the particular rule embodying site inequivalence at the microscopic level. In a situation that might be termed point-like scenario, when particles are treated as point-like objects, the effect of crowding as imposed at the microscopic level manifests in the mean-field equations only if some degree of inhomogeneity is enforced into the model. Conversely, when interacting agents are assigned a finite size, under the more realistic extended crowding framework, exclusion constraints persist in the unbiased macroscopic representation.

Simultaneous exact controllability for Maxwell equations and for a second-order hyperbolic system

Directory of Open Access Journals (Sweden)

Boris V. Kapitonov

2010-02-01

Full Text Available We present a result on "simultaneous" exact controllability for two models that describe two hyperbolic dynamics. One is the system of Maxwell equations and the other a vector-wave equation with a pressure term. We obtain the main result using modified multipliers in order to generate a necessary observability estimate which allow us to use the Hilbert Uniqueness Method (HUM introduced by Lions.

Backward Stochastic Riccati Equations and Infinite Horizon L-Q Optimal Control with Infinite Dimensional State Space and Random Coefficients

International Nuclear Information System (INIS)

Guatteri, Giuseppina; Tessitore, Gianmario

2008-01-01

We study the Riccati equation arising in a class of quadratic optimal control problems with infinite dimensional stochastic differential state equation and infinite horizon cost functional. We allow the coefficients, both in the state equation and in the cost, to be random.In such a context backward stochastic Riccati equations are backward stochastic differential equations in the whole positive real axis that involve quadratic non-linearities and take values in a non-Hilbertian space. We prove existence of a minimal non-negative solution and, under additional assumptions, its uniqueness. We show that such a solution allows to perform the synthesis of the optimal control and investigate its attractivity properties. Finally the case where the coefficients are stationary is addressed and an example concerning a controlled wave equation in random media is proposed

Modelling and simulation of process control systems for WWER

Energy Technology Data Exchange (ETDEWEB)

Pangelov, N [Energoproekt, Sofia (Bulgaria)

1996-12-31

A dynamic modelling method for simulation of process control system is developed (method for identification). It is based on the least squares method and highly efficient linear uninterrupted differential equations. The method has the following advantages: there are no significant limitations in the type of input/output signals and in the length of data time series; identification at none zero initial condition is possible; on-line identification is possible; a high accuracy is observed in case of noise. On the basis of real experiments and data time series simulated with known computer codes it is possible to construct highly efficient models of different systems for solving the following problems: real time simulation with high accuracy for training purposes; estimation of immeasurable parameters important to safety; malfunction diagnostics based on plant dynamics; prediction of dynamic behaviour; control vector estimation in regime adviser. Two real applications of this method are described: in dynamic behaviour modelling for steam generator level, and in creating of a Process Control System Simulator (PCSS) based on KASKAD-2 for WWER-1000 units of the Kozloduy NPP. 6 refs., 8 figs.

Observer-Based Perturbation Extremum Seeking Control with Input Constraints for Direct-Contact Membrane Distillation Process

KAUST Repository

Eleiwi, Fadi

2017-05-08

An Observer-based Perturbation Extremum Seeking Control (PESC) is proposed for a Direct-Contact Membrane Distillation (DCMD) process. The process is described with a dynamic model that is based on a 2D Advection-Diffusion Equation (ADE) model which has pump flow rates as process inputs. The objective of the controller is to optimize the trade-off between the permeate mass flux and the energy consumption by the pumps inside the process. Cases of single and multiple control inputs are considered through the use of only the feed pump flow rate or both the feed and the permeate pump flow rates. A nonlinear Lyapunov-based observer is designed to provide an estimation for the temperature distribution all over the designated domain of the DCMD process. Moreover, control inputs are constrained with an anti-windup technique to be within feasible and physical ranges. Performance of the proposed structure is analyzed, and simulations based on real DCMD process parameters for each control input are provided.

Observer-based perturbation extremum seeking control with input constraints for direct-contact membrane distillation process

Science.gov (United States)

Eleiwi, Fadi; Laleg-Kirati, Taous Meriem

2018-06-01

An observer-based perturbation extremum seeking control is proposed for a direct-contact membrane distillation (DCMD) process. The process is described with a dynamic model that is based on a 2D advection-diffusion equation model which has pump flow rates as process inputs. The objective of the controller is to optimise the trade-off between the permeate mass flux and the energy consumption by the pumps inside the process. Cases of single and multiple control inputs are considered through the use of only the feed pump flow rate or both the feed and the permeate pump flow rates. A nonlinear Lyapunov-based observer is designed to provide an estimation for the temperature distribution all over the designated domain of the DCMD process. Moreover, control inputs are constrained with an anti-windup technique to be within feasible and physical ranges. Performance of the proposed structure is analysed, and simulations based on real DCMD process parameters for each control input are provided.

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

Science.gov (United States)

Frank, T. D.

2008-02-01

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.

Optimal Control Problems for Partial Differential Equations on Reticulated Domains

CERN Document Server

Kogut, Peter I

2011-01-01

In the development of optimal control, the complexity of the systems to which it is applied has increased significantly, becoming an issue in scientific computing. In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. Moving from abstract explanations to examples and applications with a focus on structural network problems, they aim at combining techniques of homogenization and approximation. Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference tool for gradu

A control volume based finite difference method for solving the equilibrium equations in terms of displacements

DEFF Research Database (Denmark)

Hattel, Jesper; Hansen, Preben

1995-01-01

This paper presents a novel control volume based FD method for solving the equilibrium equations in terms of displacements, i.e. the generalized Navier equations. The method is based on the widely used cv-FDM solution of heat conduction and fluid flow problems involving a staggered grid formulati....... The resulting linear algebraic equations are solved by line-Gauss-Seidel....

Real-time economic optimization for a fermentation process using Model Predictive Control

DEFF Research Database (Denmark)

Petersen, Lars Norbert; Jørgensen, John Bagterp

2014-01-01

Fermentation is a widely used process in production of many foods, beverages, and pharmaceuticals. The main goal of the control system is to maximize profit of the fermentation process, and thus this is also the main goal of this paper. We present a simple dynamic model for a fermentation process...... and demonstrate its usefulness in economic optimization. The model is formulated as an index-1 differential algebraic equation (DAE), which guarantees conservation of mass and energy in discrete form. The optimization is based on recent advances within Economic Nonlinear Model Predictive Control (E......-NMPC), and also utilizes the index-1 DAE model. The E-NMPC uses the single-shooting method and the adjoint method for computation of the optimization gradients. The process constraints are relaxed to soft-constraints on the outputs. Finally we derive the analytical solution to the economic optimization problem...

A Structural Equation Modeling Analysis of Influences on Juvenile Delinquency

Science.gov (United States)

Barrett, David E.; Katsiyannis, Antonis; Zhang, Dalun; Zhang, Dake

2014-01-01

This study examined influences on delinquency and recidivism using structural equation modeling. The sample comprised 199,204 individuals: 99,602 youth whose cases had been processed by the South Carolina Department of Juvenile Justice and a matched control group of 99,602 youth without juvenile records. Structural equation modeling for the…

Comparison of Control Approaches in Genetic Regulatory Networks by Using Stochastic Master Equation Models, Probabilistic Boolean Network Models and Differential Equation Models and Estimated Error Analyzes

Science.gov (United States)

Caglar, Mehmet Umut; Pal, Ranadip

2011-03-01

Central dogma of molecular biology states that ``information cannot be transferred back from protein to either protein or nucleic acid''. However, this assumption is not exactly correct in most of the cases. There are a lot of feedback loops and interactions between different levels of systems. These types of interactions are hard to analyze due to the lack of cell level data and probabilistic - nonlinear nature of interactions. Several models widely used to analyze and simulate these types of nonlinear interactions. Stochastic Master Equation (SME) models give probabilistic nature of the interactions in a detailed manner, with a high calculation cost. On the other hand Probabilistic Boolean Network (PBN) models give a coarse scale picture of the stochastic processes, with a less calculation cost. Differential Equation (DE) models give the time evolution of mean values of processes in a highly cost effective way. The understanding of the relations between the predictions of these models is important to understand the reliability of the simulations of genetic regulatory networks. In this work the success of the mapping between SME, PBN and DE models is analyzed and the accuracy and affectivity of the control policies generated by using PBN and DE models is compared.

New prospects in direct, inverse and control problems for evolution equations

CERN Document Server

Fragnelli, Genni; Mininni, Rosa

2014-01-01

This book, based on a selection of talks given at a dedicated meeting in Cortona, Italy, in June 2013, shows the high degree of interaction between a number of fields related to applied sciences. Applied sciences consider situations in which the evolution of a given system over time is observed, and the related models can be formulated in terms of evolution equations (EEs). These equations have been studied intensively in theoretical research and are the source of an enormous number of applications. In this volume, particular attention is given to direct, inverse and control problems for EEs. The book provides an updated overview of the field, revealing its richness and vitality.

A Modular Approach to Model Oscillating Control Surfaces Using Navier Stokes Equations

Science.gov (United States)

Guruswamy, Guru P.; Lee, Henry

2014-01-01

The use of active controls for rotorcraft is becoming more important for modern aerospace configurations. Efforts to reduce the vibrations of helicopter blades with use of active-controls are in progress. Modeling oscillating control surfaces using the linear aerodynamics theory is well established. However, higher-fidelity methods are needed to account for nonlinear effects, such as those that occur in transonic flow. The aeroelastic responses of a wing with an oscillating control surface, computed using the transonic small perturbation (TSP) theory, have been shown to cause important transonic flow effects such as a reversal of control surface effectiveness that occurs as the shock wave crosses the hinge line. In order to account for flow complexities such as blade-vortex interactions of rotor blades higher-fidelity methods based on the Navier-Stokes equations are used. Reference 6 presents a procedure that uses the Navier-Stokes equations with moving-sheared grids and demonstrates up to 8 degrees of control-surface amplitude, using a single grid. Later, this procedure was extended to accommodate larger amplitudes, based on sliding grid zones. The sheared grid method implemented in EulerlNavier-Stokes-based aeroelastic code ENS AERO was successfully applied to active control design by industry. Recently there are several papers that present results for oscillating control surface using Reynolds Averaged Navier-Stokes (RANS) equations. References 9 and 10 report 2-D cases by filling gaps with overset grids. Reference 9 compares integrated forces with the experiment at low oscillating frequencies whereas Ref. 10 reports parametric studies but with no validation. Reference II reports results for a 3D case by modeling the gap region with a deformed grid and compares force results with the experiment only at the mid-span of flap. In Ref. II grid is deformed to match the control surface deflections at the section where the measurements are made. However, there is no

Power balance equation in electron beam evaporation process

International Nuclear Information System (INIS)

Blumenfeld, L.; Soubbaramayer.

1994-01-01

The aim of the paper is to solve the equation giving the total power of the gun, used in the electron beam evaporation process, in terms of the power used to generated the vapor stream and the three main power losses due to three parasite phenomena: turbulent thermal convection in the molten pool, electron back scattering and heat radiation from the vapor emitting surface. Scaling laws are first reviewed and results are given with the example of the evaporation of aluminium with a 5 kW axisymmetric gun working in steady state mode. The influence of an applied magnetic field on the evaporation rate is also examined. 5 refs., 3 figs., 1 tab

Non-Markovianity in the optimal control of an open quantum system described by hierarchical equations of motion

Science.gov (United States)

Mangaud, E.; Puthumpally-Joseph, R.; Sugny, D.; Meier, C.; Atabek, O.; Desouter-Lecomte, M.

2018-04-01

Optimal control theory is implemented with fully converged hierarchical equations of motion (HEOM) describing the time evolution of an open system density matrix strongly coupled to the bath in a spin-boson model. The populations of the two-level sub-system are taken as control objectives; namely, their revivals or exchange when switching off the field. We, in parallel, analyze how the optimal electric field consequently modifies the information back flow from the environment through different non-Markovian witnesses. Although the control field has a dipole interaction with the central sub-system only, its indirect influence on the bath collective mode dynamics is probed through HEOM auxiliary matrices, revealing a strong correlation between control and dissipation during a non-Markovian process. A heterojunction is taken as an illustrative example for modeling in a realistic way the two-level sub-system parameters and its spectral density function leading to a non-perturbative strong coupling regime with the bath. Although, due to strong system-bath couplings, control performances remain rather modest, the most important result is a noticeable increase of the non-Markovian bath response induced by the optimally driven processes.

Stationary distributions of stochastic processes described by a linear neutral delay differential equation

International Nuclear Information System (INIS)

Frank, T D

2005-01-01

Stationary distributions of processes are derived that involve a time delay and are defined by a linear stochastic neutral delay differential equation. The distributions are Gaussian distributions. The variances of the Gaussian distributions are either monotonically increasing or decreasing functions of the time delays. The variances become infinite when fixed points of corresponding deterministic processes become unstable. (letter to the editor)

Irreversible thermodynamics models and constitutive equations of the irradiation induced deformation and damage accumulating processes

International Nuclear Information System (INIS)

Wassilew, C.

1989-11-01

This report gives an overall evaluation of several in-reactor deformation and creep-rupture experiments performed in BR-2, FFTF, and Rapsodie on pressurised tubes of the stabilized austenitic stainless steels 1.4970, 1.4981, 1.4988, and the nickel base alloy Hastelloy-X. The irradiation induced deformation processes observed in the components operating in a neutron environment can be divided into two main groups: 1. volume conserving creep and 2. volumetric swelling. Since the observed deformation as well as damage accumulating phenomena are caused by the same constrained generated and free disposable point defects and helium atoms, it is obvious and advisable to analyze, and to model simultaneously the ensemble of the elementary mechanisms and processes effective at the same time. Phenomenological models based on the thermodynamics of irreversible processes have been developed, with the aim of: 1. grasping the partial relationships between the external variables and the response functions (creep, swelling, creep driven swelling, and time to rupture), 2. fathoming the rate-controlling mechanisms, 3. providing insight into the structural details and changes occurring during the deformation and the damage accumulating processes, 4. integrating the damage accumulating processes comprehensively, and 5. formulating the constitutive equations required to describe the elementary processes that generate plastic deformations as well as damage accumulation. (orig./MM)

Integration of Design and Control through Model Analysis

DEFF Research Database (Denmark)

Russel, Boris Mariboe; Henriksen, Jens Peter; Jørgensen, Sten Bay

2002-01-01

A systematic computer aided analysis of the process model is proposed as a pre-solution step for integration of design and control problems. The process model equations are classified in terms of balance equations, constitutive equations and conditional equations. Analysis of the phenomena models...... (structure selection) issues for the integrated problems are considered. (C) 2002 Elsevier Science Ltd. All rights reserved....... representing the constitutive equations identify the relationships between the important process and design variables, which help to understand, define and address some of the issues related to integration of design and control. Furthermore, the analysis is able to identify a set of process (control) variables...

Process control device

International Nuclear Information System (INIS)

Hayashi, Toshifumi; Kobayashi, Hiroshi.

1994-01-01

A process control device comprises a memory device for memorizing a plant operation target, a plant state or a state of equipments related with each other as control data, a read-only memory device for storing programs, a plant instrumentation control device or other process control devices, an input/output device for performing input/output with an operator, and a processing device which conducts processing in accordance with the program and sends a control demand or a display demand to the input/output device. The program reads out control data relative to a predetermined operation target, compares and verify them with actual values to read out control data to be a practice premise condition which is further to be a practice premise condition if necessary, thereby automatically controlling the plant or requiring or displaying input. Practice presuming conditions for the operation target can be examined succesively in accordance with the program without constituting complicated logical figures and AND/OR graphs. (N.H.)

Experimental evaluation of optimal Vehicle Dynamic Control based on the State Dependent Riccati Equation technique

NARCIS (Netherlands)

Alirezaei, M.; Kanarachos, S.A.; Scheepers, B.T.M.; Maurice, J.P.

2013-01-01

Development and experimentally evaluation of an optimal Vehicle Dynamic Control (VDC) strategy based on the State Dependent Riccati Equation (SDRE) control technique is presented. The proposed nonlinear controller is based on a nonlinear vehicle model with nonlinear tire characteristics. A novel

Controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with delay and Poisson jumps

Directory of Open Access Journals (Sweden)

Diem Dang Huan

2015-12-01

Full Text Available The current paper is concerned with the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps in Hilbert spaces. Using the theory of a strongly continuous cosine family of bounded linear operators, stochastic analysis theory and with the help of the Banach fixed point theorem, we derive a new set of sufficient conditions for the controllability of nonlocal second-order impulsive neutral stochastic functional integro-differential equations with infinite delay and Poisson jumps. Finally, an application to the stochastic nonlinear wave equation with infinite delay and Poisson jumps is given.

Controlled Nonlinear Stochastic Delay Equations: Part I: Modeling and Approximations

International Nuclear Information System (INIS)

Kushner, Harold J.

2012-01-01

This two-part paper deals with “foundational” issues that have not been previously considered in the modeling and numerical optimization of nonlinear stochastic delay systems. There are new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. There are two basic and interconnected themes for these models. The first, dealt with in this part, concerns the definition of admissible control. The classical definition of an admissible control as a nonanticipative relaxed control is inadequate for these models and needs to be extended. This is needed for the convergence proofs of numerical approximations for optimal controls as well as to have a well-defined model. It is shown that the new classes of admissible controls do not enlarge the range of the value functions, is closed (together with the associated paths) under weak convergence, and is approximatable by ordinary controls. The second theme, dealt with in Part II, concerns transportation equation representations, and their role in the development of numerical algorithms with much reduced memory and computational requirements.

Modeling delay in genetic networks: from delay birth-death processes to delay stochastic differential equations.

Science.gov (United States)

Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Bennett, Matthew R; Josić, Krešimir; Ott, William

2014-05-28

Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay.

Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations

Energy Technology Data Exchange (ETDEWEB)

Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Ott, William [Department of Mathematics, University of Houston, Houston, Texas 77004 (United States); Bennett, Matthew R. [Department of Biochemistry and Cell Biology, Rice University, Houston, Texas 77204, USA and Institute of Biosciences and Bioengineering, Rice University, Houston, Texas 77005 (United States); Josić, Krešimir [Department of Mathematics, University of Houston, Houston, Texas 77004 (United States); Department of Biology and Biochemistry, University of Houston, Houston, Texas 77204 (United States)

2014-05-28

Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay.

Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations

International Nuclear Information System (INIS)

Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Ott, William; Bennett, Matthew R.; Josić, Krešimir

2014-01-01

Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay

Boltzmann equation for a mixture of gases with non-conservative processes

International Nuclear Information System (INIS)

Martiarena, M.L.

1989-01-01

The nonlinear and non-isotropic Boltzmann equation (NLBE) including several molecular species, non-conservative channels and external forces. The general solution of that equation is obtained for a spatially homogeneous mixture of L gases, consisting of Maxwell particles, as a Generalized Laguerre expansion, within a Hilbert space. Removal and self-generation effects are included in presence of a time-dependent external force. An exact particular solution is studied generalizing the well-known BKW-mode for a mixture of L gases with inelastic processes. An homogeneous gas of test particles, in d dimension, is considered which interacts with a background host medium in the presence of an external space and time dependent force. Scattering, removal and self-generation collisions are included. The inhomogeneous Boltzmann equation for this system to an homogeneous one is reduced without background or external forces, using a generalized Nilkoskii transform. It is shown that a background of field particles can confine the test gas, even in absence of external forces. Furthermore, the solution of NLBE with non-isotropic singular initial conditions, is analyzed. The NLBE is transformed into an integral equation which is solved iteratively. The evolution of delta and step singularities in the distribution function is discussed during the initial layer and compared with the isotropic case. As an application of the methods abovementioned, the collision of a beam of ions or neutral atoms with a carbon-foil is considered. The electron experimental spectra from a transport equation is described. It is supposed that convoy electron may be produced inside the solid by single ion-atom collisions as ELC or ECC. The produced electrons lost energy by collision with the atoms of the material, which are considered at rest. The electron distribution function is numerically calculated. The ratio between the intrinsic convoy electron peak height to the background electron intensity

Local control of globally competing patterns in coupled Swift-Hohenberg equations

Science.gov (United States)

Becker, Maximilian; Frenzel, Thomas; Niedermayer, Thomas; Reichelt, Sina; Mielke, Alexander; Bär, Markus

2018-04-01

We present analytical and numerical investigations of two anti-symmetrically coupled 1D Swift-Hohenberg equations (SHEs) with cubic nonlinearities. The SHE provides a generic formulation for pattern formation at a characteristic length scale. A linear stability analysis of the homogeneous state reveals a wave instability in addition to the usual Turing instability of uncoupled SHEs. We performed weakly nonlinear analysis in the vicinity of the codimension-two point of the Turing-wave instability, resulting in a set of coupled amplitude equations for the Turing pattern as well as left- and right-traveling waves. In particular, these complex Ginzburg-Landau-type equations predict two major things: there exists a parameter regime where multiple different patterns are stable with respect to each other and that the amplitudes of different patterns interact by local mutual suppression. In consequence, different patterns can coexist in distinct spatial regions, separated by localized interfaces. We identified specific mechanisms for controlling the position of these interfaces, which distinguish what kinds of patterns the interface connects and thus allow for global pattern selection. Extensive simulations of the original SHEs confirm our results.

MANAGEMENT CONTROL SYSTEM AND THE CASE OF CSR IN THE TUNISIAN INDUSTRIAL COMPANIES: WHAT FINDINGS BY THE METHOD OF STRUCTURAL EQUATION?

Directory of Open Access Journals (Sweden)

Hichem Dkhili

2013-01-01

Full Text Available This study aims to the behavior of management control; it is providing a model to the behavior of integration of social responsibility in the management control tools. This model was validated with 306 Tunisian companies in the industrial sector. Through a questionnaire, the data collected are processed using exploratory and confirmatory analysis by the methods of structural equations. The results revealed that the management control system in industrial Tunisia is facing economic responsibility. This is in response to emerging pressures of uncertainty related to the environment, and in enrolling a strategy of domination by cost. In addition, the management control system is designed as a guidance tool actions and behaviors.

Fuzzy control with random delays using invariant cones and its application to control of energy processes in microelectromechanical motion devices

Energy Technology Data Exchange (ETDEWEB)

Sinha, A.S.C. [Purdue Univ., Indianapolis, IN (United States). Dept. of Electrical Engineering; Lyshevski, S. [Rochester Inst. of Technology, NY (United States)

2005-05-01

In this paper, a class of microelectromechanical systems described by nonlinear differential equations with random delays is examined. Robust fuzzy controllers are designed to control the energy conversion processes with the ultimate objective to guarantee optimal achievable performance. The fuzzy rule base used consists of a collection of r fuzzy IF-THEN rules defined as a function of the conditional variable. The method of the theory of cones and Lyapunov functionals is used to design a class of local fuzzy control laws. A verifiably sufficient condition for stochastic stability of fuzzy stochastic microelectromechanical systems is given. As an example, we have considered the design of a fuzzy control law for an electrostatic micromotor. (author)

Fuzzy control with random delays using invariant cones and its application to control of energy processes in microelectromechanical motion devices

International Nuclear Information System (INIS)

Sinha, A.S.C.; Lyshevski, S.

2005-01-01

In this paper, a class of microelectromechanical systems described by nonlinear differential equations with random delays is examined. Robust fuzzy controllers are designed to control the energy conversion processes with the ultimate objective to guarantee optimal achievable performance. The fuzzy rule base used consists of a collection of r fuzzy IF-THEN rules defined as a function of the conditional variable. The method of the theory of cones and Lyapunov functionals is used to design a class of local fuzzy control laws. A verifiably sufficient condition for stochastic stability of fuzzy stochastic microelectromechanical systems is given. As an example, we have considered the design of a fuzzy control law for an electrostatic micromotor

The usage of Maxwell fractional equations for the investigation of the waveguide processes

International Nuclear Information System (INIS)

Maksyuta, M.V.; Slinchenko, Yu.A.; Grygoruk, V.I.

2016-01-01

By means of nabla operator written down with using both of some differential operators with integer orders and fractional differential Caputo operators, gradient, divergence and rotor operators are determined, it is checked up the fulfillment of vector relations in fractional vector analysis, fractional Green, Stocks and Ostrogradsky-Gauss formulas. For a specific expression of nabla operator (nabla components along x and y axes have a unit order and along z axis, correspondingly, a fractional value in the interval from zero till unit) Maxwell fractional equations are written down. Based on the following from them some fractional wave equations, dissipative and polarization processes at electromagnetic waves distribution both in rectangular (planar) and in cylindrical waveguide structures are analyzed.

Design of a data-driven predictive controller for start-up process of AMT vehicles.

Science.gov (United States)

Lu, Xiaohui; Chen, Hong; Wang, Ping; Gao, Bingzhao

2011-12-01

In this paper, a data-driven predictive controller is designed for the start-up process of vehicles with automated manual transmissions (AMTs). It is obtained directly from the input-output data of a driveline simulation model constructed by the commercial software AMESim. In order to obtain offset-free control for the reference input, the predictor equation is gained with incremental inputs and outputs. Because of the physical characteristics, the input and output constraints are considered explicitly in the problem formulation. The contradictory requirements of less friction losses and less driveline shock are included in the objective function. The designed controller is tested under nominal conditions and changed conditions. The simulation results show that, during the start-up process, the AMT clutch with the proposed controller works very well, and the process meets the control objectives: fast clutch lockup time, small friction losses, and the preservation of driver comfort, i.e., smooth acceleration of the vehicle. At the same time, the closed-loop system has the ability to reject uncertainties, such as the vehicle mass and road grade.

Impacts of Interactive and Diagnostic Control System Use on the Innovation Process

Directory of Open Access Journals (Sweden)

Fábio Frezatti

2017-10-01

Full Text Available This research explores the innovation process in organizations based on the Management Control System (MCS. We examined the link between the diagnostic and interactive uses of management control systems and their association with the intensity of the innovation process. Motivations for the research are: (a enhance the potentiality of the model by including variables that are external to the organization, and (b offer an empirical emergent country perspective on innovation. The study is quantitative and the data were collected by means of a survey questionnaire involving a sample of 121 Brazilian companies. The analysis was supported by structural equation modeling. The contributions are: (a enhancement of the model by including the influences exerted by external stimuli on the intensity of innovation, (b confirmation of the utility of the model in an emergent country, and (c despite the controversial literature, highlighting the importance of the interactive use of the Management Control Systems process, by offering an empirical perspective on innovation control. A positive implication of the findings relates to the use of a broader and not exclusively internal model to increase its potentiality, reflecting the organizational reality by including the dynamism of external stimuli and the innovation control perspective.

Every Equation Tells a Story: Using Equation Dictionaries in Introductory Geophysics

Science.gov (United States)

Caplan-Auerbach, Jacqueline

2009-01-01

Many students view equations as a series of variables and operators into which numbers should be plugged rather than as representative of a physical process. To solve a problem they may simply look for an equation with the correct variables and assume it meets their needs, rather than selecting an equation that represents the appropriate physical…

Hot workability of γ + α2 titanium aluminide: Development of processing map and constitutive equations

International Nuclear Information System (INIS)

Gupta, R.K.; Narayana Murty, S.V.S.; Pant, Bhanu; Agarwala, Vijaya; Sinha, P.P.

2012-01-01

Highlights: ► Deformation studies of five TiAl alloys carried out through processing map. ► DRX domain and superplastic domain identified in power efficiency map. ► Safe working zone for alloys found at 1223–1423 K at strain rates (10 −2 –10 −3 s −1 ). ► Strain rate sensitivity, activation energy, Zener Hollomon parameter (Z) are obtained. ► Constitutive equations derived and verified. DRX grain size correlated with Z. - Abstract: Gamma titanium alumindes are intermetallics, which have very narrow working range. Hot isothermal working is the most suitable process for hot working of alloy. Accordingly, hot isothermal compression test is carried out on reaction synthesized and homogenized titanium aluminide alloys at different temperatures and strain rates using Gleeble thermomechanical simulator. Three alloys of Ti48Al2Cr2Nb0.1B (atom%) have been used in the study. Stress–strain data obtained from the test has been used to construct processing map, which indicates the safe and unsafe working zone. Strain rate sensitivity and Zener–Hollomon parameter has been calculated. Further, constitutive equations have been generated and verified. It is found that alloy has good workability in the temperature range of 1223–1423 K at strain rates of 0.01–0.001 s −1 . In this range of parameters, the alloys nearly follow the constitutive equations.

Adaptive Finite Element Method for Optimal Control Problem Governed by Linear Quasiparabolic Integrodifferential Equations

Directory of Open Access Journals (Sweden)

Wanfang Shen

2012-01-01

Full Text Available The mathematical formulation for a quadratic optimal control problem governed by a linear quasiparabolic integrodifferential equation is studied. The control constrains are given in an integral sense: Uad={u∈X;∫ΩUu⩾0, t∈[0,T]}. Then the a posteriori error estimates in L∞(0,T;H1(Ω-norm and L2(0,T;L2(Ω-norm for both the state and the control approximation are given.

A heat equation for freezing processes with phase change

DEFF Research Database (Denmark)

Backi, Christoph Josef; Bendtsen, Jan Dimon; Leth, John-Josef

2016-01-01

In this work, the stability properties as well as possible applications of a partial differential equation (PDE) with state-dependent parameters are investigated. Among other things, the PDE describes freezing of foodstuff, and is closely related to the (potential) Burgers’ equation. We show that...

Optimal Control of Beer Fermentation Process Using Differential ...

African Journals Online (AJOL)

ADOWIE PERE

ABSTRACT: In this paper, the mathematical model of batch fermentation process of ethanol was formulated. The method of differential transform was used to obtain the solution governing the fermentation process; the system of equation was transformed using the differential transform method. The result obtained from the ...

Second-Order Necessary Optimality Conditions for Some State-Constrained Control Problems of Semilinear Elliptic Equations

International Nuclear Information System (INIS)

Casas, E.; Troeltzsch, F.

1999-01-01

In this paper we are concerned with some optimal control problems governed by semilinear elliptic equations. The case of a boundary control is studied. We consider pointwise constraints on the control and a finite number of equality and inequality constraints on the state. The goal is to derive first- and second-order optimality conditions satisfied by locally optimal solutions of the problem

Stochastic processes in cell biology

CERN Document Server

Bressloff, Paul C

2014-01-01

This book develops the theory of continuous and discrete stochastic processes within the context of cell biology.  A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods.   This text is primarily...

Approximate controllability of Sobolev type fractional stochastic nonlocal nonlinear differential equations in Hilbert spaces

Directory of Open Access Journals (Sweden)

Mourad Kerboua

2014-12-01

Full Text Available We introduce a new notion called fractional stochastic nonlocal condition, and then we study approximate controllability of class of fractional stochastic nonlinear differential equations of Sobolev type in Hilbert spaces. We use Hölder's inequality, fixed point technique, fractional calculus, stochastic analysis and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions is formulated and proved for the fractional stochastic control system to be approximately controllable. An example is given to illustrate the abstract results.

Robot welding process control

Science.gov (United States)

Romine, Peter L.

1991-01-01

This final report documents the development and installation of software and hardware for Robotic Welding Process Control. Primary emphasis is on serial communications between the CYRO 750 robotic welder, Heurikon minicomputer running Hunter & Ready VRTX, and an IBM PC/AT, for offline programming and control and closed-loop welding control. The requirements for completion of the implementation of the Rocketdyne weld tracking control are discussed. The procedure for downloading programs from the Intergraph, over the network, is discussed. Conclusions are made on the results of this task, and recommendations are made for efficient implementation of communications, weld process control development, and advanced process control procedures using the Heurikon.

Preconditioning for partial differential equation constrained optimization with control constraints

KAUST Repository

Stoll, Martin

2011-10-18

Optimal control problems with partial differential equations play an important role in many applications. The inclusion of bound constraints for the control poses a significant additional challenge for optimization methods. In this paper, we propose preconditioners for the saddle point problems that arise when a primal-dual active set method is used. We also show for this method that the same saddle point system can be derived when the method is considered as a semismooth Newton method. In addition, the projected gradient method can be employed to solve optimization problems with simple bounds, and we discuss the efficient solution of the linear systems in question. In the case when an acceleration technique is employed for the projected gradient method, this again yields a semismooth Newton method that is equivalent to the primal-dual active set method. We also consider the Moreau-Yosida regularization method for control constraints and efficient preconditioners for this technique. Numerical results illustrate the competitiveness of these approaches. © 2011 John Wiley & Sons, Ltd.

Preconditioning for partial differential equation constrained optimization with control constraints

KAUST Repository

Stoll, Martin; Wathen, Andy

2011-01-01

Optimal control problems with partial differential equations play an important role in many applications. The inclusion of bound constraints for the control poses a significant additional challenge for optimization methods. In this paper, we propose preconditioners for the saddle point problems that arise when a primal-dual active set method is used. We also show for this method that the same saddle point system can be derived when the method is considered as a semismooth Newton method. In addition, the projected gradient method can be employed to solve optimization problems with simple bounds, and we discuss the efficient solution of the linear systems in question. In the case when an acceleration technique is employed for the projected gradient method, this again yields a semismooth Newton method that is equivalent to the primal-dual active set method. We also consider the Moreau-Yosida regularization method for control constraints and efficient preconditioners for this technique. Numerical results illustrate the competitiveness of these approaches. © 2011 John Wiley & Sons, Ltd.

Memory loss process and non-Gibbsian equilibrium solutions of master equations

International Nuclear Information System (INIS)

Cataldo, H.M.; Hernandez, E.S.

1988-01-01

The phonon dynamics of a harmonic oscillator coupled to a steady reservoir is studied. In the Markovian limit, the equilibrium is reached through a progressive loss of memory process which involves the moments of the initial distribution. The relationship to the non-Markovian equations of motion and its resolvent poles is settled. As a particular model of the coupling mechanism is adopted, the possibility of non-Gibbsian equilibrium distribution arises, which is analyzed focusing upon the dependence of various parameters of the system on an effective equilibrium temperature

Stabilization of a semilinear parabolic equation in the exterior of a bounded domain by means of boundary controls

International Nuclear Information System (INIS)

Gorshkov, A V

2003-01-01

The problem of the stabilization of a semilinear equation in the exterior of a bounded domain is considered. In view of the impossibility of an exponential stabilization of the form e -σt of the solution of a parabolic equation in an unbounded domain no matter what the boundary control is, one poses the problem of power-like stabilization by means of a boundary control. For a fixed initial condition and parameter k>0 of the rate of stabilization the existence of a boundary control such that the solution approaches zero at the rate 1/t k is demonstrated

DIAGRAM SOLVE THE USE OF SIMULINK BLOCK DIAGRAM TO SOLVE MATHEMA THEMATICAL CONTROL EQU MATHEMATICAL MODELS AND CONTROL EQUATIONS

Directory of Open Access Journals (Sweden)

N.M. Ghasem

2003-12-01

Full Text Available In this paper, the simulink block diagram is used to solve a model consists of a set of ordinary differential and algebraic equations to control the temperature inside a simple stirred tank heater. The flexibility of simulink block diagram gives students a better understanding of the control systems. The simulink also allows solution of mathematical models and easy visualization of the system variables. A polyethylene fluidized bed reactor is considered as an industrial example and the effect of the Proportional, Integral and Derivative control policy is presented for comparison.

Opportunities and challenges for process control in process intensification

NARCIS (Netherlands)

Nikacevic, N.M.; Huesman, A.E.M.; Hof, Van den P.M.J.; Stankiewicz, A.

2012-01-01

This is a review and position article discussing the role and prospective for process control in process intensification. Firstly, the article outlines the classical role of control in process systems, presenting an overview of control systems’ development, from basic PID control to the advanced

Set-Valued Stochastic Equation with Set-Valued Square Integrable Martingale

Directory of Open Access Journals (Sweden)

Li Jun-Gang

2017-01-01

Full Text Available In this paper, we shall introduce the stochastic integral of a stochastic process with respect to set-valued square integrable martingale. Then we shall give the Aumann integral measurable theorem, and give the set-valued stochastic Lebesgue integral and set-valued square integrable martingale integral equation. The existence and uniqueness of solution to set-valued stochastic integral equation are proved. The discussion will be useful in optimal control and mathematical finance in psychological factors.

Process control using modern systems of information processing

International Nuclear Information System (INIS)

Baldeweg, F.

1984-01-01

Modern digital automation techniques allow the application of demanding types of process control. These types of process control are characterized by their belonging to higher levels in a multilevel model. Functional and technical aspects of the performance of digital automation plants are presented and explained. A modern automation system is described considering special procedures of process control (e.g. real time diagnosis)

Process control program development

International Nuclear Information System (INIS)

Dameron, H.J.

1985-01-01

This paper details the development and implementation of a ''Process Control Program'' at Duke Power's three nuclear stations - Oconee, McGuire, and Catawba. Each station is required by Technical Specification to have a ''Process Control Program'' (PCP) to control all dewatering and/or solidification activities for radioactive wastes

Chemical process control using Mat lab

International Nuclear Information System (INIS)

Kang, Sin Chun; Kim, Raeh Yeon; Kim, Yang Su; Oh, Min; Yeo, Yeong Gu; Jung, Yeon Su

2001-07-01

This book is about chemical process control, which includes the basis of process control with conception, function, composition of system and summary, change of laplace and linearization, modeling of chemical process, transfer function and block diagram, the first dynamic property of process, the second dynamic property of process, the dynamic property of combined process, control structure of feedback on component of control system, the dynamic property of feedback control loop, stability of closed loop control structure, expression of process, modification and composition of controller, analysis of vibration response and adjustment controller using vibration response.

IDENTIFICATION ASPECT OF METHODOLOGY DESIGN OF CONTROL SYSTEM TIME-VARIANT PROCESS

Directory of Open Access Journals (Sweden)

M. M. Blagoveshchenskaia

2014-01-01

Full Text Available Summary. Specificity of a food manufacture demands perfection of automatic control systems of processes in devices, units and installations. Creation of an adaptive control system by technological process of a food on the basis of model of control object it is necessary to carry out the additional analysis for choice algorithm of identification on real enough to representative sample of input data and output signal/data. In article on the basis of simulation it is analyzed over 53 algorithms of recurrent identification plus the basic modifications of these algorithms by 47 criteria for time-varying multivariable linear dynamic objects. On the basis of this analysis for engineering practice for a considered class of objects some algorithms are recommended. Possibilities of the software suite having for today the fullest set of parametrical identification algorithms are discussed. For given specific conditions of comparison in the package identification algorithms for identification of stationary coefficients in the equation object of the most effective were: Yzerman-1, Kaczmarz, Nagumo-Noda, Rastrigin, Kalman filter, the forgetting factor, Zipkin. When pointwise object - Kaczmarz, Nagumo-Noda, Kalman filter; showed the best result identification algorithm-Nagumo Noda.

Simulation, optimal control and parametric sensitivity analysis of a molten carbonate fuel cell using a partial differential algebraic dynamic equation system; Simulation, Optimale Steuerung und Sensitivitaetsanalyse einer Schmelzkarbonat-Brennstoffzelle mithilfe eines partiellen differential-algebraischen dynamischen Gleichungssystems

Energy Technology Data Exchange (ETDEWEB)

Sternberg, K

2007-02-08

Molten carbonate fuel cells (MCFCs) allow an efficient and environmentally friendly energy production by converting the chemical energy contained in the fuel gas in virtue of electro-chemical reactions. In order to predict the effect of the electro-chemical reactions and to control the dynamical behavior of the fuel cell a mathematical model has to be found. The molten carbonate fuel cell (MCFC) can indeed be described by a highly complex,large scale, semi-linear system of partial differential algebraic equations. This system includes a reaction-diffusion-equation of parabolic type, several reaction-transport-equations of hyperbolic type, several ordinary differential equations and finally a system of integro-differential algebraic equations which describes the nonlinear non-standard boundary conditions for the entire partial differential algebraic equation system (PDAE-system). The existence of an analytical or the computability of a numerical solution for this high-dimensional PDAE-system depends on the kind of the differential equations and their special characteristics. Apart from theoretical investigations, the real process has to be controlled, more precisely optimally controlled. Hence, on the basis of the PDAE-system an optimal control problem is set up, whose analytical and numerical solvability is closely linked to the solvability of the PDAE-system. Moreover the solution of that optimal control problem is made more difficult by inaccuracies in the underlying database, which does not supply sufficiently accurate values for the model parameters. Therefore the optimal control problem must also be investigated with respect to small disturbances of model parameters. The aim of this work is to analyze the relevant dynamic behavior of MCFCs and to develop concepts for their optimal process control. Therefore this work is concerned with the simulation, the optimal control and the sensitivity analysis of a mathematical model for MCDCs, which can be characterized

DUAL-PROCESS, a highly reliable process control system

International Nuclear Information System (INIS)

Buerger, L.; Gossanyi, A.; Parkanyi, T.; Szabo, G.; Vegh, E.

1983-02-01

A multiprocessor process control system is described. During its development the reliability was the most important aspect because it is used in the computerized control of a 5 MW research reactor. DUAL-PROCESS is fully compatible with the earlier single processor control system PROCESS-24K. The paper deals in detail with the communication, synchronization, error detection and error recovery problems of the operating system. (author)

Output-Feedback Control of Unknown Linear Discrete-Time Systems With Stochastic Measurement and Process Noise via Approximate Dynamic Programming.

Science.gov (United States)

Wang, Jun-Sheng; Yang, Guang-Hong

2017-07-25

This paper studies the optimal output-feedback control problem for unknown linear discrete-time systems with stochastic measurement and process noise. A dithered Bellman equation with the innovation covariance matrix is constructed via the expectation operator given in the form of a finite summation. On this basis, an output-feedback-based approximate dynamic programming method is developed, where the terms depending on the innovation covariance matrix are available with the aid of the innovation covariance matrix identified beforehand. Therefore, by iterating the Bellman equation, the resulting value function can converge to the optimal one in the presence of the aforementioned noise, and the nearly optimal control laws are delivered. To show the effectiveness and the advantages of the proposed approach, a simulation example and a velocity control experiment on a dc machine are employed.

Modeling simulation and control of the wood drying process. Part 1: A set of PDE`s as an internal model

Energy Technology Data Exchange (ETDEWEB)

Tarasiewicz, S. [Laval Univ., Sainte-Foy, Quebec (Canada). Dept. of Mechanical Engineering; Leger, F. [Forintek Canada Corp. East Div., Sainte-Foy, Quebec (Canada)

1998-07-01

The internal model proposed is a nonlinear system of a few partial differential equations. The boundary conditions for the differential equations are specified at the lumber board entrance and between the wood and air. The initial conditions are calibrated by solving the static model and by the technical experiment. In conclusion, it can be said that the consistency of the model with experimental results seems to be reasonably good and can be used for process simulation and control.

Birth–death process of local structures in defect turbulence described by the one-dimensional complex Ginzburg–Landau equation

Energy Technology Data Exchange (ETDEWEB)

Uchiyama, Yusuke, E-mail: r1230160@risk.tsukuba.ac.jp; Konno, Hidetoshi

2014-04-01

Defect turbulence described by the one-dimensional complex Ginzburg–Landau equation is investigated and analyzed via a birth–death process of the local structures composed of defects, holes, and modulated amplitude waves (MAWs). All the number statistics of each local structure, in its stationary state, are subjected to Poisson statistics. In addition, the probability density functions of interarrival times of defects, lifetimes of holes, and MAWs show the existence of long-memory and some characteristic time scales caused by zigzag motions of oscillating traveling holes. The corresponding stochastic process for these observations is fully described by a non-Markovian master equation.

State-Space Equations and the First-Phase Algorithm for Signal Control of Single Intersections

Institute of Scientific and Technical Information of China (English)

LI Jinyuan; PAN Xin; WANG Xiqin

2007-01-01

State-space equations were applied to formulate the queuing and delay of traffic at a single intersection in this paper. The signal control of a single intersection was then modeled as a discrete-time optimal control problem, with consideration of the constraints of stream conflicts, saturation flow rate, minimum green time, and maximum green time. The problem cannot be solved directly due to the nonlinear constraints.However, the results of qualitative analysis were used to develop a first-phase signal control algorithm. Simulation results show that the algorithm substantially reduces the total delay compared to fixed-time control.

Dynamic data analysis modeling data with differential equations

CERN Document Server

Ramsay, James

2017-01-01

This text focuses on the use of smoothing methods for developing and estimating differential equations following recent developments in functional data analysis and building on techniques described in Ramsay and Silverman (2005) Functional Data Analysis. The central concept of a dynamical system as a buffer that translates sudden changes in input into smooth controlled output responses has led to applications of previously analyzed data, opening up entirely new opportunities for dynamical systems. The technical level has been kept low so that those with little or no exposure to differential equations as modeling objects can be brought into this data analysis landscape. There are already many texts on the mathematical properties of ordinary differential equations, or dynamic models, and there is a large literature distributed over many fields on models for real world processes consisting of differential equations. However, a researcher interested in fitting such a model to data, or a statistician interested in...

Statistical Methods for Stochastic Differential Equations

CERN Document Server

Kessler, Mathieu; Sorensen, Michael

2012-01-01

The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to the topic at hand and builds gradually towards discussing recent research. The book covers Wiener-driven equations as well as stochastic differential equations with jumps, including continuous-time ARMA processes and COGARCH processes. It presents a sp

Development of rubber mixing process mathematical model and synthesis of control correction algorithm by process temperature mode using an artificial neural network

Directory of Open Access Journals (Sweden)

V. S. Kudryashov

2016-01-01

Full Text Available The article is devoted to the development of a correction control algorithm by temperature mode of a periodic rubber mixing process for JSC "Voronezh tire plant". The algorithm is designed to perform in the main controller a section of rubber mixing Siemens S7 CPU319F-3 PN/DP, which forms tasks for the local temperature controllers HESCH HE086 and Jumo dTRON304, operating by tempering stations. To compile the algorithm was performed a systematic analysis of rubber mixing process as an object of control and was developed a mathematical model of the process based on the heat balance equations describing the processes of heat transfer through the walls of technological devices, the change of coolant temperature and the temperature of the rubber compound mixing until discharge from the mixer chamber. Due to the complexity and nonlinearity of the control object – Rubber mixers and the availability of methods and a wide experience of this device control in an industrial environment, a correction algorithm is implemented on the basis of an artificial single-layer neural network and it provides the correction of tasks for local controllers on the cooling water temperature and air temperature in the workshop, which may vary considerably depending on the time of the year, and during prolonged operation of the equipment or its downtime. Tempering stations control is carried out by changing the flow of cold water from the cooler and on/off control of the heating elements. The analysis of the model experiments results and practical research at the main controller programming in the STEP 7 environment at the enterprise showed a decrease in the mixing time for different types of rubbers by reducing of heat transfer process control error.

Active flow control insight gained from a modified integral boundary layer equation

Science.gov (United States)

Seifert, Avraham

2016-11-01

Active Flow Control (AFC) can alter the development of boundary layers with applications (e.g., reducing drag by separation delay or separating the boundary layers and enhancing vortex shedding to increase drag). Historically, significant effects of steady AFC methods were observed. Unsteady actuation is significantly more efficient than steady. Full-scale AFC tests were conducted with varying levels of success. While clearly relevant to industry, AFC implementation relies on expert knowledge with proven intuition and or costly and lengthy computational efforts. This situation hinders the use of AFC while simple, quick and reliable design method is absent. An updated form of the unsteady integral boundary layer (UIBL) equations, that include AFC terms (unsteady wall transpiration and body forces) can be used to assist in AFC analysis and design. With these equations and given a family of suitable velocity profiles, the momentum thickness can be calculated and matched with an outer, potential flow solution in 2D and 3D manner to create an AFC design tool, parallel to proven tools for airfoil design. Limiting cases of the UIBL equation can be used to analyze candidate AFC concepts in terms of their capability to modify the boundary layers development and system performance.

MODEL REPRESENTATION OF THE SPRAY DRYING PROCESS OF THE DISTILLERY STILLAGE FILTRATE BASED ON NAVIERSTOKES EQUATIONS

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A. A. Shevtsov

2015-01-01

Full Text Available Spray drying of solutions and suspensions is among the most common methods of producing a wide range of powdered products in chemical, food and pharmaceutical industries. For the drying of heat-sensitive materials, which is fully applicable to the distillery stillage filtrate continuous-flow type of contact of drying agent and the solution droplets is examined. Two-phase simulation method of computational hydrodynamics in a stationary state for studying the process of drying of the distillery stillage filtrate in the pilot spray dryer under the following assumptions was used. The components form an ideal mixture, the properties of which are calculated directly from the properties of the components and their proportions. The droplets were presented in spherical form. The density and specific heat of the solution and the coefficient of vapors diffusion in the gas phase remained unchanged. To solve the heat exchange equations between the drying agent and the drops by the finite volume method the software package ANSYS CFX was used. The bind between the two phases was established by Navier-Stokes equations. The continuous phase (droplets of the distillery stillage filtrate was described by the k-ε turbulence model. The results obtained showed that the interaction of "drop-wall" causes a significant change of velocity, temperature and humidity both of a drying agent and the product particles. The behavior of the particles by spraying, collision with walls and deposition of the finished product allowed to determine the dependence of physical parameters of the drying process, of the geometric dimensions of the dryer. Comparison of simulation results with experimental data showed satisfactory convergence of the results: for the temperature of the powder 10% its humidity of 12% and temperature of the spent drying agent at the outlet from the drier of 13%. The possibility of using the model in the spray dryers designing, and control of the drying process

On several aspects and applications of the multigrid method for solving partial differential equations

Science.gov (United States)

Dinar, N.

1978-01-01

Several aspects of multigrid methods are briefly described. The main subjects include the development of very efficient multigrid algorithms for systems of elliptic equations (Cauchy-Riemann, Stokes, Navier-Stokes), as well as the development of control and prediction tools (based on local mode Fourier analysis), used to analyze, check and improve these algorithms. Preliminary research on multigrid algorithms for time dependent parabolic equations is also described. Improvements in existing multigrid processes and algorithms for elliptic equations were studied.

Approximation to the Modelling of Charge and Discharge Processes in Electrochemical Batteries by Integral Equations

International Nuclear Information System (INIS)

Balenzategui, J. L.

1999-01-01

A new way for the modelling of the charge and discharge processes in electrochemical batteries based on the use of integral equations is presented. The proposed method models the charge curves by the so called fractional or cumulative integrals of a certain objective function f(t) that must be sought. The charge figures can be easily fitted by breaking down this objective function as the addition of two different Lorentz type functions: the first one is associated to the own charge process and the second one to the overcharge process. The method allows calculating the starting voltage for overcharge as the intersection between both functions. The curve fitting of this model to different experimental charge curves, by using the Marquart algorithm, has shown very accurate results. In the case of discharge curves, two possible methods for modelling purposes are suggested, well by using the same kind of integral equations, well by the simple subtraction of an objective function f(t) from a constant value V O D. Many other aspects for the study and analysis of this method in order to improve its results in further developments are also discussed. (Author) 10 refs

Differentiated Learning Environment--A Classroom for Quadratic Equation, Function and Graphs

Science.gov (United States)

Dinç, Emre

2017-01-01

This paper will cover the design of a learning environment as a classroom regarding the Quadratic Equations, Functions and Graphs. The goal of the learning environment offered in the paper is to design a classroom where students will enjoy the process, use their skills they already have during the learning process, control and plan their learning…

International Conference on Delay Differential and Difference Equations and Applications

CERN Document Server

Pituk, Mihály; Recent Advances in Delay Differential and Difference Equations

2014-01-01

Delay differential and difference equations serve as models for a range of processes in biology, physics, engineering, and control theory. In this volume, the participants of the International Conference on Delay Differential and Difference Equations and Applications, Balatonfüred, Hungary, July 15-19, 2013 present recent research in this quickly-evolving field. The papers relate to the existence, asymptotic, and oscillatory properties of the solutions; stability theory; numerical approximations; and applications to real world phenomena using deterministic and stochastic discrete and continuous dynamical systems.

On some control problems of dynamic of reactor

Science.gov (United States)

Baskakov, A. V.; Volkov, N. P.

2017-12-01

The paper analyzes controllability of the transient processes in some problems of nuclear reactor dynamics. In this case, the mathematical model of nuclear reactor dynamics is described by a system of integro-differential equations consisting of the non-stationary anisotropic multi-velocity kinetic equation of neutron transport and the balance equation of delayed neutrons. The paper defines the formulation of the linear problem on control of transient processes in nuclear reactors with application of spatially distributed actions on internal neutron sources, and the formulation of the nonlinear problems on control of transient processes with application of spatially distributed actions on the neutron absorption coefficient and the neutron scattering indicatrix. The required control actions depend on the spatial and velocity coordinates. The theorems on existence and uniqueness of these control actions are proved in the paper. To do this, the control problems mentioned above are reduced to equivalent systems of integral equations. Existence and uniqueness of the solution for this system of integral equations is proved by the method of successive approximations, which makes it possible to construct an iterative scheme for numerical analyses of transient processes in a given nuclear reactor with application of the developed mathematical model. Sufficient conditions for controllability of transient processes are also obtained. In conclusion, a connection is made between the control problems and the observation problems, which, by to the given information, allow us to reconstruct either the function of internal neutron sources, or the neutron absorption coefficient, or the neutron scattering indicatrix....

Translational control of a graphically simulated robot arm by kinematic rate equations that overcome elbow joint singularity

Science.gov (United States)

Barker, L. K.; Houck, J. A.; Carzoo, S. W.

1984-01-01

An operator commands a robot hand to move in a certain direction relative to its own axis system by specifying a velocity in that direction. This velocity command is then resolved into individual joint rotational velocities in the robot arm to effect the motion. However, the usual resolved-rate equations become singular when the robot arm is straightened. To overcome this elbow joint singularity, equations were developed which allow continued translational control of the robot hand even though the robot arm is (or is nearly) fully extended. A feature of the equations near full arm extension is that an operator simply extends and retracts the robot arm to reverse the direction of the elbow bend (difficult maneuver for the usual resolved-rate equations). Results show successful movement of a graphically simulated robot arm.

CFORM- LINEAR CONTROL SYSTEM DESIGN AND ANALYSIS: CLOSED FORM SOLUTION AND TRANSIENT RESPONSE OF THE LINEAR DIFFERENTIAL EQUATION

Science.gov (United States)

Jamison, J. W.

1994-01-01

CFORM was developed by the Kennedy Space Center Robotics Lab to assist in linear control system design and analysis using closed form and transient response mechanisms. The program computes the closed form solution and transient response of a linear (constant coefficient) differential equation. CFORM allows a choice of three input functions: the Unit Step (a unit change in displacement); the Ramp function (step velocity); and the Parabolic function (step acceleration). It is only accurate in cases where the differential equation has distinct roots, and does not handle the case for roots at the origin (s=0). Initial conditions must be zero. Differential equations may be input to CFORM in two forms - polynomial and product of factors. In some linear control analyses, it may be more appropriate to use a related program, Linear Control System Design and Analysis (KSC-11376), which uses root locus and frequency response methods. CFORM was written in VAX FORTRAN for a VAX 11/780 under VAX VMS 4.7. It has a central memory requirement of 30K. CFORM was developed in 1987.

Feedback control of chlorine inductively coupled plasma etch processing

International Nuclear Information System (INIS)

Lin Chaung; Leou, K.-C.; Shiao, K.-M.

2005-01-01

Feedback control has been applied to poly-Si etch processing using a chlorine inductively coupled plasma. Since the positive ion flux and ion energy incident upon the wafer surface are the key factors that influence the etch rate, the ion current and the root mean square (rms) rf voltage on the wafer stage, which are measured using an impedance meter connected to the wafer stage, are adopted as the controlled variables to enhance etch rate. The actuators are two 13.56 MHz rf power generators, which adjust ion density and ion energy, respectively. The results of closed-loop control show that the advantages of feedback control can be achieved. For example, with feedback control, etch rate variation under the transient chamber wall condition is reduced roughly by a factor of 2 as compared to the open-loop case. In addition, the capability of the disturbance rejection was also investigated. For a gas pressure variation of 20%, the largest etch rate variation is about 2.4% with closed-loop control as compared with as large as about 6% variation using open-loop control. Also the effect of ion current and rms rf voltage on etch rate was studied using 2 2 factorial design whose results were used to derive a model equation. The obtained formula was used to adjust the set point of ion current and rf voltage so that the desired etch rate was obtained

Controlled Nonlinear Stochastic Delay Equations: Part II: Approximations and Pipe-Flow Representations

International Nuclear Information System (INIS)

Kushner, Harold J.

2012-01-01

This is the second part of a work dealing with key issues that have not been addressed in the modeling and numerical optimization of nonlinear stochastic delay systems. We consider new classes of models, such as those with nonlinear functions of several controls (such as products), each with is own delay, controlled random Poisson measure driving terms, admissions control with delayed retrials, and others. Part I was concerned with issues concerning the class of admissible controls and their approximations, since the classical definitions are inadequate for our models. This part is concerned with transportation equation representations and their approximations. Such representations of nonlinear stochastic delay models have been crucial in the development of numerical algorithms with much reduced memory and computational requirements. The representations for the new models are not obvious and are developed. They also provide a template for the adaptation of the Markov chain approximation numerical methods.

Characteristic Equation of the Modified Smith predictor to MIMO Systems

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Jorge A. Herrera-Cuartas

2013-11-01

Full Text Available The delay in control systems is a feature frequently in real systems due to the transport of objects or information, a series connection of multiple systems or own processing and sensors delay, among others. Recently there have been several studies to identify the external delay MIMO systems, these works are focused on identification and on-line control of MIMO systems and use a multimodel structure based on modified Smith predictor using different search method. It is clear that for the implementation of the algorithm, and to obtain the convergence and stability analysis, it is necessary to have closed-loop equations of modified Smith predictor. However, in these works is not presented the analytical procedure, not be the main object, displaying only the closed loop equations without the procedure for obtaining it. Therefore, to respond, in this paper, we present an analytical way to derive the closed-loop equations of a modified Smith predictor.  

Test equating methods and practices

CERN Document Server

Kolen, Michael J

1995-01-01

In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...

Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation

Science.gov (United States)

Prentice, J. S. C.

2012-01-01

An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm,…

Modeling of Flexible Polyurethane Foam Shrinkage for Bra Cup Moulding Process Control

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Long Wu

2018-04-01

Full Text Available Nowadays, moulding technology has become a remarkable manufacturing process in the intimate apparel industry. Polyurethane (PU foam sheets are used to mould three-dimensional (3D seamless bra cups of various softness and shapes, which eliminate bulky seams and reduce production costs. However, it has been challenging to accurately and effectively control the moulding process and bra cup thickness. In this study, the theoretical mechanism of heat transfer and the thermal conductivity of PU foams are first examined. Experimental studies are carried out to investigate the changes in foam materials at various moulding conditions (viz., temperatures, and lengths of dwell time in terms of surface morphology and thickness by using electron and optical microscopy. Based on the theoretical and experimental investigations of the thermal conductivity of the foam materials, empirical equations of shrinkage ratio and thermal conduction of foam materials were established. A regression model to predict flexible PU foam shrinkage during the bra cup moulding process was formulated by using the Levenberg-Marquardt method of nonlinear least squares algorithm and verified for accuracy. This study therefore provides an effective approach that optimizes control of the bra cup moulding process and assures the ultimate quality and thickness of moulded foam cups.

MATHEMATICAL MODELING, AUTOMATION AND CONTROL OF THE BIOCONVERSION OF SORBITOL TO SORBOSE IN THE VITAMIN C PRODUCTION PROCESS I. MATHEMATICAL MODELING

Directory of Open Access Journals (Sweden)

A. Bonomi

1997-12-01

Full Text Available In 1990, the Biotechnology and the Control Systems Groups of IPT started developing a system for the control and automation of fermentation processes, applied to the oxidation of sorbitol to sorbose by the bacteria Gluconobacter oxydans, the microbial step of the vitamin C production process, that was chosen as a case study. Initially, a thirteen-parameter model was fitted to represent the batch operation of the system utilizing a nonlinear regression analysis, the flexible polyhedron method. Based on these results, a model for the continuous process (with the same kinetic equations was constructed and its optimum operating point obtained

Numerical evaluation of path-integral solutions to Fokker-Planck equations. II. Restricted stochastic processes

International Nuclear Information System (INIS)

Wehner, M.F.

1983-01-01

A path-integral solution is derived for processes described by nonlinear Fokker-Plank equations together with externally imposed boundary conditions. This path-integral solution is written in the form of a path sum for small time steps and contains, in addition to the conventional volume integral, a surface integral which incorporates the boundary conditions. A previously developed numerical method, based on a histogram representation of the probability distribution, is extended to a trapezoidal representation. This improved numerical approach is combined with the present path-integral formalism for restricted processes and is show t give accurate results. 35 refs., 5 figs

Stochastic differential equations and diffusion processes

CERN Document Server

Ikeda, N

1989-01-01

Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.A considerable number of corrections and improvements have been made for the second edition of this classic work. In particular, major and substantial changes are in Chapter III and Chapter V where the sections treating excursions of Brownian Motion and the Malliavin Calculus have been expanded and refined. Sectio

Process control in biogas plants

DEFF Research Database (Denmark)

Holm-Nielsen, Jens Bo; Oleskowicz-Popiel, Piotr

2013-01-01

Efficient monitoring and control of anaerobic digestion (AD) processes are necessary in order to enhance biogas plant performance. The aim of monitoring and controlling the biological processes is to stabilise and optimise the production of biogas. The principles of process analytical technology...

Control by Interconnection and Energy-Shaping Methods of Port Hamiltonian Models. Application to the Shallow Water Equations

OpenAIRE

Hamroun , Boussad; Dimofte , Alexandru; Lefevre , Laurent; Mendes , Eduardo

2010-01-01

International audience; — In this paper a control algorithm for the reduced port-Controlled Hamiltonian model (PCH) of the shallow water equations (PDEs) is developed. This control is developed using the Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) method on the reduced PCH model without the natural dissipation. It allows to assign desired structure and energy function to the closed loop system. The same control law is then derived using an energy shaping method ba...

A generalized fractional sub-equation method for fractional differential equations with variable coefficients

International Nuclear Information System (INIS)

Tang, Bo; He, Yinnian; Wei, Leilei; Zhang, Xindong

2012-01-01

In this Letter, a generalized fractional sub-equation method is proposed for solving fractional differential equations with variable coefficients. Being concise and straightforward, this method is applied to the space–time fractional Gardner equation with variable coefficients. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the considered method provides a very effective, convenient and powerful mathematical tool for solving many other fractional differential equations in mathematical physics. -- Highlights: ► Study of fractional differential equations with variable coefficients plays a role in applied physical sciences. ► It is shown that the proposed algorithm is effective for solving fractional differential equations with variable coefficients. ► The obtained solutions may give insight into many considerable physical processes.

General solution of the aerosol dynamic equation: growth and diffusion processes

International Nuclear Information System (INIS)

Elgarayhi, A.; Elhanbaly, A.

2004-01-01

The dispersion of aerosol particles in a fluid media is studied considering the main mechanism for condensation and diffusion. This has been done when the technique of Lie is used for solving the aerosol dynamic equation. This method is very useful in sense that it reduces the partial differential equation to some ordinary differential equations. So, different classes of similarity solutions have been obtained. The quantity of well-defined physical interest is the mean particle volume has been calculated

Application of partial differential equation modeling of the control/structural dynamics of flexible spacecraft

Science.gov (United States)

Taylor, Lawrence W., Jr.; Rajiyah, H.

1991-01-01

Partial differential equations for modeling the structural dynamics and control systems of flexible spacecraft are applied here in order to facilitate systems analysis and optimization of these spacecraft. Example applications are given, including the structural dynamics of SCOLE, the Solar Array Flight Experiment, the Mini-MAST truss, and the LACE satellite. The development of related software is briefly addressed.

The complete information for phenomenal distributed parameter control of multicomponent chemical processes in gas, fluid and solid phase

International Nuclear Information System (INIS)

Niemiec, W.

1985-01-01

A constitutive mathematical model of distributed parameters of multicomponent chemical processes in gas, fluid and solid phase is utilized to the realization of phenomenal distributed parameter control of these processes. Original systems of partial differential constitutive state equations, in the following derivative forms /I/, /II/ and /III/ are solved in this paper from the point of view of information for phenomenal distributed parameter control of considered processes. Obtained in this way for multicomponent chemical processes in gas, fluid and solid phase: -dynamical working space-time characteristics/analytical solutions in working space-time of chemical reactors/, -dynamical phenomenal Green functions as working space-time transfer functions, -statical working space characteristics /analytical solutions in working space of chemical reactors/, -statical phenomenal Green functions as working space transfer functions, are applied, as information for realization of constitutive distributed parameter control of mass, energy and momentum aspects of above processes. Two cases are considered by existence of: A/sup o/ - initial conditions, B/sup o/ - initial and boundary conditions, for multicomponent chemical processes in gas, fluid and solid phase

Equations involving Malliavin calculus operators applications and numerical approximation

CERN Document Server

Levajković, Tijana

2017-01-01

This book provides a comprehensive and unified introduction to stochastic differential equations and related optimal control problems. The material is new and the presentation is reader-friendly. A major contribution of the book is the development of generalized Malliavin calculus in the framework of white noise analysis, based on chaos expansion representation of stochastic processes and its application for solving several classes of stochastic differential equations with singular data involving the main operators of Malliavin calculus. In addition, applications in optimal control and numerical approximations are discussed.  The book is divided into four chapters. The first, entitled White Noise Analysis and Chaos Expansions, includes notation and provides the reader with the theoretical background needed to understand the subsequent chapters.  In Chapter 2, Generalized Operators of Malliavin Calculus, the Malliavin derivative operator, the Skorokhod integral and the Ornstein-Uhlenbeck operator are introdu...

Real-time nonlinear feedback control of pattern formation in (bio)chemical reaction-diffusion processes: a model study.

Science.gov (United States)

Brandt-Pollmann, U; Lebiedz, D; Diehl, M; Sager, S; Schlöder, J

2005-09-01

Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion. We show how the computed optimal feedback control strategy exploits the system inherent physical property of wave propagation to achieve desired control aims. We discuss various applications of our approach to optimal control of spatiotemporal dynamics.

Microcrystalline silicon deposition: Process stability and process control

International Nuclear Information System (INIS)

Donker, M.N. van den; Kilper, T.; Grunsky, D.; Rech, B.; Houben, L.; Kessels, W.M.M.; Sanden, M.C.M. van de

2007-01-01

Applying in situ process diagnostics, we identified several process drifts occurring in the parallel plate plasma deposition of microcrystalline silicon (μc-Si:H). These process drifts are powder formation (visible from diminishing dc-bias and changing spatial emission profile on a time scale of 10 0 s), transient SiH 4 depletion (visible from a decreasing SiH emission intensity on a time scale of 10 2 s), plasma heating (visible from an increasing substrate temperature on a time scale of 10 3 s) and a still puzzling long-term drift (visible from a decreasing SiH emission intensity on a time scale of 10 4 s). The effect of these drifts on the crystalline volume fraction in the deposited films is investigated by selected area electron diffraction and depth-profiled Raman spectroscopy. An example shows how the transient depletion and long-term drift can be prevented by suitable process control. Solar cells deposited using this process control show enhanced performance. Options for process control of plasma heating and powder formation are discussed

Modeling nuclear processes by Simulink

Energy Technology Data Exchange (ETDEWEB)

Rashid, Nahrul Khair Alang Md, E-mail: nahrul@iium.edu.my [Faculty of Engineering, International Islamic University Malaysia, Jalan Gombak, Selangor (Malaysia)

2015-04-29

Modelling and simulation are essential parts in the study of dynamic systems behaviours. In nuclear engineering, modelling and simulation are important to assess the expected results of an experiment before the actual experiment is conducted or in the design of nuclear facilities. In education, modelling can give insight into the dynamic of systems and processes. Most nuclear processes can be described by ordinary or partial differential equations. Efforts expended to solve the equations using analytical or numerical solutions consume time and distract attention from the objectives of modelling itself. This paper presents the use of Simulink, a MATLAB toolbox software that is widely used in control engineering, as a modelling platform for the study of nuclear processes including nuclear reactor behaviours. Starting from the describing equations, Simulink models for heat transfer, radionuclide decay process, delayed neutrons effect, reactor point kinetic equations with delayed neutron groups, and the effect of temperature feedback are used as examples.

Modeling nuclear processes by Simulink

International Nuclear Information System (INIS)

Rashid, Nahrul Khair Alang Md

2015-01-01

Modelling and simulation are essential parts in the study of dynamic systems behaviours. In nuclear engineering, modelling and simulation are important to assess the expected results of an experiment before the actual experiment is conducted or in the design of nuclear facilities. In education, modelling can give insight into the dynamic of systems and processes. Most nuclear processes can be described by ordinary or partial differential equations. Efforts expended to solve the equations using analytical or numerical solutions consume time and distract attention from the objectives of modelling itself. This paper presents the use of Simulink, a MATLAB toolbox software that is widely used in control engineering, as a modelling platform for the study of nuclear processes including nuclear reactor behaviours. Starting from the describing equations, Simulink models for heat transfer, radionuclide decay process, delayed neutrons effect, reactor point kinetic equations with delayed neutron groups, and the effect of temperature feedback are used as examples

Equations of mathematical physics

CERN Document Server

Tikhonov, A N

2011-01-01

Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri

Stochastic reliability analysis using Fokker Planck equations

International Nuclear Information System (INIS)

Hari Prasad, M.; Rami Reddy, G.; Srividya, A.; Verma, A.K.

2011-01-01

The Fokker-Planck equation describes the time evolution of the probability density function of the velocity of a particle, and can be generalized to other observables as well. It is also known as the Kolmogorov forward equation (diffusion). Hence, for any process, which evolves with time, the probability density function as a function of time can be represented with Fokker-Planck equation. In stochastic reliability analysis one is more interested in finding out the reliability or failure probability of the components or structures as a function of time rather than instantaneous failure probabilities. In this analysis the variables are represented with random processes instead of random variables. A random processes can be either stationary or non stationary. If the random process is stationary then the failure probability doesn't change with time where as in the case of non stationary processes the failure probability changes with time. In the present paper Fokker Planck equations have been used to find out the probability density function of the non stationary random processes. In this paper a flow chart has been provided which describes step by step process for carrying out stochastic reliability analysis using Fokker-Planck equations. As a first step one has to identify the failure function as a function of random processes. Then one has to solve the Fokker-Planck equation for each random process. In this paper the Fokker-Planck equation has been solved by using Finite difference method. As a result one gets the probability density values of the random process in the sample space as well as time space. Later at each time step appropriate probability distribution has to be identified based on the available probability density values. For checking the better fitness of the data Kolmogorov-Smirnov Goodness of fit test has been performed. In this way one can find out the distribution of the random process at each time step. Once one has the probability distribution

Group foliation of finite difference equations

Science.gov (United States)

Thompson, Robert; Valiquette, Francis

2018-06-01

Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.

An integrated approach to process control

NARCIS (Netherlands)

Schippers, W.A.J.

2001-01-01

The control of production processes is the subject of several disciplines, such as statistical process control (SPC), total productive maintenance (TPM), and automated process control (APC). Although these disciplines are traditionally separated (both in science and in business practice), their

An approximation theory for nonlinear partial differential equations with applications to identification and control

Science.gov (United States)

Banks, H. T.; Kunisch, K.

1982-01-01

Approximation results from linear semigroup theory are used to develop a general framework for convergence of approximation schemes in parameter estimation and optimal control problems for nonlinear partial differential equations. These ideas are used to establish theoretical convergence results for parameter identification using modal (eigenfunction) approximation techniques. Results from numerical investigations of these schemes for both hyperbolic and parabolic systems are given.

Statistical process control in wine industry using control cards

OpenAIRE

Dimitrieva, Evica; Atanasova-Pacemska, Tatjana; Pacemska, Sanja

2013-01-01

This paper is based on the research of the technological process of automatic filling of bottles of wine in winery in Stip, Republic of Macedonia. The statistical process control using statistical control card is created. The results and recommendations for improving the process are discussed.

Memory-type control charts in statistical process control

NARCIS (Netherlands)

Abbas, N.

2012-01-01

Control chart is the most important statistical tool to manage the business processes. It is a graph of measurements on a quality characteristic of the process on the vertical axis plotted against time on the horizontal axis. The graph is completed with control limits that cause variation mark. Once

Numerical simulation of temperature distribution using finite difference equations and estimation of the grain size during friction stir processing

International Nuclear Information System (INIS)

Arora, H.S.; Singh, H.; Dhindaw, B.K.

2012-01-01

Highlights: ► Magnesium alloy AE42 was friction stir processed under different cooling conditions. ► Heat flow model was developed using finite difference heat equations. ► Generalized MATLAB code was developed for solving heat flow model. ► Regression equation for estimation of grain size was developed. - Abstract: The present investigation is aimed at developing a heat flow model to simulate temperature history during friction stir processing (FSP). A new approach of developing implicit form of finite difference heat equations solved using MATLAB code was used. A magnesium based alloy AE42 was friction stir processed (FSPed) at different FSP parameters and cooling conditions. Temperature history was continuously recorded in the nugget zone during FSP using data acquisition system and k type thermocouples. The developed code was validated at different FSP parameters and cooling conditions during FSP experimentation. The temperature history at different locations in the nugget zone at different instants of time was further utilized for the estimation of grain growth rate and final average grain size of the FSPed specimen. A regression equation relating the final grain size, maximum temperature during FSP and the cooling rate was developed. The metallurgical characterization was done using optical microscopy, SEM, and FIB-SIM analysis. The simulated temperature profiles and final average grain size were found to be in good agreement with the experimental results. The presence of fine precipitate particles generated in situ in the investigated magnesium alloy also contributed in the evolution of fine grain structure through Zener pining effect at the grain boundaries.

Neural network based online simultaneous policy update algorithm for solving the HJI equation in nonlinear H∞ control.

Science.gov (United States)

Wu, Huai-Ning; Luo, Biao

2012-12-01

It is well known that the nonlinear H∞ state feedback control problem relies on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that has proven to be impossible to solve analytically. In this paper, a neural network (NN)-based online simultaneous policy update algorithm (SPUA) is developed to solve the HJI equation, in which knowledge of internal system dynamics is not required. First, we propose an online SPUA which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment. The proposed online SPUA updates control and disturbance policies simultaneously; thus, only one iterative loop is needed. Second, the convergence of the online SPUA is established by proving that it is mathematically equivalent to Newton's method for finding a fixed point in a Banach space. Third, we develop an actor-critic structure for the implementation of the online SPUA, in which only one critic NN is needed for approximating the cost function, and a least-square method is given for estimating the NN weight parameters. Finally, simulation studies are provided to demonstrate the effectiveness of the proposed algorithm.

The forced nonlinear Schroedinger equation

International Nuclear Information System (INIS)

Kaup, D.J.; Hansen, P.J.

1985-01-01

The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)

Fuzzy control of pressurizer dynamic process

International Nuclear Information System (INIS)

Ming Zhedong; Zhao Fuyu

2006-01-01

Considering the characteristics of pressurizer dynamic process, the fuzzy control system that takes the advantages of both fuzzy controller and PID controller is designed for the dynamic process in pressurizer. The simulation results illustrate this type of composite control system is with better qualities than those of single fuzzy controller and single PID controller. (authors)

Statistical Process Control for KSC Processing

Science.gov (United States)

Ford, Roger G.; Delgado, Hector; Tilley, Randy

1996-01-01

The 1996 Summer Faculty Fellowship Program and Kennedy Space Center (KSC) served as the basis for a research effort into statistical process control for KSC processing. The effort entailed several tasks and goals. The first was to develop a customized statistical process control (SPC) course for the Safety and Mission Assurance Trends Analysis Group. The actual teaching of this course took place over several weeks. In addition, an Internet version of the same course complete with animation and video excerpts from the course when it was taught at KSC was developed. The application of SPC to shuttle processing took up the rest of the summer research project. This effort entailed the evaluation of SPC use at KSC, both present and potential, due to the change in roles for NASA and the Single Flight Operations Contractor (SFOC). Individual consulting on SPC use was accomplished as well as an evaluation of SPC software for KSC use in the future. A final accomplishment of the orientation of the author to NASA changes, terminology, data format, and new NASA task definitions will allow future consultation when the needs arise.

Control system for technological processes in tritium processing plants with process analysis

International Nuclear Information System (INIS)

Retevoi, Carmen Maria; Stefan, Iuliana; Balteanu, Ovidiu; Stefan, Liviu; Bucur, Ciprian

2005-01-01

Integration of a large variety of installations and equipment into a unitary system for controlling the technological process in tritium processing nuclear facilities appears to be a rather complex approach particularly when experimental or new technologies are developed. Ensuring a high degree of versatility allowing easy modifications in configurations and process parameters is a major requirement imposed on experimental installations. The large amount of data which must be processed, stored and easily accessed for subsequent analyses imposes development of a large information network based on a highly integrated system containing the acquisition, control and technological process analysis data as well as data base system. On such a basis integrated systems of computation and control able to conduct the technological process could be developed as well protection systems for cases of failures or break down. The integrated system responds to the control and security requirements in case of emergency and of the technological processes specific to the industry that processes radioactive or toxic substances with severe consequences in case of technological failure as in the case of tritium processing nuclear plant. In order to lower the risk technological failure of these processes an integrated software, data base and process analysis system are developed, which, based on identification algorithm of the important parameters for protection and security systems, will display the process evolution trend. The system was checked on a existing plant that includes a removal tritium unit, finally used in a nuclear power plant, by simulating the failure events as well as the process. The system will also include a complete data base monitoring all the parameters and a process analysis software for the main modules of the tritium processing plant, namely, isotope separation, catalytic purification and cryogenic distillation

Systematic Equation Formulation

DEFF Research Database (Denmark)

Lindberg, Erik

2007-01-01

A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....

Nonlinear optimal control theory

CERN Document Server

Berkovitz, Leonard David

2012-01-01

Nonlinear Optimal Control Theory presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ordinary differential equations and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. Drawing on classroom-tested material from Purdue University and North Carolina State University, the book gives a unified account of bounded state problems governed by ordinary, integrodifferential, and delay systems. It also dis

An integral equation approach to the interval reliability of systems modelled by finite semi-Markov processes

International Nuclear Information System (INIS)

Csenki, A.

1995-01-01

The interval reliability for a repairable system which alternates between working and repair periods is defined as the probability of the system being functional throughout a given time interval. In this paper, a set of integral equations is derived for this dependability measure, under the assumption that the system is modelled by an irreducible finite semi-Markov process. The result is applied to the semi-Markov model of a two-unit system with sequential preventive maintenance. The method used for the numerical solution of the resulting system of integral equations is a two-point trapezoidal rule. The system of implementation is the matrix computation package MATLAB on the Apple Macintosh SE/30. The numerical results are discussed and compared with those from simulation

Welding process modelling and control

Science.gov (United States)

Romine, Peter L.; Adenwala, Jinen A.

1993-01-01

The research and analysis performed, and software developed, and hardware/software recommendations made during 1992 in development of the PC-based data acquisition system for support of Welding Process Modeling and Control is reported. A need was identified by the Metals Processing Branch of NASA Marshall Space Flight Center, for a mobile data aquisition and analysis system, customized for welding measurement and calibration. Several hardware configurations were evaluated and a PC-based system was chosen. The Welding Measurement System (WMS) is a dedicated instrument, strictly for the use of data aquisition and analysis. Although the WMS supports many of the functions associated with the process control, it is not the intention for this system to be used for welding process control.

Variation and Control of Process Behavior

International Nuclear Information System (INIS)

Pawlicki, Todd; Whitaker, Matthew

2008-01-01

The purpose of this work was to highlight the importance of controlling process variability for successful quality assurance (QA). We describe the method of statistical process control for characterizing and controlling a process. Traditionally, QA has been performed by comparing some important measurement (e.g., linear accelerator output) against a corresponding specification. Although useful in determining the fitness of a particular measurement, this approach does not provide information about the underlying process behavior over time. A modern view of QA is to consider the time-ordered behavior of a process. Every process displays characteristic behaviors that are independent of the specifications imposed on it. The goal of modern QA is, not only to ensure that a process is on-target, but that it is also operating with minimal variation. This is accomplished by way of a data-driven approach using process behavior charts. The development of process behavior charts, historically known as control charts, and process behavior (action) limits are described. The effect these concepts have on quality management is also discussed

IT vendor selection model by using structural equation model & analytical hierarchy process

Science.gov (United States)

Maitra, Sarit; Dominic, P. D. D.

2012-11-01

Selecting and evaluating the right vendors is imperative for an organization's global marketplace competitiveness. Improper selection and evaluation of potential vendors can dwarf an organization's supply chain performance. Numerous studies have demonstrated that firms consider multiple criteria when selecting key vendors. This research intends to develop a new hybrid model for vendor selection process with better decision making. The new proposed model provides a suitable tool for assisting decision makers and managers to make the right decisions and select the most suitable vendor. This paper proposes a Hybrid model based on Structural Equation Model (SEM) and Analytical Hierarchy Process (AHP) for long-term strategic vendor selection problems. The five steps framework of the model has been designed after the thorough literature study. The proposed hybrid model will be applied using a real life case study to assess its effectiveness. In addition, What-if analysis technique will be used for model validation purpose.

Science-based information processing in the process control of power stations

International Nuclear Information System (INIS)

Weisang, C.

1992-01-01

Through the application of specialized systems, future-orientated information processing integrates the sciences of processes, control systems, process control strategies, user behaviour and ergonomics. Improvements in process control can be attained, inter alia, by the preparation of the information contained (e.g. by suppressing the flow of signals and replacing it with signals which are found on substance) and also by an ergonomic representation of the study of the process. (orig.) [de

Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

Energy Technology Data Exchange (ETDEWEB)

Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)

2013-01-01

In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

Oscillating patterns in image processing and nonlinear evolution equations the fifteenth Dean Jacqueline B. Lewis memorial lectures

CERN Document Server

Meyer, Yves

2001-01-01

Image compression, the Navier-Stokes equations, and detection of gravitational waves are three seemingly unrelated scientific problems that, remarkably, can be studied from one perspective. The notion that unifies the three problems is that of "oscillating patterns", which are present in many natural images, help to explain nonlinear equations, and are pivotal in studying chirps and frequency-modulated signals. The first chapter of this book considers image processing, more precisely algorithms of image compression and denoising. This research is motivated in particular by the new standard for compression of still images known as JPEG-2000. The second chapter has new results on the Navier-Stokes and other nonlinear evolution equations. Frequency-modulated signals and their use in the detection of gravitational waves are covered in the final chapter. In the book, the author describes both what the oscillating patterns are and the mathematics necessary for their analysis. It turns out that this mathematics invo...

Extension of the GroIMP modelling platform to allow easy specification of differential equations describing biological processes within plant models

NARCIS (Netherlands)

Hemmerling, R.; Evers, J.B.; Smolenova, K.; Buck-Sorlin, G.H.; Kurth, W.

2013-01-01

In simulation models of plant development, physiological processes taking place in plants are typically described in terms of ODEs (Ordinary Differential Equations). On the one hand, those processes drive the development of the plant structure and on the other hand, the developed structure again

Process control for a continuous uranyl nitrate evaporator

International Nuclear Information System (INIS)

Peterson, S.F.; MacIntyre, L.P.

1984-07-01

A continuous uranyl nitrate evaporator at the Savannah River Plant (SRP) in Aiken, South Carolina ws the subject of this work. A rigorous mathematical model of the evaporator was developed. A difference equation form of the model was then constructed and used for control studies. Relative gain analysis was done on the system in order to identify any promising multivariable control schemes. Several alternate control schemes were modeled, tuned, and compared against the scheme presently in use at SRP. As the pneumatic specific gravity instrumentation at SRP is very noisy, the noise was simulated and used in the second phase of the control study. In this phase, alternate tuning methods and filters were invesigated and compared. The control studies showed that the control algorithm now in use at SRP is the simplest and best available. 10 references, 53 figures, 22 tables

Notes on the infinity Laplace equation

CERN Document Server

Lindqvist, Peter

2016-01-01

This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures by the author. The Infinity.Laplace Equation has delightful counterparts to the Dirichlet integral, the mean value property, the Brownian motion, Harnack's inequality, and so on. This "fully non-linear" equation has applications to image processing and to mass transfer problems, and it provides optimal Lipschitz extensions of boundary values.

Structural Equation Modeling of Multivariate Time Series

Science.gov (United States)

du Toit, Stephen H. C.; Browne, Michael W.

2007-01-01

The covariance structure of a vector autoregressive process with moving average residuals (VARMA) is derived. It differs from other available expressions for the covariance function of a stationary VARMA process and is compatible with current structural equation methodology. Structural equation modeling programs, such as LISREL, may therefore be…

Applied partial differential equations

CERN Document Server

Logan, J David

2004-01-01

This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...

Diffusion equations and hard collisions in multiple scattering of charged particles

International Nuclear Information System (INIS)

Papiez, Lech; Tulovsky, Vladimir

1998-01-01

The processes of angular-spatial evolution of multiple scattering of charged particles are described by the Lewis (special case of Boltzmann) integro-differential equation. The underlying stochastic process for this evolution is the compound Poisson process with transition densities satisfying the Lewis equation. In this paper we derive the Lewis equation from the compound Poisson process and show that the effective method of the solution of this equation can be based on the idea of decomposition of the compound Poisson process into processes of soft and hard collisions. Formulas for transition densities of soft and hard collision processes are provided in this paper together with the formula expressing the general solution of the Lewis equation in terms of those transition densities

Diffusion equations and hard collisions in multiple scattering of charged particles

Energy Technology Data Exchange (ETDEWEB)

Papiez, Lech [Department of Radiation Oncology, Indiana University, Indianapolis, IN (United States); Tulovsky, Vladimir [Department of Mathematics, St. John' s College, Staten Island, New York, NY (United States)

1998-09-01

The processes of angular-spatial evolution of multiple scattering of charged particles are described by the Lewis (special case of Boltzmann) integro-differential equation. The underlying stochastic process for this evolution is the compound Poisson process with transition densities satisfying the Lewis equation. In this paper we derive the Lewis equation from the compound Poisson process and show that the effective method of the solution of this equation can be based on the idea of decomposition of the compound Poisson process into processes of soft and hard collisions. Formulas for transition densities of soft and hard collision processes are provided in this paper together with the formula expressing the general solution of the Lewis equation in terms of those transition densities.

Well-posedness and exact controllability of a fourth order Schrodinger equation with variable coefficients and Neumann boundary control and collocated observation

Directory of Open Access Journals (Sweden)

Ruili Wen

2016-08-01

Full Text Available We consider an open-loop system of a fourth order Schrodinger equation with variable coefficients and Neumann boundary control and collocated observation. Using the multiplier method on Riemannian manifold we show that that the system is well-posed in the sense of Salamon. This implies that the exponential stability of the closed-loop system under the direct proportional output feedback control and the exact controllability of open-loop system are equivalent. So in order to conclude feedback stabilization from well-posedness, we study the exact controllability under a uniqueness assumption by presenting the observability inequality for the dual system. In addition, we show that the system is regular in the sense of Weiss, and that the feedthrough operator is zero.

Critical Dynamics : The Expansion of the Master Equation Including a Critical Point

NARCIS (Netherlands)

Dekker, H.

1980-01-01

In this thesis it is shown how to solve the master equation for a Markov process including a critical point by means of successive approximations in terms of a small parameter. A critical point occurs if, by adjusting an externally controlled quantity, the system shows a transition from normal

Students' Understanding of Quadratic Equations

Science.gov (United States)

López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

2016-01-01

Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

Supporting Cross-Organizational Process Control

Science.gov (United States)

Angelov, Samuil; Vonk, Jochem; Vidyasankar, Krishnamurthy; Grefen, Paul

E-contracts express the rights and obligations of parties through a formal, digital representation of the contract provisions. In process intensive relationships, e-contracts contain business processes that a party promises to perform for the counter party, optionally allowing monitoring of the execution of the promised processes. In this paper, we describe an approach in which the counter party is allowed to control the process execution. This approach will lead to more flexible and efficient business relations which are essential in the context of modern, highly dynamic and complex collaborations among companies. We present a specification of the process controls available to the consumer and their support in the private process specification of the provider.

Trends in differential equations and applications

CERN Document Server

Neble, María; Galván, José

2016-01-01

This work collects the most important results presented at the Congress on Differential Equations and Applications/Congress on Applied Mathematics (CEDYA/CMA) in Cádiz (Spain) in 2015. It supports further research in differential equations, numerical analysis, mechanics, control and optimization. In particular, it helps readers gain an overview of specific problems of interest in the current mathematical research related to different branches of applied mathematics. This includes the analysis of nonlinear partial differential equations, exact solutions techniques for ordinary differential equations, numerical analysis and numerical simulation of some models arising in experimental sciences and engineering, control and optimization, and also trending topics on numerical linear Algebra, dynamical systems, and applied mathematics for Industry. This volume is mainly addressed to any researcher interested in the applications of mathematics, especially in any subject mentioned above. It may be also useful to PhD s...

Processes subject to integrated pollution control. Petroleum processes: oil refining and associated processes

International Nuclear Information System (INIS)

1995-01-01

This document, part of a series offering guidance on pollution control regulations issued by Her Majesty's Inspectorate of Pollution, (HMIP) focuses on petroleum processes such as oil refining and other associated processes. The various industrial processes used, their associated pollution release routes into the environment and techniques for controlling these releases are all discussed. Environmental quality standards are related to national and international agreements on pollution control and abatement. HMIP's work on air, water and land pollution monitoring is also reported. (UK)

Some New Trends in Differential Equations

Indian Academy of Sciences (India)

Mythily Ramaswamy TIFR Centre for Applicable Mathematics, Bangalore

2008-04-05

Apr 5, 2008 ... Optimal Control Problems. Controllability. Stabilizability. Overview. 1 Differential Equations as Models. Mathematical Models. Brief History. Main Questions. 2 Optimal Control Problems. Mathematical Model. Optimal Control. Dynamic Programming. Pontryagin Maximum Principle. 3 Controllability. A Model.

Applicability of statistical process control techniques

NARCIS (Netherlands)

Schippers, W.A.J.

1998-01-01

This paper concerns the application of Process Control Techniques (PCTs) for the improvement of the technical performance of discrete production processes. Successful applications of these techniques, such as Statistical Process Control Techniques (SPC), can be found in the literature. However, some

Model predictive Controller for Mobile Robot

OpenAIRE

Alireza Rezaee

2017-01-01

This paper proposes a Model Predictive Controller (MPC) for control of a P2AT mobile robot. MPC refers to a group of controllers that employ a distinctly identical model of process to predict its future behavior over an extended prediction horizon. The design of a MPC is formulated as an optimal control problem. Then this problem is considered as linear quadratic equation (LQR) and is solved by making use of Ricatti equation. To show the effectiveness of the proposed method this controller is...

Dynamic optimisation of an industrial web process

Directory of Open Access Journals (Sweden)

M Soufian

2008-09-01

Full Text Available An industrial web process has been studied and it is shown that theunderlying physics of such processes governs by the Navier-Stokes partialdifferential equations with moving boundary conditions, which in turn have tobe determined by the solution of the thermodynamics equations. Thedevelopment of a two-dimensional continuous-discrete model structurebased on this study is presented. Other models are constructed based onthis model for better identification and optimisation purposes. Theparameters of the proposed models are then estimated using real dataobtained from the identification experiments with the process plant. Varioussimulation tests for validation are accompanied with the design, developmentand real-time industrial implementation of an optimal controller for dynamicoptimisation of this web process. It is shown that in comparison with thetraditional controller, the new controller resulted in a better performance, animprovement in film quality and saving in raw materials. This demonstrates theefficiency and validation of the developed models.

Microprocessors control of fermentation process

Energy Technology Data Exchange (ETDEWEB)

Fawzy, A S; Hinton, O R

1980-01-01

This paper presents three schemes for the solution of the optimal control of fermentation process. It also shows the advantages of using microprocessors in controlling and monitoring this process. A linear model of the system is considered. An optimal feedback controller is determined which maintains the states (substrate and organisms concentration) at desired values when the system is subjected to disturbances in the influent substrate and organisms concentration. Simulation results are presented for the three cases.

Lectures on the Numerical Solution of Partial Differential Equations.

Science.gov (United States)

1981-12-01

Mathematics Rockefeller University Professor F. Brezzi New York, New York 10021 Laboratorio di Analisi Numerica Universita di Pavia Professor Amiram Harten...equations and to control the spacing of the points sj. In the MFE process the grid points move with the solution and cluster atound areas of roughness...149-159. [28] Fichera, G.: Analisi essistenziale per le soluzioni die problemi al contorno misti relativi alle equazione ed ai sistemi di equazioni

Controllability for Semilinear Functional and Neutral Functional Evolution Equations with Infinite Delay in Frechet Spaces

International Nuclear Information System (INIS)

Agarwal, Ravi P.; Baghli, Selma; Benchohra, Mouffak

2009-01-01

The controllability of mild solutions defined on the semi-infinite positive real interval for two classes of first order semilinear functional and neutral functional differential evolution equations with infinite delay is studied in this paper. Our results are obtained using a recent nonlinear alternative due to Avramescu for sum of compact and contraction operators in Frechet spaces, combined with the semigroup theory

Association between product quality control and process quality control of bulk milk

NARCIS (Netherlands)

Velthuis, A.; Asseldonk, van M.A.P.M.

2010-01-01

Assessment of dairy-milk quality is based on product quality control (testing bulk-milk samples) and process quality control (auditing dairy farms). It is unknown whether process control improves product quality. To quantify possible association between product control and process control a

Process and apparatus for controlling control rods

International Nuclear Information System (INIS)

Gebelin, B.; Couture, R.

1987-01-01

This process and apparatus is characterized by 2 methods, for examination of cluster of nuclear control rods. Foucault current analyzer which examines fraction by fraction all the control rods. This examination is made by rotation of the cluster. Doubtful rods are then analysed by ultrasonic probe [fr

On matrix fractional differential equations

Directory of Open Access Journals (Sweden)

Adem Kılıçman

2017-01-01

Full Text Available The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.

Third Dutch Process Security Control Event

NARCIS (Netherlands)

Luiijf, H.A.M.

2009-01-01

On June 4th, 2009, the third Dutch Process Control Security Event took place in Amsterdam. The event, organised by the Dutch National Infrastructure against Cybercrime (NICC), attracted both Dutch process control experts and members of the European SCADA and Control Systems Information Exchange

Control measurement system in purex process

International Nuclear Information System (INIS)

Mani, V.V.S.

1985-01-01

The dependence of a bulk facility handling Purex Process on the control measurement system for evaluating the process performance needs hardly be emphasized. process control, Plant control, inventory control and quality control are the four components of the control measurement system. The scope and requirements of each component are different and the measurement methods are selected accordingly. However, each measurement system has six important elements. These are described in detail. The quality assurance programme carried out by the laboratory as a mechanism through which the quality of measurements is regularly tested and stated in quantitative terms is also explained in terms of internal and external quality assurance, with examples. Suggestions for making the control measurement system more responsive to the operational needs in future are also briefly discussed. (author)

Differential Equations Compatible with KZ Equations

International Nuclear Information System (INIS)

Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

2000-01-01

We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions

A Comparative Study of Temperature Optimal Control in a Solid State Fermentation Process for Edible Mushroom Growing

Directory of Open Access Journals (Sweden)

K. J. Gurubel

2017-04-01

Full Text Available In this paper, optimal control strategies for temperature trajectory determination in order to maximize thermophilic bacteria in a fed-batch solid-state fermentation reactor are proposed. This process is modeled by nonlinear differential equations, which has been previously validated experimentally with scale reactor temperature profiles. The dynamic input aeration rate of the reactor is determined to increase microorganisms growth of a selective substrate for edible mushroom cultivation. In industrial practice, the process is comprised of three thermal stages with constant input air flow and three types of microorganisms in a 150-hour lapse. Scytalidium thermophilum and actinobacteria are desired in order to obtain a final biomass composition with acceptable microorganisms concentration. The Steepest Descent gradient algorithm in continuous time and the Gradient Projection algorithm in discrete-time are used for the process optimal control. A comparison of simulation results in the presence of disturbances is presented, where the resulting temperature trajectories exhibit similar tendencies as industrial data.

Reinforcement learning solution for HJB equation arising in constrained optimal control problem.

Science.gov (United States)

Luo, Biao; Wu, Huai-Ning; Huang, Tingwen; Liu, Derong

2015-11-01

The constrained optimal control problem depends on the solution of the complicated Hamilton-Jacobi-Bellman equation (HJBE). In this paper, a data-based off-policy reinforcement learning (RL) method is proposed, which learns the solution of the HJBE and the optimal control policy from real system data. One important feature of the off-policy RL is that its policy evaluation can be realized with data generated by other behavior policies, not necessarily the target policy, which solves the insufficient exploration problem. The convergence of the off-policy RL is proved by demonstrating its equivalence to the successive approximation approach. Its implementation procedure is based on the actor-critic neural networks structure, where the function approximation is conducted with linearly independent basis functions. Subsequently, the convergence of the implementation procedure with function approximation is also proved. Finally, its effectiveness is verified through computer simulations. Copyright © 2015 Elsevier Ltd. All rights reserved.

Robust control charts in statistical process control

NARCIS (Netherlands)

Nazir, H.Z.

2014-01-01

The presence of outliers and contaminations in the output of the process highly affects the performance of the design structures of commonly used control charts and hence makes them of less practical use. One of the solutions to deal with this problem is to use control charts which are robust

Optimal control of stretching process of flexible solar arrays on spacecraft based on a hybrid optimization strategy

Directory of Open Access Journals (Sweden)

Qijia Yao

2017-07-01

Full Text Available The optimal control of multibody spacecraft during the stretching process of solar arrays is investigated, and a hybrid optimization strategy based on Gauss pseudospectral method (GPM and direct shooting method (DSM is presented. First, the elastic deformation of flexible solar arrays was described approximately by the assumed mode method, and a dynamic model was established by the second Lagrangian equation. Then, the nonholonomic motion planning problem is transformed into a nonlinear programming problem by using GPM. By giving fewer LG points, initial values of the state variables and control variables were obtained. A serial optimization framework was adopted to obtain the approximate optimal solution from a feasible solution. Finally, the control variables were discretized at LG points, and the precise optimal control inputs were obtained by DSM. The optimal trajectory of the system can be obtained through numerical integration. Through numerical simulation, the stretching process of solar arrays is stable with no detours, and the control inputs match the various constraints of actual conditions. The results indicate that the method is effective with good robustness. Keywords: Motion planning, Multibody spacecraft, Optimal control, Gauss pseudospectral method, Direct shooting method

GENERAL EQUATIONS OF CARBONIZATION OF EUCALYPTUS SPP KINETIC MECHANISMS

Directory of Open Access Journals (Sweden)

Túlio Jardim Raad

2006-06-01

Full Text Available In the present work, a set of general equations related to kinetic mechanism of wood compound carbonization: hemicelluloses, cellulose and lignin was obtained by Avrami-Eroffev and Arrhenius equations and Thermogravimetry of Eucalyptus cloeziana, Eucalyptus camaldulensis, Corymbia citriodora, Eucalyptus urophylla and Eucalyptus grandis samples, TG-Isothermal and TG-Dynamic. The different thermal stabilities and decomposition temperature bands of those species compounds were applied as strategy to obtain the kinetic parameters: activation energy, exponential factor and reaction order. The kinetic model developed was validated by thermogravimetric curves from carbonization of others biomass such as coconut. The kinetic parameters found were - Hemicelluloses: E=98,6 kJmol, A=3,5x106s-1 n=1,0; - Cellulose: E=182,2 kJmol, A=1,2x1013s-1 n=1,5; - Lignin: E=46,6 kJmol, A=2,01s-1 n=0,41. The set of equations can be implemented in a mathematical model of wood carbonization simulation (with heat and mass transfer equations with the aim of optimizing the control and charcoal process used to produce pig iron.

Full Equations (FEQ) model for the solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures

Science.gov (United States)

Franz, Delbert D.; Melching, Charles S.

1997-01-01

The Full EQuations (FEQ) model is a computer program for solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures. A stream system that is simulated by application of FEQ is subdivided into stream reaches (branches), parts of the stream system for which complete information on flow and depth are not required (dummy branches), and level-pool reservoirs. These components are connected by special features; that is, hydraulic control structures, including junctions, bridges, culverts, dams, waterfalls, spillways, weirs, side weirs, and pumps. The principles of conservation of mass and conservation of momentum are used to calculate the flow and depth throughout the stream system resulting from known initial and boundary conditions by means of an implicit finite-difference approximation at fixed points (computational nodes). The hydraulic characteristics of (1) branches including top width, area, first moment of area with respect to the water surface, conveyance, and flux coefficients and (2) special features (relations between flow and headwater and (or) tail-water elevations, including the operation of variable-geometry structures) are stored in function tables calculated in the companion program, Full EQuations UTiLities (FEQUTL). Function tables containing other information used in unsteady-flow simulation (boundary conditions, tributary inflows or outflows, gate settings, correction factors, characteristics of dummy branches and level-pool reservoirs, and wind speed and direction) are prepared by the user as detailed in this report. In the iterative solution scheme for flow and depth throughout the stream system, an interpolation of the function tables corresponding to the computational nodes throughout the stream system is done in the model. FEQ can be applied in the simulation of a wide range of stream configurations (including loops), lateral-inflow conditions, and special features. The

Modeling and control design of hydrogen production process for an active hydrogen/wind hybrid power system

Energy Technology Data Exchange (ETDEWEB)

Zhou, Tao; Francois, Bruno [L2EP, Ecole Centrale de Lille, Cite Scientifique, BP48, 59651, Villeneuve d' Ascq (France)

2009-01-15

This paper gives a control oriented modeling of an electrolyzer, as well as the ancillary system for the hydrogen production process. A Causal Ordering Graph of all necessary equations has been used to illustrate the global scheme for an easy understanding. The model is capable of characterizing the relations among the different physical quantities and can be used to determine the control system ensuring efficient and reliable operation of the electrolyzer. The proposed control method can manage the power flow and the hydrogen flow. The simulation results have highlighted the variation domains and the relations among the different physical quantities. The model has also been experimentally tested in real time with a Hardware-In-the-Loop Simulation before being integrated in the test bench of the active wind energy conversion system. (author)

Neural PID Control Strategy for Networked Process Control

Directory of Open Access Journals (Sweden)

Jianhua Zhang

2013-01-01

Full Text Available A new method with a two-layer hierarchy is presented based on a neural proportional-integral-derivative (PID iterative learning method over the communication network for the closed-loop automatic tuning of a PID controller. It can enhance the performance of the well-known simple PID feedback control loop in the local field when real networked process control applied to systems with uncertain factors, such as external disturbance or randomly delayed measurements. The proposed PID iterative learning method is implemented by backpropagation neural networks whose weights are updated via minimizing tracking error entropy of closed-loop systems. The convergence in the mean square sense is analysed for closed-loop networked control systems. To demonstrate the potential applications of the proposed strategies, a pressure-tank experiment is provided to show the usefulness and effectiveness of the proposed design method in network process control systems.

Neutral Backward Stochastic Functional Differential Equations and Their Application

OpenAIRE

Wei, Wenning

2013-01-01

In this paper we are concerned with a new type of backward equations with anticipation which we call neutral backward stochastic functional differential equations. We obtain the existence and uniqueness and prove a comparison theorem. As an application, we discuss the optimal control of neutral stochastic functional differential equations, establish a Pontryagin maximum principle, and give an explicit optimal value for the linear optimal control.

Numerical Oscillations Analysis for Nonlinear Delay Differential Equations in Physiological Control Systems

Directory of Open Access Journals (Sweden)

Qi Wang

2012-01-01

Full Text Available This paper deals with the oscillations of numerical solutions for the nonlinear delay differential equations in physiological control systems. The exponential θ-method is applied to p′(t=β0ωμp(t−τ/(ωμ+pμ(t−τ−γp(t and it is shown that the exponential θ-method has the same order of convergence as that of the classical θ-method. Several conditions under which the numerical solutions oscillate are derived. Moreover, it is proven that every nonoscillatory numerical solution tends to positive equilibrium of the continuous system. Finally, the main results are illustrated with numerical examples.

Synthesis of sequential control algorithms for pneumatic drives controlled by monostable valves

Directory of Open Access Journals (Sweden)

Ł. Dworzak

2009-07-01

Full Text Available Application of the Grafpol method [1] for synthesising sequential control algorithms for pneumatic drives controlled by monostable valves is presented. The developed principles simplify the MTS method of programming production processes in the scope of the memory realisation [2]. Thanks to this, time for synthesising the schematic equation can be significantly reduced in comparison to the network transformation method [3]. The designed schematic equation makes a ground for writing an application program of a PLC using any language defined in IEC 61131-3.

Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations.

Science.gov (United States)

Vorobev, Anatoliy

2010-11-01

We use the Cahn-Hilliard approach to model the slow dissolution dynamics of binary mixtures. An important peculiarity of the Cahn-Hilliard-Navier-Stokes equations is the necessity to use the full continuity equation even for a binary mixture of two incompressible liquids due to dependence of mixture density on concentration. The quasicompressibility of the governing equations brings a short time-scale (quasiacoustic) process that may not affect the slow dynamics but may significantly complicate the numerical treatment. Using the multiple-scale method we separate the physical processes occurring on different time scales and, ultimately, derive the equations with the filtered-out quasiacoustics. The derived equations represent the Boussinesq approximation of the Cahn-Hilliard-Navier-Stokes equations. This approximation can be further employed as a universal theoretical model for an analysis of slow thermodynamic and hydrodynamic evolution of the multiphase systems with strongly evolving and diffusing interfacial boundaries, i.e., for the processes involving dissolution/nucleation, evaporation/condensation, solidification/melting, polymerization, etc.

A NEW BENCHMARK FOR PLANTWIDE PROCESS CONTROL

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N. Klafke

Full Text Available Abstract The hydrodealkylation process of toluene (HDA has been used as a case study in a large number of control studies. However, in terms of industrial application, this process has become obsolete and is nowadays superseded by new technologies capable of processing heavy aromatic compounds, which increase the added value of the raw materials, such as the process of transalkylation and disproportionation of toluene (TADP. TADP also presents more complex feed and product streams and challenging operational characteristics both in the reactor and separator sections than in HDA. This work is aimed at proposing the TADP process as a new benchmark for plantwide control studies in lieu of the HAD process. For this purpose, a nonlinear dynamic rigorous model for the TADP process was developed using Aspen Plus™ and Aspen Dynamics™ and industrial conditions. Plantwide control structures (oriented to control and to the process were adapted and applied for the first time for this process. The results show that, even though both strategies are similar in terms of control performance, the optimization of economic factors must still be sought.

Closed-Loop Process Control for Electron Beam Freeform Fabrication and Deposition Processes

Science.gov (United States)

Taminger, Karen M. (Inventor); Hafley, Robert A. (Inventor); Martin, Richard E. (Inventor); Hofmeister, William H. (Inventor)

2013-01-01

A closed-loop control method for an electron beam freeform fabrication (EBF(sup 3)) process includes detecting a feature of interest during the process using a sensor(s), continuously evaluating the feature of interest to determine, in real time, a change occurring therein, and automatically modifying control parameters to control the EBF(sup 3) process. An apparatus provides closed-loop control method of the process, and includes an electron gun for generating an electron beam, a wire feeder for feeding a wire toward a substrate, wherein the wire is melted and progressively deposited in layers onto the substrate, a sensor(s), and a host machine. The sensor(s) measure the feature of interest during the process, and the host machine continuously evaluates the feature of interest to determine, in real time, a change occurring therein. The host machine automatically modifies control parameters to the EBF(sup 3) apparatus to control the EBF(sup 3) process in a closed-loop manner.

Markov processes and controlled Markov chains

CERN Document Server

Filar, Jerzy; Chen, Anyue

2002-01-01

The general theory of stochastic processes and the more specialized theory of Markov processes evolved enormously in the second half of the last century. In parallel, the theory of controlled Markov chains (or Markov decision processes) was being pioneered by control engineers and operations researchers. Researchers in Markov processes and controlled Markov chains have been, for a long time, aware of the synergies between these two subject areas. However, this may be the first volume dedicated to highlighting these synergies and, almost certainly, it is the first volume that emphasizes the contributions of the vibrant and growing Chinese school of probability. The chapters that appear in this book reflect both the maturity and the vitality of modern day Markov processes and controlled Markov chains. They also will provide an opportunity to trace the connections that have emerged between the work done by members of the Chinese school of probability and the work done by the European, US, Central and South Ameri...

An Eulerian description of the streaming process in the lattice Boltzmann equation

CERN Document Server

Lee Tae Hun

2003-01-01

This paper presents a novel strategy for solving discrete Boltzmann equation (DBE) for simulation of fluid flows. This strategy splits the solution procedure into streaming and collision steps as in the lattice Boltzmann equation (LBE) method. The streaming step can then be carried out by solving pure linear advection equations in an Eulerian framework. This offers two significant advantages over previous methods. First, the relationship between the relaxation parameter and the discretization of the collision term developed from the LBE method is directly applicable to the DBE method. The resulting DBE collision step remains local and poses no constraint on time step. Second, decoupling of the advection step from the collision step facilitates implicit discretization of the advection equation on arbitrary meshes. An implicit unstructured DBE method is constructed based on this strategy and is evaluated using several test cases of flow over a backward-facing step, lid-driven cavity flow, and flow past a circul...

Fundamentals of semiconductor manufacturing and process control

CERN Document Server

May, Gary S

2006-01-01

A practical guide to semiconductor manufacturing from process control to yield modeling and experimental design Fundamentals of Semiconductor Manufacturing and Process Control covers all issues involved in manufacturing microelectronic devices and circuits, including fabrication sequences, process control, experimental design, process modeling, yield modeling, and CIM/CAM systems. Readers are introduced to both the theory and practice of all basic manufacturing concepts. Following an overview of manufacturing and technology, the text explores process monitoring methods, including those that focus on product wafers and those that focus on the equipment used to produce wafers. Next, the text sets forth some fundamentals of statistics and yield modeling, which set the foundation for a detailed discussion of how statistical process control is used to analyze quality and improve yields. The discussion of statistical experimental design offers readers a powerful approach for systematically varying controllable p...

Optimal Control Method of Parabolic Partial Differential Equations and Its Application to Heat Transfer Model in Continuous Cast Secondary Cooling Zone

Directory of Open Access Journals (Sweden)

Yuan Wang

2015-01-01

Full Text Available Our work is devoted to a class of optimal control problems of parabolic partial differential equations. Because of the partial differential equations constraints, it is rather difficult to solve the optimization problem. The gradient of the cost function can be found by the adjoint problem approach. Based on the adjoint problem approach, the gradient of cost function is proved to be Lipschitz continuous. An improved conjugate method is applied to solve this optimization problem and this algorithm is proved to be convergent. This method is applied to set-point values in continuous cast secondary cooling zone. Based on the real data in a plant, the simulation experiments show that the method can ensure the steel billet quality. From these experiment results, it is concluded that the improved conjugate gradient algorithm is convergent and the method is effective in optimal control problem of partial differential equations.

Pion production and the nuclear equation of state

International Nuclear Information System (INIS)

Harris, J.W.; Odyniec, G.; Pugh, H.G.

1984-10-01

There has been considerable recent interest in the nuclear equation of state and how it may be determined in relativistic nucleus-nucleus collisions. In these collisions extremely high temperatures are reached and compression to densities several times that of normal nuclear matter are predicted. This affords us the unique opportunity to study, in a somewhat controlled manner, the behavior of nuclear matter under these extreme conditions. If the observables that are measured in experiments can be related in a quantitative way to state variables of the system then the equation of state can be extracted. This relation plays a very important role in understanding the formation and collapse of supernovae and the stability and structure of neutron stars. Furthermore, it can be used to test and constrain field theoretical approaches to nuclear matter and to help to better understand the dynamics of high energy nucleus-nucleus collisions. In this presentation the relationship between the nuclear equation of state and relativistic nucleus-nucleus collisions will be discussed with an emphasis on how to extract the former. That a high density state of the collision should exist will be shown. One observable, namely the pion multiplicity, will be shown to survive the succeeding stages of the collision process to provide information on the equation of state at high densities. The resulting equation of state will be presented and discussed in the light of recent theoretical development. 34 refs., 12 figs

Control System Design for Cylindrical Tank Process Using Neural Model Predictive Control Technique

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M. Sridevi

2010-10-01

Full Text Available Chemical manufacturing and process industry requires innovative technologies for process identification. This paper deals with model identification and control of cylindrical process. Model identification of the process was done using ARMAX technique. A neural model predictive controller was designed for the identified model. The performance of the controllers was evaluated using MATLAB software. The performance of NMPC controller was compared with Smith Predictor controller and IMC controller based on rise time, settling time, overshoot and ISE and it was found that the NMPC controller is better suited for this process.

A survey of process control computers at the Idaho Chemical Processing Plant

International Nuclear Information System (INIS)

Dahl, C.A.

1989-01-01

The Idaho Chemical Processing Plant (ICPP) at the Idaho National Engineering Laboratory is charged with the safe processing of spent nuclear fuel elements for the United States Department of Energy. The ICPP was originally constructed in the late 1950s and used state-of-the-art technology for process control at that time. The state of process control instrumentation at the ICPP has steadily improved to keep pace with emerging technology. Today, the ICPP is a college of emerging computer technology in process control with some systems as simple as standalone measurement computers while others are state-of-the-art distributed control systems controlling the operations in an entire facility within the plant. The ICPP has made maximal use of process computer technology aimed at increasing surety, safety, and efficiency of the process operations. Many benefits have been derived from the use of the computers for minimal costs, including decreased misoperations in the facility, and more benefits are expected in the future

Formulation and validation of applied engineering equations for heat transfer processes in the food industry

DEFF Research Database (Denmark)

Christensen, Martin Gram

The study is focused on convective heat transfer in the processing of solid foods, specifically with the scope to develop simple analytical calculation tools that can be incorporated into spreadsheet solutions. In areas of food engineering such as equipment manufacture the use of predictive...... calculations, modelling activities and simulations for improved design is employed to a high degree. In food manufacture the use process calculations are seldom applied. Even though, the calculation of thermal processes is not a challenging task in academia; this is not the case for food manufacture. However......; the calculations need fundamental validation and a generality that ensures a wide application, thus also the development of simplified approximations and engineering equations have to be conducted in academia. The focus group for the utilization of the presented work is; food manufacture, authorities ensuring food...

State Equation Determination of Cow Dung Biogas

Science.gov (United States)

Marzuki, A.; Wicaksono, L. B.

2017-08-01

A state function is a thermodynamic function which relates various macroscopically measurable properties of a system (state variable) describing the state of matter under a given set of physical conditions. A good understanding of a biogas state function plays a very important role in an effort to maximize biogas processes and to help predicting combation performance. This paper presents a step by step process of an experimental study aimed at determining the equation of state of cow dung biogas. The equation was derived from the data obtained from the experimental results of compressibility (κ) and expansivity (β) following the general form of gas state equation dV = βdT + κdP. In this equation, dV is gas volume variation, dT is temperature variation, and dP is pressure variation. From these results, we formulated a unique state equation from which the biogas critical temperature (Tc) and critical pressure were then determined (Tc = 266.7 K, Pc = 5096647.5 Pa).

Control of Pressure Process Using Infineon Microcontroller

Directory of Open Access Journals (Sweden)

A. Siddique

2007-07-01

Full Text Available The main objective of this paper is to design a cost effective controller for real time implementation of pressure process using Infineon micro controller (SAB 80C517A. Model Identification is performed and it is found to be First Order Plus Dead Time Process (FOPDT. The performance measure is tabulated for different parameter and it is found that Proportional (P controller is suitable for controlling the process.

Second-order Optimality Conditions for Optimal Control of the Primitive Equations of the Ocean with Periodic Inputs

International Nuclear Information System (INIS)

Tachim Medjo, T.

2011-01-01

We investigate in this article the Pontryagin's maximum principle for control problem associated with the primitive equations (PEs) of the ocean with periodic inputs. We also derive a second-order sufficient condition for optimality. This work is closely related to Wang (SIAM J. Control Optim. 41(2):583-606, 2002) and He (Acta Math. Sci. Ser. B Engl. Ed. 26(4):729-734, 2006), in which the authors proved similar results for the three-dimensional Navier-Stokes (NS) systems.

Direct and iterative algorithms for the parallel solution of the one-dimensional macroscopic Navier-Stokes equations

International Nuclear Information System (INIS)

Doster, J.M.; Sills, E.D.

1986-01-01

Current efforts are under way to develop and evaluate numerical algorithms for the parallel solution of the large sparse matrix equations associated with the finite difference representation of the macroscopic Navier-Stokes equations. Previous work has shown that these equations can be cast into smaller coupled matrix equations suitable for solution utilizing multiple computer processors operating in parallel. The individual processors themselves may exhibit parallelism through the use of vector pipelines. This wor, has concentrated on the one-dimensional drift flux form of the Navier-Stokes equations. Direct and iterative algorithms that may be suitable for implementation on parallel computer architectures are evaluated in terms of accuracy and overall execution speed. This work has application to engineering and training simulations, on-line process control systems, and engineering workstations where increased computational speeds are required

Dynamic modeling of ultrafiltration membranes for whey separation processes

NARCIS (Netherlands)

Saltik, M.B.; Ozkan, L.; Jacobs, M.; van der Padt, A.

2017-01-01

In this paper, we present a control relevant rigorous dynamic model for an ultrafiltration membrane unit in a whey separation process. The model consists of a set of differential algebraic equations and is developed for online model based applications such as model based control and process

Exact analytic solutions for a global equation of plant cell growth.

Science.gov (United States)

Pietruszka, Mariusz

2010-05-21

A generalization of the Lockhart equation for plant cell expansion in isotropic case is presented. The goal is to account for the temporal variation in the wall mechanical properties--in this case by making the wall extensibility a time dependent parameter. We introduce a time-differential equation describing the plant growth process with some key biophysical aspects considered. The aim of this work was to improve prior modeling efforts by taking into account the dynamic character of the plant cell wall with characteristics reminiscent of damped (aperiodic) motion. The equations selected to encapsulate the time evolution of the wall extensibility offer a new insight into the control of cell wall expansion. We find that the solutions to the time dependent second order differential equation reproduce much of the known experimental data for long- and short-time scales. Additionally, in order to support the biomechanical approach, a new growth equation based on the action of expansin proteins is proposed. Remarkably, both methods independently converge to the same kind, sigmoid-shaped, growth description functional V(t) proportional, exp(-exp(-t)), properly describing the volumetric growth and, consequently, growth rate as its time derivative. Copyright (c) 2010 Elsevier Ltd. All rights reserved.

Polygons of differential equations for finding exact solutions

International Nuclear Information System (INIS)

Kudryashov, Nikolai A.; Demina, Maria V.

2007-01-01

A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of polygons corresponding to nonlinear differential equations. It allows one to express exact solutions of the equation studied through solutions of another equation using properties of the basic equation itself. The ideas of power geometry are used and developed. Our approach has a pictorial interpretation, which is illustrative and effective. The method can be also applied for finding transformations between solutions of differential equations. To demonstrate the method application exact solutions of several equations are found. These equations are: the Korteveg-de Vries-Burgers equation, the generalized Kuramoto-Sivashinsky equation, the fourth-order nonlinear evolution equation, the fifth-order Korteveg-de Vries equation, the fifth-order modified Korteveg-de Vries equation and the sixth-order nonlinear evolution equation describing turbulent processes. Some new exact solutions of nonlinear evolution equations are given

Low Activity Waste Feed Process Control Strategy

International Nuclear Information System (INIS)

STAEHR, T.W.

2000-01-01

The primary purpose of this document is to describe the overall process control strategy for monitoring and controlling the functions associated with the Phase 1B high-level waste feed delivery. This document provides the basis for process monitoring and control functions and requirements needed throughput the double-shell tank system during Phase 1 high-level waste feed delivery. This document is intended to be used by (1) the developers of the future Process Control Plan and (2) the developers of the monitoring and control system

Entropy equilibrium equation and dynamic entropy production in environment liquid

Institute of Scientific and Technical Information of China (English)

无

2002-01-01

The entropy equilibrium equation is the basis of the nonequilibrium state thermodynamics. But the internal energy implies the kinetic energy of the fluid micelle relative to mass center in the classical entropy equilibrium equation at present. This internal energy is not the mean kinetic energy of molecular movement in thermodynamics. Here a modified entropy equilibrium equation is deduced, based on the concept that the internal energy is just the mean kinetic energy of the molecular movement. A dynamic entropy production is introduced into the entropy equilibrium equation to describe the dynamic process distinctly. This modified entropy equilibrium equation can describe not only the entropy variation of the irreversible processes but also the reversible processes in a thermodynamic system. It is more reasonable and suitable for wider applications.

Multivariate Statistical Process Control

DEFF Research Database (Denmark)

Kulahci, Murat

2013-01-01

As sensor and computer technology continues to improve, it becomes a normal occurrence that we confront with high dimensional data sets. As in many areas of industrial statistics, this brings forth various challenges in statistical process control (SPC) and monitoring for which the aim...... is to identify “out-of-control” state of a process using control charts in order to reduce the excessive variation caused by so-called assignable causes. In practice, the most common method of monitoring multivariate data is through a statistic akin to the Hotelling’s T2. For high dimensional data with excessive...... amount of cross correlation, practitioners are often recommended to use latent structures methods such as Principal Component Analysis to summarize the data in only a few linear combinations of the original variables that capture most of the variation in the data. Applications of these control charts...

A model for construction of efficiency and stability maps of hot working processes in polycrystalline metallic materials using the Garofalo's equation

International Nuclear Information System (INIS)

Rieiro, I.; Fernandez, A.; Martinez, A.; Casi, M.

1998-01-01

Has been developed a fast and easy method for to evaluate the efficiency of the process and some or possible stabilities situations in the hot working process for the polycrystalline metallic materials (p.m.m.), by the obtained dates in the Garofalo's equation resolution for the steady state creep and for wide ranges of the work variables, stress, strain rate and temperature. These method use the fitting parameters obtained for the equation mentioned and of their physical meaning. Has been developed the numerical treatment from our previously developed software for the analysis of creep and we can obtained the efficiency energetic maps for the creep and the more generally advises areas for the hot working. Further more has been obtained maps for parameters of great physical significance; f.e. the effective activation energy for different areas of the materials hot working, and in addition has been developed a method for obtained the values of {n P L} for the different ranges of power-law application, when has been obtained the value of { n G } in the Garofalo's equation. (Author) 13 refs

Fractional hydrodynamic equations for fractal media

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2005-01-01

We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the 'fractional' continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier-Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for fractional media are considered

Linearizing control of continuous anaerobic fermentation processes

Energy Technology Data Exchange (ETDEWEB)

Babary, J.P. [Centre National d`Etudes Spatiales (CNES), 31 - Toulouse (France). Laboratoire d`Analyse et d`Architecture des Systemes; Simeonov, I. [Institute of Microbiology, Bulgarian Academy of Sciences (Bulgaria); Ljubenova, V. [Institute of Control and System Research, BAS (Country unknown/Code not available); Dochain, D. [Universite Catholique de Louvain (UCL), Louvain-la-Neuve (Belgium)

1997-09-01

Biotechnological processes (BTP) involve living organisms. In the anaerobic fermentation (biogas production process) the organic matter is mineralized by microorganisms into biogas (methane and carbon dioxide) in the absence of oxygen. The biogas is an additional energy source. Generally this process is carried out as a continuous BTP. It has been widely used in life process and has been confirmed as a promising method of solving some energy and ecological problems in the agriculture and industry. Because of the very restrictive on-line information the control of this process in continuous mode is often reduced to control of the biogas production rate or the concentration of the polluting organic matter (de-pollution control) at a desired value in the presence of some perturbations. Investigations show that classical linear controllers have good performances only in the linear zone of the strongly non-linear input-output characteristics. More sophisticated robust and with variable structure (VSC) controllers are studied. Due to the strongly non-linear dynamics of the process the performances of the closed loop system may be degrading in this case. The aim of this paper is to investigate different linearizing algorithms for control of a continuous non-linear methane fermentation process using the dilution rate as a control action and taking into account some practical implementation aspects. (authors) 8 refs.

Cognitive process modelling of controllers in en route air traffic control.

Science.gov (United States)

Inoue, Satoru; Furuta, Kazuo; Nakata, Keiichi; Kanno, Taro; Aoyama, Hisae; Brown, Mark

2012-01-01

In recent years, various efforts have been made in air traffic control (ATC) to maintain traffic safety and efficiency in the face of increasing air traffic demands. ATC is a complex process that depends to a large degree on human capabilities, and so understanding how controllers carry out their tasks is an important issue in the design and development of ATC systems. In particular, the human factor is considered to be a serious problem in ATC safety and has been identified as a causal factor in both major and minor incidents. There is, therefore, a need to analyse the mechanisms by which errors occur due to complex factors and to develop systems that can deal with these errors. From the cognitive process perspective, it is essential that system developers have an understanding of the more complex working processes that involve the cooperative work of multiple controllers. Distributed cognition is a methodological framework for analysing cognitive processes that span multiple actors mediated by technology. In this research, we attempt to analyse and model interactions that take place in en route ATC systems based on distributed cognition. We examine the functional problems in an ATC system from a human factors perspective, and conclude by identifying certain measures by which to address these problems. This research focuses on the analysis of air traffic controllers' tasks for en route ATC and modelling controllers' cognitive processes. This research focuses on an experimental study to gain a better understanding of controllers' cognitive processes in air traffic control. We conducted ethnographic observations and then analysed the data to develop a model of controllers' cognitive process. This analysis revealed that strategic routines are applicable to decision making.

Stochastic control with rough paths

International Nuclear Information System (INIS)

Diehl, Joscha; Friz, Peter K.; Gassiat, Paul

2017-01-01

We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).

Stochastic control with rough paths

Energy Technology Data Exchange (ETDEWEB)

Diehl, Joscha [University of California San Diego (United States); Friz, Peter K., E-mail: friz@math.tu-berlin.de [TU & WIAS Berlin (Germany); Gassiat, Paul [CEREMADE, Université Paris-Dauphine, PSL Research University (France)

2017-04-15

We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).

Neoclassical MHD equations for tokamaks

International Nuclear Information System (INIS)

Callen, J.D.; Shaing, K.C.

1986-03-01

The moment equation approach to neoclassical-type processes is used to derive the flows, currents and resistive MHD-like equations for studying equilibria and instabilities in axisymmetric tokamak plasmas operating in the banana-plateau collisionality regime (ν* approx. 1). The resultant ''neoclassical MHD'' equations differ from the usual reduced equations of resistive MHD primarily by the addition of the important viscous relaxation effects within a magnetic flux surface. The primary effects of the parallel (poloidal) viscous relaxation are: (1) Rapid (approx. ν/sub i/) damping of the poloidal ion flow so the residual flow is only toroidal; (2) addition of the bootstrap current contribution to Ohm's laws; and (3) an enhanced (by B 2 /B/sub theta/ 2 ) polarization drift type term and consequent enhancement of the perpendicular dielectric constant due to parallel flow inertia, which causes the equations to depend only on the poloidal magnetic field B/sub theta/. Gyroviscosity (or diamagnetic vfiscosity) effects are included to properly treat the diamagnetic flow effects. The nonlinear form of the neoclassical MHD equations is derived and shown to satisfy an energy conservation equation with dissipation arising from Joule and poloidal viscous heating, and transport due to classical and neoclassical diffusion

FORSIM-6, Automatic Solution of Coupled Differential Equation System

International Nuclear Information System (INIS)

Carver, M.B.; Stewart, D.G.; Blair, J.M.; Selander, W.N.

1983-01-01

1 - Description of problem or function: The FORSIM program is a versatile package which automates the solution of coupled differential equation systems. The independent variables are time, and up to three space coordinates, and the equations may be any mixture of partial and/or ordinary differential equations. The philosophy of the program is to provide a tool which will solve a system of differential equations for a user who has basic but unspecialized knowledge of numerical analysis and FORTRAN. The equations to be solved, together with the initial conditions and any special instructions, may be specified by the user in a single FORTRAN subroutine, although he may write a number of routines if this is more suitable. These are then loaded with the control routines, which perform the solution and any requested input and output. 2 - Method of solution: Partial differential equations are automatically converted into sets of coupled ordinary differential equations by variable order discretization in the spatial dimensions. These and other ordinary differential equations are integrated continuously in time using efficient variable order, variable step, error-controlled algorithms

A numerical technique for solving fractional optimal control problems and fractional Riccati differential equations

Directory of Open Access Journals (Sweden)

F. Ghomanjani

2016-10-01

Full Text Available In the present paper, we apply the Bezier curves method for solving fractional optimal control problems (OCPs and fractional Riccati differential equations. The main advantage of this method is that it can reduce the error of the approximate solutions. Hence, the solutions obtained using the Bezier curve method give good approximations. Some numerical examples are provided to confirm the accuracy of the proposed method. All of the numerical computations have been performed on a PC using several programs written in MAPLE 13.

A taxonomy of control in intensified processes

International Nuclear Information System (INIS)

Barzin, R.; Abd Shukor, S.R.; Ahmad, A.L.

2006-01-01

Process Intensification (PI) is a revolutionary approach to design, development and implementation of process and plant. PI technology offers improved environment in a chemical process in terms of better products, and processes which are safer, cleaner, smaller - and cheaper. PI is a strategy of making dramatic reductions in the size of unit operations within chemical plants, in order to achieve given production objectives. However, PI technology would be handicapped if such system is not properly controlled. There are some foreseeable problems in order to control such processes for instance, dynamic interaction between components that make up a control loop, response time of the instrumentations, availability of proper sensor and etc. In some cases, in order to control these systems, advanced control solutions have been applied i.e. model predictive controllers (MPC) and its different algorithms such as quadratic generalized predictive control (QGPC) and self tuning quadratic generalized predictive control (STQGPC). Nevertheless in some cases simpler solutions could be applied to control such system for example proportional integral controller in the control of reactive distillation systems. As mentioned, conventional control systems like proportional-integral, proportional-integral-derivative (PID) controllers and their different structures can be used in PI systems but due to inherent nonlinearity and fast responsiveness of PI systems, digital controllers-regarding to their robustness-are mostly applied in order to control PI systems. Regarding to the fact that choosing the appropriate control strategy is the most essential part of making PI systems possible to be handle easily, taxonomy of the usage of various control structure in controlling PI systems is proposed. This paper offers an overview and discussion on identifying potential problems of instrumentation in PI technology and available control strategies

Dosimetry and process control for radiation processing

International Nuclear Information System (INIS)

Mod Ali, N.

2002-01-01

Complete text of publication follows. Accurate radiation dosimetry can provide quality assurance in radiation processing. Considerable relevant experiences in dosimetry by the SSDL-MINT has necessitate the development of methods making measurement at gamma plant traceable to the national standard. It involves the establishment of proper calibration procedure and selection of appropriate transfer system/technique to assure adequate traceability to a primary radiation standard. The effort forms the basis for irradiation process control, the legal approval of the process by the public health authorities (medical product sterilization and food preservation) and the safety and acceptance of the product

Stochastic porous media equations

CERN Document Server

Barbu, Viorel; Röckner, Michael

2016-01-01

Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.

Balancing Chemical Equations.

Science.gov (United States)

Savoy, L. G.

1988-01-01

Describes a study of students' ability to balance equations. Answers to a test on this topic were analyzed to determine the level of understanding and processes used by the students. Presented is a method to teach this skill to high school chemistry students. (CW)

Assessing Tsunami Vulnerabilities of Geographies with Shallow Water Equations

Science.gov (United States)

Aras, Rifat; Shen, Yuzhong

2012-01-01

Tsunami preparedness is crucial for saving human lives in case of disasters that involve massive water movement. In this work, we develop a framework for visual assessment of tsunami preparedness of geographies. Shallow water equations (also called Saint Venant equations) are a set of hyperbolic partial differential equations that are derived by depth-integrating the Navier-Stokes equations and provide a great abstraction of water masses that have lower depths compared to their free surface area. Our specific contribution in this study is to use Microsoft's XNA Game Studio to import underwater and shore line geographies, create different tsunami scenarios, and visualize the propagation of the waves and their impact on the shore line geography. Most importantly, we utilized the computational power of graphical processing units (GPUs) as HLSL based shader files and delegated all of the heavy computations to the GPU. Finally, we also conducted a validation study, in which we have tested our model against a controlled shallow water experiment. We believe that such a framework with an easy to use interface that is based on readily available software libraries, which are widely available and easily distributable, would encourage not only researchers, but also educators to showcase ideas.

Ensuring Control Processes Quality in Relay System Without Speed Sensor

Directory of Open Access Journals (Sweden)

R. P. Simonyants

2014-01-01

Full Text Available The paper considers topical issues of constructing relay systems to control spacecraft attitude and stabilization with no speed sensors (SS owing to use of internal feedback (IF. To research this system by point methods, e.g. a point mapping method, is difficult because of the need to solve the transcendent equations containing parameters both of control object and of IF. We propose the “diagram of superimpositions" (DS method based on topological transformations of the phase space and introduction of a relative time, which enables us to solve engineering problems in analysis and synthesis effectively.The concept of the method is based on the assertion that there is an unambiguous dependence between quality of dynamical regimes in the control system and characteristics of IF transition function. To justify the method a simplified mathematical model of spacecraft motion is applied. The following conditions are accepted: perturbations can be neglected; when the control function is activated, the signal of IF is equal to zero. To the phase surfaces are applied topological symmetry transformations, alignment and projection onto the plane with one of its coordinates being the relative time.The paper gives specific examples of systems with aperiodic feedback (AF for two versions of parameters to satisfy the requirements: I – in quality of self-oscillation mode (by pulse width in the limit cycle; II – in quality of transition process (lack of sliding modes. It is shown that the requirements II and I are contradictory for the system with AF while the sliding modes are unacceptable.It is shown that DS can be used to synthesize the IF to meet requirements of both steady and transient processes consistently. Using the IF it is possible to implement the shutdown laws of the control action on the DS without SS, the same as in case of using the SS. It is shown that in sliding modes transient processes poor in quality can be completely eliminated by

Modeling and Advanced Control for Sustainable Process ...

Science.gov (United States)

This book chapter introduces a novel process systems engineering framework that integrates process control with sustainability assessment tools for the simultaneous evaluation and optimization of process operations. The implemented control strategy consists of a biologically-inspired, multi-agent-based method. The sustainability and performance assessment of process operating points is carried out using the U.S. E.P.A.’s GREENSCOPE assessment tool that provides scores for the selected economic, material management, environmental and energy indicators. The indicator results supply information on whether the implementation of the controller is moving the process towards a more sustainable operation. The effectiveness of the proposed framework is illustrated through a case study of a continuous bioethanol fermentation process whose dynamics are characterized by steady-state multiplicity and oscillatory behavior. This book chapter contribution demonstrates the application of novel process control strategies for sustainability by increasing material management, energy efficiency, and pollution prevention, as needed for SHC Sustainable Uses of Wastes and Materials Management.

Model Process Control Language

Data.gov (United States)

National Aeronautics and Space Administration — The MPC (Model Process Control) language enables the capture, communication and preservation of a simulation instance, with sufficient detail that it can be...

Welding process decoupling for improved control

International Nuclear Information System (INIS)

Hardt, D.E.; Eagar, T.W.; Lang, J.H.; Jones, L.

1993-01-01

The Gas Metal Arc Welding Process is characterized by many important process outputs, all of which should be controlled to ensure consistent high performance joints. However, application of multivariable control methods is confounded by the strong physical coupling of typical outputs of bead shape and thermal properties. This coupling arises from the three dimensional thermal diffusion processes inherent in welding, and cannot be overcome without significant process modification. This paper presents data on the extent of coupling of the process, and proposes process changes to overcome such strong output coupling. Work in rapid torch vibration to change the heat input distribution is detailed, and methods for changing the heat balance between base and fill material heat are described

Cognitive Load in Algebra: Element Interactivity in Solving Equations

Science.gov (United States)

Ngu, Bing Hiong; Chung, Siu Fung; Yeung, Alexander Seeshing

2015-01-01

Central to equation solving is the maintenance of equivalence on both sides of the equation. However, when the process involves an interaction of multiple elements, solving an equation can impose a high cognitive load. The balance method requires operations on both sides of the equation, whereas the inverse method involves operations on one side…

Internal Decoupling in Nonlinear Process Control

Directory of Open Access Journals (Sweden)

Jens G. Balchen

1988-07-01

Full Text Available A simple method has been investigated for the total or partial removal of the effect of non-linear process phenomena in multi-variable feedback control systems. The method is based upon computing the control variables which will drive the process at desired rates. It is shown that the effect of model errors in the linearization of the process can be partly removed through the use of large feedback gains. In practice there will be limits on how large gains can he used. The sensitivity to parameter errors is less pronounced and the transient behaviour is superior to that of ordinary PI controllers.

The Freudenstein Equation

Indian Academy of Sciences (India)

research, teaching and practice related to the analysis and design ... its variants, are present in a large number of ma- chines used in daily ... with advanced electronics, sensors, control systems and computing ... ted perfectly well with the rapidly developing comput- .... velopment of the Freudenstein equation using Figure 3.

Oscillation results for certain fractional difference equations

Directory of Open Access Journals (Sweden)

Zhiyun WANG

2017-08-01

Full Text Available Fractional calculus is a theory that studies the properties and application of arbitrary order differentiation and integration. It can describe the physical properties of some systems more accurately, and better adapt to changes in the system, playing an important role in many fields. For example, it can describe the process of tumor growth (growth stimulation and growth inhibition in biomedical science. The oscillation of solutions of two kinds of fractional difference equations is studied, mainly using the proof by contradiction, that is, assuming the equation has a nonstationary solution. For the first kind of equation, the function symbol is firstly determined, and by constructing the Riccati function, the difference is calculated. Then the condition of the function is used to satisfy the contradiction, that is, the assumption is false, which verifies the oscillation of the solution. For the second kind of equation with initial condition, the equivalent fractional sum form of the fractional difference equation are firstly proved. With considering 0<α≤1 and α>1, respectively, by using the properties of Stirling formula and factorial function, the contradictory is got through enhanced processing, namely the assuming is not established, and the sufficient condition for the bounded solutions of the fractional difference equation is obtained. The above results will optimize the relevant conclusions and enrich the relevant results. The results are applied to the specific equations, and the oscillation of the solutions of equations is proved.

Pseudodifferential equations over non-Archimedean spaces

CERN Document Server

Zúñiga-Galindo, W A

2016-01-01

Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular equations are studied, such as the p-adic analogues of the Klein-Gordon equation. Pseudodifferential equations for complex-valued functions on non-Archimedean local fields are central to contemporary harmonic analysis and mathematical physics and their theory reveals a deep connection with probability and number theory. The results of this book extend and complement the material presented by Vladimirov, Volovich and Zelenov (1994) and Kochubei (2001), which emphasize spectral theory and evolution equations in a single variable, and Albeverio, Khrennikov and Shelkovich (2010), which deals mainly with the theory and applica...

Stochastic differential equations and a biological system

DEFF Research Database (Denmark)

Wang, Chunyan

1994-01-01

The purpose of this Ph.D. study is to explore the property of a growth process. The study includes solving and simulating of the growth process which is described in terms of stochastic differential equations. The identification of the growth and variability parameters of the process based...... on experimental data is considered. As an example, the growth of bacteria Pseudomonas fluorescens is taken. Due to the specific features of stochastic differential equations, namely that their solutions do not exist in the general sense, two new integrals - the Ito integral and the Stratonovich integral - have...... description. In order to identify the parameters, a Maximum likelihood estimation method is used together with a simplified truncated second order filter. Because of the continuity feature of the predictor equation, two numerical integration methods, called the Odeint and the Discretization method...

Hidden Statistics of Schroedinger Equation

Science.gov (United States)

Zak, Michail

2011-01-01

Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.

Statistical process control for serially correlated data

NARCIS (Netherlands)

Wieringa, Jakob Edo

1999-01-01

Statistical Process Control (SPC) aims at quality improvement through reduction of variation. The best known tool of SPC is the control chart. Over the years, the control chart has proved to be a successful practical technique for monitoring process measurements. However, its usefulness in practice

Expert systems in process control systems

International Nuclear Information System (INIS)

Wittig, T.

1987-01-01

To illustrate where the fundamental difference between expert systems in classical diagnosis and in industrial control lie, the work of process control instrumentation is used as an example for the job of expert systems. Starting from the general process of problem-solving, two classes of expert systems can be defined accordingly. (orig.) [de

Engineering Process Monitoring for Control Room Operation

CERN Document Server

Bätz, M

2001-01-01

A major challenge in process operation is to reduce costs and increase system efficiency whereas the complexity of automated process engineering, control and monitoring systems increases continuously. To cope with this challenge the design, implementation and operation of process monitoring systems for control room operation have to be treated as an ensemble. This is only possible if the engineering of the monitoring information is focused on the production objective and is lead in close collaboration of control room teams, exploitation personnel and process specialists. In this paper some principles for the engineering of monitoring information for control room operation are developed at the example of the exploitation of a particle accelerator at the European Laboratory for Nuclear Research (CERN).

Non-local quasi-linear parabolic equations

International Nuclear Information System (INIS)

Amann, H

2005-01-01

This is a survey of the most common approaches to quasi-linear parabolic evolution equations, a discussion of their advantages and drawbacks, and a presentation of an entirely new approach based on maximal L p regularity. The general results here apply, above all, to parabolic initial-boundary value problems that are non-local in time. This is illustrated by indicating their relevance for quasi-linear parabolic equations with memory and, in particular, for time-regularized versions of the Perona-Malik equation of image processing

Generalized Fokker-Planck equations for coloured, multiplicative Gaussian noise

International Nuclear Information System (INIS)

Cetto, A.M.; Pena, L. de la; Velasco, R.M.

1984-01-01

With the help of Novikov's theorem, it is possible to derive a master equation for a coloured, multiplicative, Gaussian random process; the coefficients of this master equation satisfy a complicated auxiliary integro-differential equation. For small values of the Kubo number, the master equation reduces to an approximate generalized Fokker-Planck equation. The diffusion coefficient is explicitly written in terms of correlation functions. Finally, a straightforward and elementary second order perturbative treatment is proposed to derive the same approximate Fokker-Planck equation. (author)

Integral propagator solvers for Vlasov-Fokker-Planck equations

International Nuclear Information System (INIS)

Donoso, J M; Rio, E del

2007-01-01

We briefly discuss the use of short-time integral propagators on solving the so-called Vlasov-Fokker-Planck equation for the dynamics of a distribution function. For this equation, the diffusion tensor is singular and the usual Gaussian representation of the short-time propagator is no longer valid. However, we prove that the path-integral approach on solving the equation is, in fact, reliable by means of our generalized propagator, which is obtained through the construction of an auxiliary solvable Fokker-Planck equation. The new representation of the grid-free advancing scheme describes the inherent cross- and self-diffusion processes, in both velocity and configuration spaces, in a natural manner, although these processes are not explicitly depicted in the differential equation. We also show that some splitting methods, as well as some finite-difference schemes, could fail in describing the aforementioned diffusion processes, governed in the whole phase space only by the velocity diffusion tensor. The short-time transition probability offers a stable and robust numerical algorithm that preserves the distribution positiveness and its norm, ensuring the smoothness of the evolving solution at any time step. (fast track communication)

Modern control of mineral wool production process

Directory of Open Access Journals (Sweden)

Stankov Stanko P.

2013-01-01

Full Text Available In this paper, the control of the plant for mineral wool production consisting of a number of the technological units of different sizes and complexity is considered. The application of modern equipment based on PLC (Programmable Logic Controller and SCADA (Supervisory Control And Data Acquisition configuration provides optimal control of technological process. Described supervisory and control system is consisting of a number of units doing decentralized distributed control of technological entities where all possible situation are considered during work of machines and devices, which are installed in electric drive and are protected from technological and electrical accident. Transformer station and diesel engine, raw materials transport and dosage, processes in dome oven, centrifuges, polycondensation (PC chamber, burners, compressor station, binder preparation and dosage, wool cutting, completed panel packing and their transport to storehouse are controlled. Process variables and parameters like as level, flow, velocity, temperature, pressure, etc. are controlled. Control system is doing identification of process states changes, diagnostic and prediction of errors and provides prediction of behavior of control objects when input flows of materials and generates optimal values of control variables due to decreasing downtime and technic - economical requires connected to wool quality to be achieved. Supervisory and control system either eliminates unwanted changes in the production line or restricts them within the allowable limits according to the technology. In this way, the optimization of energy and raw materials consumption and appropriate products quality is achieved, where requirements are satisfied in accordance with process safety and environmental standards. SCADA provides a visual representation of controlled and uncontrolled parts of the technological process, processing alarms and events, monitoring of the changes of relevant

New Process Controls for the Hera Cryogenic Plant

Science.gov (United States)

Böckmann, T.; Clausen, M.; Gerke, Chr.; Prüß, K.; Schoeneburg, B.; Urbschat, P.

2010-04-01

The cryogenic plant built for the HERA accelerator at DESY in Hamburg (Germany) is now in operation for more than two decades. The commercial process control system for the cryogenic plant is in operation for the same time period. Ever since the operator stations, the control network and the CPU boards in the process controllers went through several upgrade stages. Only the centralized Input/Output system was kept unchanged. Many components have been running beyond the expected lifetime. The control system for one at the three parts of the cryogenic plant has been replaced recently by a distributed I/O system. The I/O nodes are connected to several Profibus-DP field busses. Profibus provides the infrastructure to attach intelligent sensors and actuators directly to the process controllers which run the open source process control software EPICS. This paper describes the modification process on all levels from cabling through I/O configuration, the process control software up to the operator displays.

Advanced Map For Real-Time Process Control

Science.gov (United States)

Shiobara, Yasuhisa; Matsudaira, Takayuki; Sashida, Yoshio; Chikuma, Makoto

1987-10-01

MAP, a communications protocol for factory automation proposed by General Motors [1], has been accepted by users throughout the world and is rapidly becoming a user standard. In fact, it is now a LAN standard for factory automation. MAP is intended to interconnect different devices, such as computers and programmable devices, made by different manufacturers, enabling them to exchange information. It is based on the OSI intercomputer com-munications protocol standard under development by the ISO. With progress and standardization, MAP is being investigated for application to process control fields other than factory automation [2]. The transmission response time of the network system and centralized management of data exchanged with various devices for distributed control are import-ant in the case of a real-time process control with programmable controllers, computers, and instruments connected to a LAN system. MAP/EPA and MINI MAP aim at reduced overhead in protocol processing and enhanced transmission response. If applied to real-time process control, a protocol based on point-to-point and request-response transactions limits throughput and transmission response. This paper describes an advanced MAP LAN system applied to real-time process control by adding a new data transmission control that performs multicasting communication voluntarily and periodically in the priority order of data to be exchanged.

On-line optimal control improves gas processing

International Nuclear Information System (INIS)

Berkowitz, P.N.; Papadopoulos, M.N.

1992-01-01

This paper reports that the authors' companies jointly funded the first phase of a gas processing liquids optimization project that has the specific purposes to: Improve the return of processing natural gas liquids, Develop sets of control algorithms, Make available a low-cost solution suitable for small to medium-sized gas processing plants, Test and demonstrate the feasibility of line control. The ARCO Willard CO 2 gas recovery processing plant was chosen as the initial test site to demonstrate the application of multivariable on-line optimal control. One objective of this project is to support an R ampersand D effort to provide a standardized solution to the various types of gas processing plants in the U.S. Processes involved in these gas plants include cryogenic separations, demethanization, lean oil absorption, fractionation and gas treating. Next, the proposed solutions had to be simple yet comprehensive enough to allow an operator to maintain product specifications while operating over a wide range of gas input flow and composition. This had to be a supervisors system that remained on-line more than 95% of the time, and achieved reduced plant operating variability and improved variable cost control. It took more than a year to study various gas processes and to develop a control approach before a real application was finally exercised. An initial process for C 2 and CO 2 recoveries was chosen

PROCESS VARIABILITY REDUCTION THROUGH STATISTICAL PROCESS CONTROL FOR QUALITY IMPROVEMENT

Directory of Open Access Journals (Sweden)

B.P. Mahesh

2010-09-01

Full Text Available Quality has become one of the most important customer decision factors in the selection among the competing product and services. Consequently, understanding and improving quality is a key factor leading to business success, growth and an enhanced competitive position. Hence quality improvement program should be an integral part of the overall business strategy. According to TQM, the effective way to improve the Quality of the product or service is to improve the process used to build the product. Hence, TQM focuses on process, rather than results as the results are driven by the processes. Many techniques are available for quality improvement. Statistical Process Control (SPC is one such TQM technique which is widely accepted for analyzing quality problems and improving the performance of the production process. This article illustrates the step by step procedure adopted at a soap manufacturing company to improve the Quality by reducing process variability using Statistical Process Control.

Quantum Control of Molecular Processes

CERN Document Server

Shapiro, Moshe

2012-01-01

Written by two of the world's leading researchers in the field, this is a systematic introduction to the fundamental principles of coherent control, and to the underlying physics and chemistry.This fully updated second edition is enhanced by 80% and covers the latest techniques and applications, including nanostructures, attosecond processes, optical control of chirality, and weak and strong field quantum control. Developments and challenges in decoherence-sensitive condensed phase control as well as in bimolecular control are clearly described.Indispensable for atomic, molecular and chemical

Practical Implementations of Advanced Process Control for Linear Systems

DEFF Research Database (Denmark)

Knudsen, Jørgen K . H.; Huusom, Jakob Kjøbsted; Jørgensen, John Bagterp

2013-01-01

This paper describes some practical problems encountered, when implementing Advanced Process Control, APC, schemes on linear processes. The implemented APC controllers discussed will be LQR, Riccati MPC and Condensed MPC controllers illustrated by simulation of the Four Tank Process and a lineari......This paper describes some practical problems encountered, when implementing Advanced Process Control, APC, schemes on linear processes. The implemented APC controllers discussed will be LQR, Riccati MPC and Condensed MPC controllers illustrated by simulation of the Four Tank Process...... on pilot plant equipment on the department of Chemical Engineering DTU Lyngby....

The Vivitron process control

International Nuclear Information System (INIS)

Lutz, J.R.; Marsaudon, J.C.

1989-10-01

The operation of the VIVITRON electrostatic accelerator designed since 1981 and under construction at the CRN since 1985 needs a dedicated process control set up. The study and design of this control system started in 1987. The electrostatic accelerators are rarely operated by a modern control system. So little knowledge is available in this field. The timing problems are generally weak but the Vivitron specific structure, with seven porticos in the tank and sophisticated beam handling in the terminal, imposes control equipment inside the tank under extreme severe conditions. Several steps are necessary to achieve the full size control system. Some tests in the MP used as a pilot machine supplied practical information about surrounding accelerator conditions inside the tank. They also provided better knowledge of the beam behavior, especially inside the accelerator tube

Intelligent Controller Design for a Chemical Process

OpenAIRE

Mr. Glan Devadhas G; Dr.Pushpakumar S.

2010-01-01

Chemical process control is a challenging problem due to the strong on*line non*linearity and extreme sensitivity to disturbances of the process. Ziegler – Nichols tuned PI and PID controllers are found to provide poor performances for higher*order and non–linear systems. This paper presents an application of one*step*ahead fuzzy as well as ANFIS (adaptive*network*based fuzzy inference system) tuning scheme for an Continuous Stirred Tank Reactor CSTR process. The controller is designed based ...

General particle transport equation. Final report

International Nuclear Information System (INIS)

Lafi, A.Y.; Reyes, J.N. Jr.

1994-12-01

The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence

Fermentation process using specific oxygen uptake rates as a process control

Science.gov (United States)

Van Hoek, Pim [Minnetonka, MN; Aristidou, Aristos [Maple Grove, MN; Rush, Brian [Minneapolis, MN

2011-05-10

Specific oxygen uptake (OUR) is used as a process control parameter in fermentation processes. OUR is determined during at least the production phase of a fermentation process, and process parameters are adjusted to maintain the OUR within desired ranges. The invention is particularly applicable when the fermentation is conducted using a microorganism having a natural PDC pathway that has been disrupted so that it no longer functions. Microorganisms of this sort often produce poorly under strictly anaerobic conditions. Microaeration controlled by monitoring OUR allows the performance of the microorganism to be optimized.

Examining Potential Boundary Bias Effects in Kernel Smoothing on Equating: An Introduction for the Adaptive and Epanechnikov Kernels.

Science.gov (United States)

Cid, Jaime A; von Davier, Alina A

2015-05-01

Test equating is a method of making the test scores from different test forms of the same assessment comparable. In the equating process, an important step involves continuizing the discrete score distributions. In traditional observed-score equating, this step is achieved using linear interpolation (or an unscaled uniform kernel). In the kernel equating (KE) process, this continuization process involves Gaussian kernel smoothing. It has been suggested that the choice of bandwidth in kernel smoothing controls the trade-off between variance and bias. In the literature on estimating density functions using kernels, it has also been suggested that the weight of the kernel depends on the sample size, and therefore, the resulting continuous distribution exhibits bias at the endpoints, where the samples are usually smaller. The purpose of this article is (a) to explore the potential effects of atypical scores (spikes) at the extreme ends (high and low) on the KE method in distributions with different degrees of asymmetry using the randomly equivalent groups equating design (Study I), and (b) to introduce the Epanechnikov and adaptive kernels as potential alternative approaches to reducing boundary bias in smoothing (Study II). The beta-binomial model is used to simulate observed scores reflecting a range of different skewed shapes.

Using fundamental equations to describe basic phenomena

DEFF Research Database (Denmark)

Jakobsen, Arne; Rasmussen, Bjarne D.

1999-01-01

When the fundamental thermodynamic balance equations (mass, energy, and momentum) are used to describe the processes in a simple refrigeration system, then one finds that the resulting equation system will have a degree of freedom equal to one. Further investigations reveal that it is the equatio...

The modified simple equation method for solving some fractional ...

Indian Academy of Sciences (India)

... and processes in various areas of natural science. Thus, many effective and powerful methods have been established and improved. In this study, we establish exact solutions of the time fractional biological population model equation and nonlinearfractional Klein–Gordon equation by using the modified simple equation ...

Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations

Science.gov (United States)

Athanassoulis, Agissilaos

2018-03-01

We consider the semiclassical limit of nonlinear Schrödinger equations with initial data that are well localized in both position and momentum (non-parametric wavepackets). We recover the Wigner measure (WM) of the problem, a macroscopic phase-space density which controls the propagation of the physical observables such as mass, energy and momentum. WMs have been used to create effective models for wave propagation in: random media, quantum molecular dynamics, mean field limits, and the propagation of electrons in graphene. In nonlinear settings, the Vlasov-type equations obtained for the WM are often ill-posed on the physically interesting spaces of initial data. In this paper we are able to select the measure-valued solution of the 1  +  1 dimensional Vlasov-Poisson equation which correctly captures the semiclassical limit, thus finally resolving the non-uniqueness in the seminal result of Zhang et al (2012 Comm. Pure Appl. Math. 55 582-632). The same approach is also applied to the Vlasov-Dirac-Benney equation with small wavepacket initial data, extending several known results.

A General Linear Method for Equating with Small Samples

Science.gov (United States)

Albano, Anthony D.

2015-01-01

Research on equating with small samples has shown that methods with stronger assumptions and fewer statistical estimates can lead to decreased error in the estimated equating function. This article introduces a new approach to linear observed-score equating, one which provides flexible control over how form difficulty is assumed versus estimated…

Screen-based process control in nuclear plants

International Nuclear Information System (INIS)

Hinz, W.; Arnoldt, C.; Hessler, C.

1993-01-01

Requirements, development and conceptual design of a screen-based control room for nuclear power plants are outlined. The control room consists of three or four equally equipped operator workstations comprising screens for process information and manual process control. A plant overview will assist the coordination among the operators. A safety classified backup system (safety control area) is provided to cover postulated failures of the control means. Some aspects of ergonomical validation and of future development trends are discussed. (orig.) [de

Microeconomics of process control in semiconductor manufacturing

Science.gov (United States)

Monahan, Kevin M.

2003-06-01

Process window control enables accelerated design-rule shrinks for both logic and memory manufacturers, but simple microeconomic models that directly link the effects of process window control to maximum profitability are rare. In this work, we derive these links using a simplified model for the maximum rate of profit generated by the semiconductor manufacturing process. We show that the ability of process window control to achieve these economic objectives may be limited by variability in the larger manufacturing context, including measurement delays and process variation at the lot, wafer, x-wafer, x-field, and x-chip levels. We conclude that x-wafer and x-field CD control strategies will be critical enablers of density, performance and optimum profitability at the 90 and 65nm technology nodes. These analyses correlate well with actual factory data and often identify millions of dollars in potential incremental revenue and cost savings. As an example, we show that a scatterometry-based CD Process Window Monitor is an economically justified, enabling technology for the 65nm node.

Security of legacy process control systems : Moving towards secure process control systems

NARCIS (Netherlands)

Oosterink, M.

2012-01-01

This white paper describes solutions which organisations may use to improve the security of their legacy process control systems. When we refer to a legacy system, we generally refer to old methodologies, technologies, computer systems or applications which are still in use, despite the fact that

State-space representation of the reactor dynamics equations

International Nuclear Information System (INIS)

Bernard, J.A.

1995-01-01

This paper describes a novel formulation of the reactor space-independent kinetics equations. The intent is to present these equations in a form that is both compatible with modern control theory and mathematically rigorous. It is desired to write the kinetics equations in the standard state variable representation, x = Ax, where x is the state vector and A is the system matrix and, at the same time, avoid mathematical compromises such as the linearization of an equation about a particular operating point. The advantage to this proposed formulation is that it may allow the lateral transfer of existing control concepts, some that have been developed for other fields, to the operation of nuclear reactors. For example, sliding mode control has been developed to allow robots to function in a robust manner in the presence of changes in the system model. This is necessary because a robot is expected to be capable of picking up an object of unknown mass and moving that object along a specified trajectory. The variability of the object's mass introduces an uncertainty into the system model that is used to deduce the appropriate control action. Thus, the robot controller must be made robust against such variations. Sliding mode control is one means of accomplishing this. A reactor controller might benefit from the same concept if its objective were to cause the reactor power to move along a demanded trajectory despite the presence of some uncertainty in the net amount of reactivity that is present

[Statistical process control applied to intensity modulated radiotherapy pretreatment controls with portal dosimetry].

Science.gov (United States)

Villani, N; Gérard, K; Marchesi, V; Huger, S; François, P; Noël, A

2010-06-01

The first purpose of this study was to illustrate the contribution of statistical process control for a better security in intensity modulated radiotherapy (IMRT) treatments. This improvement is possible by controlling the dose delivery process, characterized by pretreatment quality control results. So, it is necessary to put under control portal dosimetry measurements (currently, the ionisation chamber measurements were already monitored by statistical process control thanks to statistical process control tools). The second objective was to state whether it is possible to substitute ionisation chamber with portal dosimetry in order to optimize time devoted to pretreatment quality control. At Alexis-Vautrin center, pretreatment quality controls in IMRT for prostate and head and neck treatments were performed for each beam of each patient. These controls were made with an ionisation chamber, which is the reference detector for the absolute dose measurement, and with portal dosimetry for the verification of dose distribution. Statistical process control is a statistical analysis method, coming from industry, used to control and improve the studied process quality. It uses graphic tools as control maps to follow-up process, warning the operator in case of failure, and quantitative tools to evaluate the process toward its ability to respect guidelines: this is the capability study. The study was performed on 450 head and neck beams and on 100 prostate beams. Control charts, showing drifts, both slow and weak, and also both strong and fast, of mean and standard deviation have been established and have shown special cause introduced (manual shift of the leaf gap of the multileaf collimator). Correlation between dose measured at one point, given with the EPID and the ionisation chamber has been evaluated at more than 97% and disagreement cases between the two measurements were identified. The study allowed to demonstrate the feasibility to reduce the time devoted to

Statistical process control applied to intensity modulated radiotherapy pretreatment controls with portal dosimetry

International Nuclear Information System (INIS)

Villani, N.; Noel, A.; Villani, N.; Gerard, K.; Marchesi, V.; Huger, S.; Noel, A.; Francois, P.

2010-01-01

Purpose The first purpose of this study was to illustrate the contribution of statistical process control for a better security in intensity modulated radiotherapy (I.M.R.T.) treatments. This improvement is possible by controlling the dose delivery process, characterized by pretreatment quality control results. So, it is necessary to put under control portal dosimetry measurements (currently, the ionisation chamber measurements were already monitored by statistical process control thanks to statistical process control tools). The second objective was to state whether it is possible to substitute ionisation chamber with portal dosimetry in order to optimize time devoted to pretreatment quality control. Patients and methods At Alexis-Vautrin center, pretreatment quality controls in I.M.R.T. for prostate and head and neck treatments were performed for each beam of each patient. These controls were made with an ionisation chamber, which is the reference detector for the absolute dose measurement, and with portal dosimetry for the verification of dose distribution. Statistical process control is a statistical analysis method, coming from industry, used to control and improve the studied process quality. It uses graphic tools as control maps to follow-up process, warning the operator in case of failure, and quantitative tools to evaluate the process toward its ability to respect guidelines: this is the capability study. The study was performed on 450 head and neck beams and on 100 prostate beams. Results Control charts, showing drifts, both slow and weak, and also both strong and fast, of mean and standard deviation have been established and have shown special cause introduced (manual shift of the leaf gap of the multi-leaf collimator). Correlation between dose measured at one point, given with the E.P.I.D. and the ionisation chamber has been evaluated at more than 97% and disagreement cases between the two measurements were identified. Conclusion The study allowed to

Application of Statistical Process Control (SPC in it´s Quality control

Directory of Open Access Journals (Sweden)

Carlos Hernández-Pedrera

2015-12-01

Full Text Available The overall objective of this paper is to use the SPC to assess the possibility of improving the process of obtaining a sanitary device. As specific objectives we set out to identify the variables to be analyzed to enter the statistical control of process (SPC, analyze possible errors and variations indicated by the control charts in addition to evaluate and compare the results achieved with the study of SPC before and after monitoring direct in the production line were used sampling methods and laboratory replacement to determine the quality of the finished product, then statistical methods were applied seeking to emphasize the importance and contribution from its application to monitor corrective actions and support processes in production. It was shown that the process is under control because the results were found within established control limits. There is a tendency to be displaced toward one end of the boundary, the distribution exceeds the limits, creating the possibility that under certain conditions the process is out of control, the results also showed that the process being within the limits of quality control is operating far from the optimal conditions. In any of the study situations were obtained products outside the limits of weight and discoloration but defective products were obtained.

A comprehensive analysis of the IMRT dose delivery process using statistical process control (SPC)

Energy Technology Data Exchange (ETDEWEB)

Gerard, Karine; Grandhaye, Jean-Pierre; Marchesi, Vincent; Kafrouni, Hanna; Husson, Francois; Aletti, Pierre [Research Center for Automatic Control (CRAN), Nancy University, CNRS, 54516 Vandoeuvre-les-Nancy (France); Department of Medical Physics, Alexis Vautrin Cancer Center, 54511 Vandoeuvre-les-Nancy Cedex (France) and DOSIsoft SA, 94230 Cachan (France); Research Laboratory for Innovative Processes (ERPI), Nancy University, EA 3767, 5400 Nancy Cedex (France); Department of Medical Physics, Alexis Vautrin Cancer Center, 54511 Vandoeuvre-les-Nancy Cedex (France); DOSIsoft SA, 94230 Cachan (France); Research Center for Automatic Control (CRAN), Nancy University, CNRS, 54516 Vandoeuvre-les-Nancy, France and Department of Medical Physics, Alexis Vautrin Cancer Center, 54511 Vandoeuvre-les-Nancy Cedex (France)

2009-04-15

The aim of this study is to introduce tools to improve the security of each IMRT patient treatment by determining action levels for the dose delivery process. To achieve this, the patient-specific quality control results performed with an ionization chamber--and which characterize the dose delivery process--have been retrospectively analyzed using a method borrowed from industry: Statistical process control (SPC). The latter consisted in fulfilling four principal well-structured steps. The authors first quantified the short term variability of ionization chamber measurements regarding the clinical tolerances used in the cancer center ({+-}4% of deviation between the calculated and measured doses) by calculating a control process capability (C{sub pc}) index. The C{sub pc} index was found superior to 4, which implies that the observed variability of the dose delivery process is not biased by the short term variability of the measurement. Then, the authors demonstrated using a normality test that the quality control results could be approximated by a normal distribution with two parameters (mean and standard deviation). Finally, the authors used two complementary tools--control charts and performance indices--to thoroughly analyze the IMRT dose delivery process. Control charts aim at monitoring the process over time using statistical control limits to distinguish random (natural) variations from significant changes in the process, whereas performance indices aim at quantifying the ability of the process to produce data that are within the clinical tolerances, at a precise moment. The authors retrospectively showed that the analysis of three selected control charts (individual value, moving-range, and EWMA control charts) allowed efficient drift detection of the dose delivery process for prostate and head-and-neck treatments before the quality controls were outside the clinical tolerances. Therefore, when analyzed in real time, during quality controls, they should

A comprehensive analysis of the IMRT dose delivery process using statistical process control (SPC).

Science.gov (United States)

Gérard, Karine; Grandhaye, Jean-Pierre; Marchesi, Vincent; Kafrouni, Hanna; Husson, François; Aletti, Pierre

2009-04-01

The aim of this study is to introduce tools to improve the security of each IMRT patient treatment by determining action levels for the dose delivery process. To achieve this, the patient-specific quality control results performed with an ionization chamber--and which characterize the dose delivery process--have been retrospectively analyzed using a method borrowed from industry: Statistical process control (SPC). The latter consisted in fulfilling four principal well-structured steps. The authors first quantified the short-term variability of ionization chamber measurements regarding the clinical tolerances used in the cancer center (+/- 4% of deviation between the calculated and measured doses) by calculating a control process capability (C(pc)) index. The C(pc) index was found superior to 4, which implies that the observed variability of the dose delivery process is not biased by the short-term variability of the measurement. Then, the authors demonstrated using a normality test that the quality control results could be approximated by a normal distribution with two parameters (mean and standard deviation). Finally, the authors used two complementary tools--control charts and performance indices--to thoroughly analyze the IMRT dose delivery process. Control charts aim at monitoring the process over time using statistical control limits to distinguish random (natural) variations from significant changes in the process, whereas performance indices aim at quantifying the ability of the process to produce data that are within the clinical tolerances, at a precise moment. The authors retrospectively showed that the analysis of three selected control charts (individual value, moving-range, and EWMA control charts) allowed efficient drift detection of the dose delivery process for prostate and head-and-neck treatments before the quality controls were outside the clinical tolerances. Therefore, when analyzed in real time, during quality controls, they should improve the

Discrete Control Processes, Dynamic Games and Multicriterion Control Problems

Directory of Open Access Journals (Sweden)

Dumitru Lozovanu

2002-07-01

Full Text Available The discrete control processes with state evaluation in time of dynamical system is considered. A general model of control problems with integral-time cost criterion by a trajectory is studied and a general scheme for solving such classes of problems is proposed. In addition the game-theoretical and multicriterion models for control problems are formulated and studied.

QCD evolution equations for high energy partons in nuclear matter

CERN Document Server

Kinder-Geiger, Klaus; Geiger, Klaus; Mueller, Berndt

1994-01-01

We derive a generalized form of Altarelli-Parisi equations to decribe the time evolution of parton distributions in a nuclear medium. In the framework of the leading logarithmic approximation, we obtain a set of coupled integro- differential equations for the parton distribution functions and equations for the virtuality (``age'') distribution of partons. In addition to parton branching processes, we take into account fusion and scattering processes that are specific to QCD in medium. Detailed balance between gain and loss terms in the resulting evolution equations correctly accounts for both real and virtual contributions which yields a natural cancellation of infrared divergences.

Electron-acoustic Instability Simulated By Modified Zakharov Equations

Science.gov (United States)

Jásenský, V.; Fiala, V.; Vána, O.; Trávnícek, P.; Hellinger, P.

We present non-linear equations describing processes in plasma when electron - acoustic waves are excited. These waves are present for instance in the vicinity of Earth's bow shock and in the polar ionosphere. Frequently they are excited by an elec- tron beam in a plasma with two electron populations, a cold and hot one. We derive modified Zakharov equations from kinetic theory for such a case together with numer- ical method for solving of this type of equations. Bispectral analysis is used to show which non-linear wave processes are of importance in course of the instability. Finally, we compare these results with similar simulations using Vlasov approach.

On optimal control of a sweeping process coupled with an ordinary differential equation

Czech Academy of Sciences Publication Activity Database

Adam, Lukáš; Outrata, Jiří

2014-01-01

Roč. 19, č. 9 (2014), s. 2709-2738 ISSN 1531-3492 R&D Projects: GA ČR(CZ) GAP201/12/0671 Grant - others:GA MŠk(CZ) SVV-2013-267315 Institutional support: RVO:67985556 Keywords : optimal control * variational inequality * variational analysis * coderivative * solution map * queuing theory Subject RIV: BA - General Mathematics Impact factor: 0.768, year: 2014 http://library.utia.cas.cz/separaty/2014/MTR/adam-0434417.pdf

Processing implicit control: evidence from reading times

Directory of Open Access Journals (Sweden)

Michael eMcCourt

2015-10-01

Full Text Available Sentences such as The ship was sunk to collect the insurance exhibit an unusual form of anaphora, implicit control, where neither anaphor nor antecedent is audible. The nonfinite reason clause has an understood subject, PRO, that is anaphoric; here it may be understood as naming the agent of the event of the host clause. Yet since the host is a short passive, this agent is realized by no audible dependent. The putative antecedent to PRO is therefore implicit, which it normally cannot be. What sorts of representations subserve the comprehension of this dependency? Here we present four self-paced reading time studies directed at this question. Previous work showed no processing cost for implicit versus explicit control, and took this to support the view that PRO is linked syntactically to a silent argument in the passive. We challenge this conclusion by reporting that we also find no processing cost for remote implicit control, as in: The ship was sunk. The reason was to collect the insurance. Here the dependency crosses two independent sentences, and so cannot, we argue, be mediated by syntax. Our Experiments 1-4 examined the processing of both implicit (short passive and explicit (active or long passive control in both local and remote configurations. Experiments 3 and 4 added either three days ago or just in order to the local conditions, to control for the distance between the passive and infinitival verbs, and for the predictability of the reason clause, respectively. We replicate the finding that implicit control does not impose an additional processing cost. But critically we show that remote control does not impose a processing cost either. Reading times at the reason clause were never slower when control was remote. In fact they were always faster. Thus efficient processing of local implicit control cannot show that implicit control is mediated by syntax; nor, in turn, that there is a silent but grammatically active argument in passives.

High-Level Waste (HLW) Feed Process Control Strategy

International Nuclear Information System (INIS)

STAEHR, T.W.

2000-01-01

The primary purpose of this document is to describe the overall process control strategy for monitoring and controlling the functions associated with the Phase 1B high-level waste feed delivery. This document provides the basis for process monitoring and control functions and requirements needed throughput the double-shell tank system during Phase 1 high-level waste feed delivery. This document is intended to be used by (1) the developers of the future Process Control Plan and (2) the developers of the monitoring and control system

Improving the Bandwidth Selection in Kernel Equating

Science.gov (United States)

Andersson, Björn; von Davier, Alina A.

2014-01-01

We investigate the current bandwidth selection methods in kernel equating and propose a method based on Silverman's rule of thumb for selecting the bandwidth parameters. In kernel equating, the bandwidth parameters have previously been obtained by minimizing a penalty function. This minimization process has been criticized by practitioners…

Linear q-nonuniform difference equations

International Nuclear Information System (INIS)

Bangerezako, Gaspard

2010-01-01

We introduce basic concepts of q-nonuniform differentiation and integration and study linear q-nonuniform difference equations and systems, as well as their application in q-nonuniform difference linear control systems. (author)

Controlling Laboratory Processes From A Personal Computer

Science.gov (United States)

Will, H.; Mackin, M. A.

1991-01-01

Computer program provides natural-language process control from IBM PC or compatible computer. Sets up process-control system that either runs without operator or run by workers who have limited programming skills. Includes three smaller programs. Two of them, written in FORTRAN 77, record data and control research processes. Third program, written in Pascal, generates FORTRAN subroutines used by other two programs to identify user commands with device-driving routines written by user. Also includes set of input data allowing user to define user commands to be executed by computer. Requires personal computer operating under MS-DOS with suitable hardware interfaces to all controlled devices. Also requires FORTRAN 77 compiler and device drivers written by user.

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions.

Science.gov (United States)

Lu, Benzhuo; Holst, Michael J; McCammon, J Andrew; Zhou, Y C

2010-09-20

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems.

Parallel Algorithm Solves Coupled Differential Equations

Science.gov (United States)

Hayashi, A.

1987-01-01

Numerical methods adapted to concurrent processing. Algorithm solves set of coupled partial differential equations by numerical integration. Adapted to run on hypercube computer, algorithm separates problem into smaller problems solved concurrently. Increase in computing speed with concurrent processing over that achievable with conventional sequential processing appreciable, especially for large problems.

INVARIANTS OF GENERALIZED RAPOPORT-LEAS EQUATIONS

Directory of Open Access Journals (Sweden)

Elena N. Kushner

2018-01-01

Full Text Available For the generalized Rapoport-Leas equations, algebra of differential invariants is constructed with respect to point transformations, that is, transformations of independent and dependent variables. The finding of a general transformation of this type reduces to solving an extremely complicated functional equation. Therefore, following the approach of Sophus Lie, we restrict ourselves to the search for infinitesimal transformations which are generated by translations along the trajectories of vector fields. The problem of finding these vector fields reduces to the redefined system decision of linear differential equations with respect to their coefficients. The Rapoport-Leas equations arise in the study of nonlinear filtration processes in porous media, as well as in other areas of natural science: for example, these equations describe various physical phenomena: two-phase filtration in a porous medium, filtration of a polytropic gas, and propagation of heat at nuclear explosion. They are vital topic for research: in recent works of Bibikov, Lychagin, and others, the analysis of the symmetries of the generalized Rapoport-Leas equations has been carried out; finite-dimensional dynamics and conditions of attractors existence have been found. Since the generalized RapoportLeas equations are nonlinear partial differential equations of the second order with two independent variables; the methods of the geometric theory of differential equations are used to study them in this paper. According to this theory differential equations generate subvarieties in the space of jets. This makes it possible to use the apparatus of modern differential geometry to study differential equations. We introduce the concept of admissible transformations, that is, replacements of variables that do not derive equations outside the class of the Rapoport-Leas equations. Such transformations form a Lie group. For this Lie group there are differential invariants that separate

Case Studies in Modelling, Control in Food Processes.

Science.gov (United States)

Glassey, J; Barone, A; Montague, G A; Sabou, V

This chapter discusses the importance of modelling and control in increasing food process efficiency and ensuring product quality. Various approaches to both modelling and control in food processing are set in the context of the specific challenges in this industrial sector and latest developments in each area are discussed. Three industrial case studies are used to demonstrate the benefits of advanced measurement, modelling and control in food processes. The first case study illustrates the use of knowledge elicitation from expert operators in the process for the manufacture of potato chips (French fries) and the consequent improvements in process control to increase the consistency of the resulting product. The second case study highlights the economic benefits of tighter control of an important process parameter, moisture content, in potato crisp (chips) manufacture. The final case study describes the use of NIR spectroscopy in ensuring effective mixing of dry multicomponent mixtures and pastes. Practical implementation tips and infrastructure requirements are also discussed.

Nonparametric predictive inference in statistical process control

NARCIS (Netherlands)

Arts, G.R.J.; Coolen, F.P.A.; Laan, van der P.

2000-01-01

New methods for statistical process control are presented, where the inferences have a nonparametric predictive nature. We consider several problems in process control in terms of uncertainties about future observable random quantities, and we develop inferences for these random quantities hased on

Fuzzy Control in the Process Industry

DEFF Research Database (Denmark)

Jantzen, Jan; Verbruggen, Henk; Østergaard, Jens-Jørgen

1999-01-01

Control problems in the process industry are dominated by non-linear and time-varying behaviour, many inner loops, and much interaction between the control loops. Fuzzy controllers have in some cases nevertheless mimicked the control actions of a human operator. Simple fuzzy controllers can...... be designed starting from PID controllers, and in more complex cases these can be used in connection with model-based predictive control. For high level control and supervisory control several simple controllers can be combined in a priority hierarchy such as the one developed in the cement industry...

Quantum Optimal Control of Single Harmonic Oscillator under Quadratic Controls together with Linear Dipole Polarizability: A Fluctuation Free Expectation Value Dynamical Perspective

International Nuclear Information System (INIS)

Ayvaz, Muzaffer; Demiralp, Metin

2011-01-01

In this study, the optimal control equations for one dimensional quantum harmonic oscillator under the quadratic control operators together with linear dipole polarizability effects are constructed in the sense of Heisenberg equation of motion. A numerical technique based on the approximation to the non-commuting quantum mechanical operators from the fluctuation free expectation value dynamics perspective in the classical limit is also proposed for the solution of optimal control equations which are ODEs with accompanying boundary conditions. The dipole interaction of the system is considered to be linear, and the observable whose expectation value will be suppressed during the control process is considered to be quadratic in terms of position operator x. The objective term operator is also assumed to be quadratic.

p-Euler equations and p-Navier-Stokes equations

Science.gov (United States)

Li, Lei; Liu, Jian-Guo

2018-04-01

We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

Equating error in observed-score equating

NARCIS (Netherlands)

van der Linden, Willem J.

2006-01-01

Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of

Control of Neutralization Process Using Soft Computing

Directory of Open Access Journals (Sweden)

G. Balasubramanian

2008-03-01

Full Text Available A novel model-based nonlinear control strategy is proposed using an experimental pH neutralization process. The control strategy involves a non linear neural network (NN model, in the context of internal model control (IMC. When integrated into the internal model control scheme, the resulting controller is shown to have favorable practical implications as well as superior performance. The designed model based online IMC controller was implemented to a laboratory scaled pH process in real time using dSPACE 1104 interface card. The responses of pH and acid flow rate shows good tracking for both the set point and load chances over the entire nonlinear region.

On the General Equation of the Second Degree

Indian Academy of Sciences (India)

IAS Admin

On the General Equation of the Second Degree. Keywords. Conics, eigenvalues, eigenvec- tors, pairs of lines. S Kesavan. S Kesavan works at the. Institute for Mathematical. Sciences, Chennai. His area of interest is partial differential equations with specialization in elliptic problems connected to homogenization, control.

Travelling wave solutions for a surface wave equation in fluid mechanics

Directory of Open Access Journals (Sweden)

Tian Yi

2016-01-01

Full Text Available This paper considers a non-linear wave equation arising in fluid mechanics. The exact traveling wave solutions of this equation are given by using G'/G-expansion method. This process can be reduced to solve a system of determining equations, which is large and difficult. To reduce this process, we used Wu elimination method. Example shows that this method is effective.

The product composition control system at Savannah River: Statistical process control algorithm

International Nuclear Information System (INIS)

Brown, K.G.

1994-01-01

The Defense Waste Processing Facility (DWPF) at the Savannah River Site (SRS) will be used to immobilize the approximately 130 million liters of high-level nuclear waste currently stored at the site in 51 carbon steel tanks. Waste handling operations separate this waste into highly radioactive insoluble sludge and precipitate and less radioactive water soluble salts. In DWPF, precipitate (PHA) is blended with insoluble sludge and ground glass frit to produce melter feed slurry which is continuously fed to the DWPF melter. The melter produces a molten borosilicate glass which is poured into stainless steel canisters for cooling and, ultimately, shipment to and storage in an geologic repository. Described here is the Product Composition Control System (PCCS) process control algorithm. The PCCS is the amalgam of computer hardware and software intended to ensure that the melt will be processable and that the glass wasteform produced will be acceptable. Within PCCS, the Statistical Process Control (SPC) Algorithm is the means which guides control of the DWPF process. The SPC Algorithm is necessary to control the multivariate DWPF process in the face of uncertainties arising from the process, its feeds, sampling, modeling, and measurement systems. This article describes the functions performed by the SPC Algorithm, characterization of DWPF prior to making product, accounting for prediction uncertainty, accounting for measurement uncertainty, monitoring a SME batch, incorporating process information, and advantages of the algorithm. 9 refs., 6 figs

Overview of advanced process control in welding within ERDA

International Nuclear Information System (INIS)

Armstrong, R.E.

1977-01-01

The special kinds of demands placed on ERDA weapons and reactors require them to have very reliable welds. Process control is critical in achieving this reliability. ERDA has a number of advanced process control projects underway with much of the emphasis being on electron beam welding. These include projects on voltage measurement, beam-current control, beam focusing, beam spot tracking, spike suppression, and computer control. A general discussion of process control in welding is followed by specific examples of some of the advanced joining process control projects in ERDA

Abecedarian School on Symmetries and Integrability of Difference Equations (ASIDE) & SIDE 12 International Conference Symmetries and Integrability of Difference Equations

CERN Document Server

Rebelo, Raphaël; Winternitz, Pavel

2017-01-01

This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers...

Functional Dual Adaptive Control with Recursive Gaussian Process Model

International Nuclear Information System (INIS)

Prüher, Jakub; Král, Ladislav

2015-01-01

The paper deals with dual adaptive control problem, where the functional uncertainties in the system description are modelled by a non-parametric Gaussian process regression model. Current approaches to adaptive control based on Gaussian process models are severely limited in their practical applicability, because the model is re-adjusted using all the currently available data, which keeps growing with every time step. We propose the use of recursive Gaussian process regression algorithm for significant reduction in computational requirements, thus bringing the Gaussian process-based adaptive controllers closer to their practical applicability. In this work, we design a bi-criterial dual controller based on recursive Gaussian process model for discrete-time stochastic dynamic systems given in an affine-in-control form. Using Monte Carlo simulations, we show that the proposed controller achieves comparable performance with the full Gaussian process-based controller in terms of control quality while keeping the computational demands bounded. (paper)

Two-process approach to electron beam welding control

International Nuclear Information System (INIS)

Lastovirya, V.N.

1987-01-01

The analysis and synthesis of multi-dimensional welding control systems, which require the usage of computers, should be conducted within the temporal range. From the general control theory point two approaches - one-process and two-process - are possible to electron beam welding. In case of two-process approach, subprocesses of heat source formation and direct metal melting are separated. Two-process approach leads to two-profile control system and provides the complete controlability of electron beam welding within the frameworks of systems with concentrated, as well as, with distributed parameters. Approach choice for the given problem solution is determined, first of all, by stability degree of heat source during welding

Temperature waves and the Boltzmann kinetic equation for phonons

International Nuclear Information System (INIS)

Urushev, D.; Borisov, M.; Vavrek, A.

1988-01-01

The ordinary parabolic equation for thermal conduction based on the Fourier empiric law as well as the generalized thermal conduction equation based on the Maxwell law have been derived from the Boltzmann equation for the phonons within the relaxation time approximation. The temperature waves of the so-called second sound in crystals at low temperatures are transformed into Fourier waves at low frequencies with respect to the characteristic frequency of the U-processes. These waves are transformed into temperature waves similar to the second sound waves in He II at frequences higher than the U-processes characteristic. 1 fig., 19 refs

Process-based quality for thermal spray via feedback control

Science.gov (United States)

Dykhuizen, R. C.; Neiser, R. A.

2006-09-01

Quality control of a thermal spray system manufacturing process is difficult due to the many input variables that need to be controlled. Great care must be taken to ensure that the process remains constant to obtain a consistent quality of the parts. Control is greatly complicated by the fact that measurement of particle velocities and temperatures is a noisy stochastic process. This article illustrates the application of quality control concepts to a wire flame spray process. A central feature of the real-time control system is an automatic feedback control scheme that provides fine adjustments to ensure that uncontrolled variations are accommodated. It is shown how the control vectors can be constructed from simple process maps to independently control particle velocity and temperature. This control scheme is shown to perform well in a real production environment. We also demonstrate that slight variations in the feed wire curvature can greatly influence the process. Finally, the geometry of the spray system and sensor must remain constant for the best reproducibility.

Improving Accuracy of Processing Through Active Control

Directory of Open Access Journals (Sweden)

N. N. Barbashov

2016-01-01

Full Text Available An important task of modern mathematical statistics with its methods based on the theory of probability is a scientific estimate of measurement results. There are certain costs under control, and under ineffective control when a customer has got defective products these costs are significantly higher because of parts recall.When machining the parts, under the influence of errors a range scatter of part dimensions is offset towards the tolerance limit. To improve a processing accuracy and avoid defective products involves reducing components of error in machining, i.e. to improve the accuracy of machine and tool, tool life, rigidity of the system, accuracy of the adjustment. In a given time it is also necessary to adapt machine.To improve an accuracy and a machining rate there, currently  become extensively popular various the in-process gaging devices and controlled machining that uses adaptive control systems for the process monitoring. Improving the accuracy in this case is compensation of a majority of technological errors. The in-cycle measuring sensors (sensors of active control allow processing accuracy improvement by one or two quality and provide a capability for simultaneous operation of several machines.Efficient use of in-cycle measuring sensors requires development of methods to control the accuracy through providing the appropriate adjustments. Methods based on the moving average, appear to be the most promising for accuracy control since they include data on the change in some last measured values of the parameter under control.

Analytical explicit formulas of average run length for long memory process with ARFIMA model on CUSUM control chart

Directory of Open Access Journals (Sweden)

Wilasinee Peerajit

2017-12-01

Full Text Available This paper proposes the explicit formulas for the derivation of exact formulas from Average Run Lengths (ARLs using integral equation on CUSUM control chart when observations are long memory processes with exponential white noise. The authors compared efficiency in terms of the percentage of absolute difference to a similar method to verify the accuracy of the ARLs between the values obtained by the explicit formulas and numerical integral equation (NIE method. The explicit formulas were based on Banach fixed point theorem which was used to guarantee the existence and uniqueness of the solution for ARFIMA(p,d,q. Results showed that the two methods are similar in good agreement with the percentage of absolute difference at less than 0.23%. Therefore, the explicit formulas are an efficient alternative for implementation in real applications because the computational CPU time for ARLs from the explicit formulas are 1 second preferable over the NIE method.

Performance prediction of gas turbines by solving a system of non-linear equations

Energy Technology Data Exchange (ETDEWEB)

Kaikko, J

1998-09-01

This study presents a novel method for implementing the performance prediction of gas turbines from the component models. It is based on solving the non-linear set of equations that corresponds to the process equations, and the mass and energy balances for the engine. General models have been presented for determining the steady state operation of single components. Single and multiple shad arrangements have been examined with consideration also being given to heat regeneration and intercooling. Emphasis has been placed upon axial gas turbines of an industrial scale. Applying the models requires no information of the structural dimensions of the gas turbines. On comparison with the commonly applied component matching procedures, this method incorporates several advantages. The application of the models for providing results is facilitated as less attention needs to be paid to calculation sequences and routines. Solving the set of equations is based on zeroing co-ordinate functions that are directly derived from the modelling equations. Therefore, controlling the accuracy of the results is easy. This method gives more freedom for the selection of the modelling parameters since, unlike for the matching procedures, exchanging these criteria does not itself affect the algorithms. Implicit relationships between the variables are of no significance, thus increasing the freedom for the modelling equations as well. The mathematical models developed in this thesis will provide facilities to optimise the operation of any major gas turbine configuration with respect to the desired process parameters. The computational methods used in this study may also be adapted to any other modelling problems arising in industry. (orig.) 36 refs.

Discretisation of the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements

Directory of Open Access Journals (Sweden)

E. D. Resende

2007-09-01

Full Text Available The freezing process is considered as a propagation problem and mathematically classified as an "initial value problem." The mathematical formulation involves a complex situation of heat transfer with simultaneous changes of phase and abrupt variation in thermal properties. The objective of the present work is to solve the non-linear heat transfer equation for food freezing processes using orthogonal collocation on finite elements. This technique has not yet been applied to freezing processes and represents an alternative numerical approach in this area. The results obtained confirmed the good capability of the numerical method, which allows the simulation of the freezing process in approximately one minute of computer time, qualifying its application in a mathematical optimising procedure. The influence of the latent heat released during the crystallisation phenomena was identified by the significant increase in heat load in the early stages of the freezing process.

Fault tolerant control of multivariable processes using auto-tuning PID controller.

Science.gov (United States)

Yu, Ding-Li; Chang, T K; Yu, Ding-Wen

2005-02-01

Fault tolerant control of dynamic processes is investigated in this paper using an auto-tuning PID controller. A fault tolerant control scheme is proposed composing an auto-tuning PID controller based on an adaptive neural network model. The model is trained online using the extended Kalman filter (EKF) algorithm to learn system post-fault dynamics. Based on this model, the PID controller adjusts its parameters to compensate the effects of the faults, so that the control performance is recovered from degradation. The auto-tuning algorithm for the PID controller is derived with the Lyapunov method and therefore, the model predicted tracking error is guaranteed to converge asymptotically. The method is applied to a simulated two-input two-output continuous stirred tank reactor (CSTR) with various faults, which demonstrate the applicability of the developed scheme to industrial processes.

Model-Based Integrated Process Design and Controller Design of Chemical Processes

DEFF Research Database (Denmark)

Abd Hamid, Mohd Kamaruddin Bin

that is typically formulated as a mathematical programming (optimization with constraints) problem is solved by the so-called reverse approach by decomposing it into four sequential hierarchical sub-problems: (i) pre-analysis, (ii) design analysis, (iii) controller design analysis, and (iv) final selection......This thesis describes the development and application of a new systematic modelbased methodology for performing integrated process design and controller design (IPDC) of chemical processes. The new methodology is simple to apply, easy to visualize and efficient to solve. Here, the IPDC problem...... are ordered according to the defined performance criteria (objective function). The final selected design is then verified through rigorous simulation. In the pre-analysis sub-problem, the concepts of attainable region and driving force are used to locate the optimal process-controller design solution...

Fuzzy systems for process identification and control

International Nuclear Information System (INIS)

Gorrini, V.; Bersini, H.

1994-01-01

Various issues related to the automatic construction and on-line adaptation of fuzzy controllers are addressed. A Direct Adaptive Fuzzy Control (this is an adaptive control methodology requiring a minimal knowledge of the processes to be coupled with) derived in a way reminiscent of neurocontrol methods, is presented. A classical fuzzy controller and a fuzzy realization of a PID controller is discussed. These systems implement a highly non-linear control law, and provide to be quite robust, even in the case of noisy inputs. In order to identify dynamic processes of order superior to one, we introduce a more complex architecture, called Recurrent Fuzzy System, that use some fuzzy internal variables to perform an inferential chaining.I

Applied analysis and differential equations

CERN Document Server

Cârj, Ovidiu

2007-01-01

This volume contains refereed research articles written by experts in the field of applied analysis, differential equations and related topics. Well-known leading mathematicians worldwide and prominent young scientists cover a diverse range of topics, including the most exciting recent developments. A broad range of topics of recent interest are treated: existence, uniqueness, viability, asymptotic stability, viscosity solutions, controllability and numerical analysis for ODE, PDE and stochastic equations. The scope of the book is wide, ranging from pure mathematics to various applied fields such as classical mechanics, biomedicine, and population dynamics.

Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbance

Directory of Open Access Journals (Sweden)

Pengcheng HAN

2017-12-01

Full Text Available In order to enrich the system stability theory of the control theories, taking Euler-Bernoulli beam equation as the research subject, the stability of Euler-Bernoulli beam equation with locally distributed disturbance is studied. A feedback controller based on output is designed to reduce the effects of the disturbances. The well-posedness of the nonlinear closed-loop system is investigated by the theory of maximal monotone operator, namely the existence and uniqueness of solutions for the closed-loop system. An appropriate state space is established, an appropriate inner product is defined, and a non-linear operator satisfying this state space is defined. Then, the system is transformed into the form of evolution equation. Based on this, the existence and uniqueness of solutions for the closed-loop system are proved. The asymptotic stability of the system is studied by constructing an appropriate Lyapunov function, which proves the asymptotic stability of the closed-loop system. The result shows that designing proper anti-interference controller is the foundation of investigating the system stability, and the research of the stability of Euler-bernoulli beam equation with locally distributed disturbance can prove the asymptotic stability of the system. This method can be extended to study the other equations such as wave equation, Timoshenko beam equation, Schrodinger equation, etc.

Parametrically Excited Oscillations of Second-Order Functional Differential Equations and Application to Duffing Equations with Time Delay Feedback

Directory of Open Access Journals (Sweden)

Mervan Pašić

2014-01-01

Full Text Available We study oscillatory behaviour of a large class of second-order functional differential equations with three freedom real nonnegative parameters. According to a new oscillation criterion, we show that if at least one of these three parameters is large enough, then the main equation must be oscillatory. As an application, we study a class of Duffing type quasilinear equations with nonlinear time delayed feedback and their oscillations excited by the control gain parameter or amplitude of forcing term. Finally, some open questions and comments are given for the purpose of further study on this topic.

Integrated Process Design, Control and Analysis of Intensified Chemical Processes

DEFF Research Database (Denmark)

Mansouri, Seyed Soheil

chemical processes; for example, intensified processes such as reactive distillation. Most importantly, it identifies and eliminates potentially promising design alternatives that may have controllability problems later. To date, a number of methodologies have been proposed and applied on various problems......, that the same principles that apply to a binary non-reactive compound system are valid also for a binary-element or a multi-element system. Therefore, it is advantageous to employ the element based method for multicomponent reaction-separation systems. It is shown that the same design-control principles...

Quantization of dynamical systems and stochastic control theory

International Nuclear Information System (INIS)

Guerra, F.; Morato, L.M.

1982-09-01

In the general framework of stochastic control theory we introduce a suitable form of stochastic action associated to the controlled process. Then a variational principle gives all main features of Nelson's stochastic mechanics. In particular we derive the expression of the current velocity field as the gradient of the phase action. Moreover the stochastic corrections to the Hamilton-Jacobi equation are in agreement with the quantum mechanical form of the Madelung fluid (equivalent to the Schroedinger equation). Therefore stochastic control theory can provide a very simple model simulating quantum mechanical behavior

Ordinary differential equations with applications in molecular biology.

Science.gov (United States)

Ilea, M; Turnea, M; Rotariu, M

2012-01-01

Differential equations are of basic importance in molecular biology mathematics because many biological laws and relations appear mathematically in the form of a differential equation. In this article we presented some applications of mathematical models represented by ordinary differential equations in molecular biology. The vast majority of quantitative models in cell and molecular biology are formulated in terms of ordinary differential equations for the time evolution of concentrations of molecular species. Assuming that the diffusion in the cell is high enough to make the spatial distribution of molecules homogenous, these equations describe systems with many participating molecules of each kind. We propose an original mathematical model with small parameter for biological phospholipid pathway. All the equations system includes small parameter epsilon. The smallness of epsilon is relative to the size of the solution domain. If we reduce the size of the solution region the same small epsilon will result in a different condition number. It is clear that the solution for a smaller region is less difficult. We introduce the mathematical technique known as boundary function method for singular perturbation system. In this system, the small parameter is an asymptotic variable, different from the independent variable. In general, the solutions of such equations exhibit multiscale phenomena. Singularly perturbed problems form a special class of problems containing a small parameter which may tend to zero. Many molecular biology processes can be quantitatively characterized by ordinary differential equations. Mathematical cell biology is a very active and fast growing interdisciplinary area in which mathematical concepts, techniques, and models are applied to a variety of problems in developmental medicine and bioengineering. Among the different modeling approaches, ordinary differential equations (ODE) are particularly important and have led to significant advances

Improving Instruction Using Statistical Process Control.

Science.gov (United States)

Higgins, Ronald C.; Messer, George H.

1990-01-01

Two applications of statistical process control to the process of education are described. Discussed are the use of prompt feedback to teachers and prompt feedback to students. A sample feedback form is provided. (CW)

Fokker-Planck equation in mirror research

International Nuclear Information System (INIS)

Post, R.F.

1983-01-01

Open confinement systems based on the magnetic mirror principle depend on the maintenance of particle distributions that may deviate substantially from Maxwellian distributions. Mirror research has therefore from the beginning relied on theoretical predictions of non-equilibrium rate processes obtained from solutions to the Fokker-Planck equation. The F-P equation plays three roles: Design of experiments, creation of classical standards against which to compare experiment, and predictions concerning mirror based fusion power systems. Analytical and computational approaches to solving the F-P equation for mirror systems will be reviewed, together with results and examples that apply to specific mirror systems, such as the tandem mirror

The Effect of Tutoring With Nonstandard Equations for Students With Mathematics Difficulty.

Science.gov (United States)

Powell, Sarah R; Driver, Melissa K; Julian, Tyler E

2015-01-01

Students often misinterpret the equal sign (=) as operational instead of relational. Research indicates misinterpretation of the equal sign occurs because students receive relatively little exposure to equations that promote relational understanding of the equal sign. No study, however, has examined effects of nonstandard equations on the equation solving and equal-sign understanding of students with mathematics difficulty (MD). In the present study, second-grade students with MD (n = 51) were randomly assigned to standard equations tutoring, combined tutoring (standard and nonstandard equations), and no-tutoring control. Combined tutoring students demonstrated greater gains on equation-solving assessments and equal-sign tasks compared to the other two conditions. Standard tutoring students demonstrated improved skill on equation solving over control students, but combined tutoring students' performance gains were significantly larger. Results indicate that exposure to and practice with nonstandard equations positively influence student understanding of the equal sign. © Hammill Institute on Disabilities 2013.

Engineering Process Monitoring for Control Room Operation

OpenAIRE

Bätz, M

2001-01-01

A major challenge in process operation is to reduce costs and increase system efficiency whereas the complexity of automated process engineering, control and monitoring systems increases continuously. To cope with this challenge the design, implementation and operation of process monitoring systems for control room operation have to be treated as an ensemble. This is only possible if the engineering of the monitoring information is focused on the production objective and is lead in close coll...

A neuro approach to solve fuzzy Riccati differential equations

Energy Technology Data Exchange (ETDEWEB)

Shahrir, Mohammad Shazri, E-mail: mshazri@gmail.com [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia); Telekom Malaysia, R& D TM Innovation Centre, LingkaranTeknokrat Timur, 63000 Cyberjaya, Selangor (Malaysia); Kumaresan, N., E-mail: drnk2008@gmail.com; Kamali, M. Z. M.; Ratnavelu, Kurunathan [InstitutSainsMatematik, Universiti Malaya 50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur (Malaysia)

2015-10-22

There are many applications of optimal control theory especially in the area of control systems in engineering. In this paper, fuzzy quadratic Riccati differential equation is estimated using neural networks (NN). Previous works have shown reliable results using Runge-Kutta 4th order (RK4). The solution can be achieved by solving the 1st Order Non-linear Differential Equation (ODE) that is found commonly in Riccati differential equation. Research has shown improved results relatively to the RK4 method. It can be said that NN approach shows promising results with the advantage of continuous estimation and improved accuracy that can be produced over RK4.

Integrated control system for electron beam processes

Science.gov (United States)

Koleva, L.; Koleva, E.; Batchkova, I.; Mladenov, G.

2018-03-01

The ISO/IEC 62264 standard is widely used for integration of the business systems of a manufacturer with the corresponding manufacturing control systems based on hierarchical equipment models, functional data and manufacturing operations activity models. In order to achieve the integration of control systems, formal object communication models must be developed, together with manufacturing operations activity models, which coordinate the integration between different levels of control. In this article, the development of integrated control system for electron beam welding process is presented as part of a fully integrated control system of an electron beam plant, including also other additional processes: surface modification, electron beam evaporation, selective melting and electron beam diagnostics.

Stochastic Differential Equations and Kondratiev Spaces

Energy Technology Data Exchange (ETDEWEB)

Vaage, G.

1995-05-01

The purpose of this mathematical thesis was to improve the understanding of physical processes such as fluid flow in porous media. An example is oil flowing in a reservoir. In the first of five included papers, Hilbert space methods for elliptic boundary value problems are used to prove the existence and uniqueness of a large family of elliptic differential equations with additive noise without using the Hermite transform. The ideas are then extended to the multidimensional case and used to prove existence and uniqueness of solution of the Stokes equations with additive noise. The second paper uses functional analytic methods for partial differential equations and presents a general framework for proving existence and uniqueness of solutions to stochastic partial differential equations with multiplicative noise, for a large family of noises. The methods are applied to equations of elliptic, parabolic as well as hyperbolic type. The framework presented can be extended to the multidimensional case. The third paper shows how the ideas from the second paper can be extended to study the moving boundary value problem associated with the stochastic pressure equation. The fourth paper discusses a set of stochastic differential equations. The fifth paper studies the relationship between the two families of Kondratiev spaces used in the thesis. 102 refs.

The effect of nonlinearity on unstable zones of Mathieu equation

Indian Academy of Sciences (India)

2017-02-09

Feb 9, 2017 ... Abstract. Mathieu equation is a well-known ordinary differential equation in which the excitation term appears as the non-constant coefficient. The mathematical modelling of many dynamic systems leads to Mathieu equation. The determination of the locus of unstable zone is important for the control of ...

Nonparametric predictive inference in statistical process control

NARCIS (Netherlands)

Arts, G.R.J.; Coolen, F.P.A.; Laan, van der P.

2004-01-01

Statistical process control (SPC) is used to decide when to stop a process as confidence in the quality of the next item(s) is low. Information to specify a parametric model is not always available, and as SPC is of a predictive nature, we present a control chart developed using nonparametric

Chaos synchronization of nonlinear Bloch equations

International Nuclear Information System (INIS)

Park, Ju H.

2006-01-01

In this paper, the problem of chaos synchronization of Bloch equations is considered. A novel nonlinear controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. A numerical example is given to illuminate the design procedure and advantage of the result derived

On-line control of a liquid-liquid extraction column by the modal control method

International Nuclear Information System (INIS)

Bonnefoi, P.; Poujol, A.; Zwingelstein, G.; Dargier, C.; Rouyer, H.

1977-02-01

The application of modal analysis to the on-line control of a liquid-liquid extraction column is presented. This process is used in reprocessing for U purification. U in the aqueous acid phase is extracted by a solvent flowing at counter-current. The process is described by 4 nonlinear equations and gives the U and acid concentrations in the two phases. An approximative model is established adapted to the control of the column. Some results of a numerical simulation are given when a single mode is controled. They show that a single sensor allows a good control [fr

Testing a Constrained MPC Controller in a Process Control Laboratory

Science.gov (United States)

Ricardez-Sandoval, Luis A.; Blankespoor, Wesley; Budman, Hector M.

2010-01-01

This paper describes an experiment performed by the fourth year chemical engineering students in the process control laboratory at the University of Waterloo. The objective of this experiment is to test the capabilities of a constrained Model Predictive Controller (MPC) to control the operation of a Double Pipe Heat Exchanger (DPHE) in real time.…

A case study: application of statistical process control tool for determining process capability and sigma level.

Science.gov (United States)

Chopra, Vikram; Bairagi, Mukesh; Trivedi, P; Nagar, Mona

2012-01-01

Statistical process control is the application of statistical methods to the measurement and analysis of variation process. Various regulatory authorities such as Validation Guidance for Industry (2011), International Conference on Harmonisation ICH Q10 (2009), the Health Canada guidelines (2009), Health Science Authority, Singapore: Guidance for Product Quality Review (2008), and International Organization for Standardization ISO-9000:2005 provide regulatory support for the application of statistical process control for better process control and understanding. In this study risk assessments, normal probability distributions, control charts, and capability charts are employed for selection of critical quality attributes, determination of normal probability distribution, statistical stability, and capability of production processes, respectively. The objective of this study is to determine tablet production process quality in the form of sigma process capability. By interpreting data and graph trends, forecasting of critical quality attributes, sigma process capability, and stability of process were studied. The overall study contributes to an assessment of process at the sigma level with respect to out-of-specification attributes produced. Finally, the study will point to an area where the application of quality improvement and quality risk assessment principles for achievement of six sigma-capable processes is possible. Statistical process control is the most advantageous tool for determination of the quality of any production process. This tool is new for the pharmaceutical tablet production process. In the case of pharmaceutical tablet production processes, the quality control parameters act as quality assessment parameters. Application of risk assessment provides selection of critical quality attributes among quality control parameters. Sequential application of normality distributions, control charts, and capability analyses provides a valid statistical

Non-instantaneous impulses in differential equations

CERN Document Server

Agarwal, Ravi; O'Regan, Donal

2017-01-01

This monograph is the first published book devoted to the theory of differential equations with non-instantaneous impulses. It aims to equip the reader with mathematical models and theory behind real life processes in physics, biology, population dynamics, ecology and pharmacokinetics. The authors examine a wide scope of differential equations with non-instantaneous impulses through three comprehensive chapters, providing an all-rounded and unique presentation on the topic, including: - Ordinary differential equations with non-instantaneous impulses (scalar and n-dimensional case) - Fractional differential equa tions with non-instantaneous impulses (with Caputo fractional derivatives of order q ϵ (0, 1)) - Ordinary differential equations with non-instantaneous impulses occurring at random moments (with exponential, Erlang, or Gamma distribution) Each chapter focuses on theory, proofs and examples, and contains numerous graphs to enrich the reader’s understanding. Additionally, a carefully selected bibliogr...