Disturbance models for offset‐free model‐predictive control
TL;DR: In this article, it was shown that a number of integrating disturbances equal to the number of measured variables is sufficient to guarantee zero offset in the controlled variables, and the results apply to square and nonsquare, open-loop stable, integrating and unstable systems.
Abstract: Model predictive control algorithms achieve offset-free control objectives by adding integrating disturbances to the process model. The purpose of these additional disturbances is to lump the plant-model mismatch and/or unmodeled disturbances. Its effectiveness has been proven for particular square cases only. For systems with a number of measured variables (p) greater than the number of manipulated variables (m), it is clear that any controller can track without offset at most m controlled variables. One may think that m integrating disturbances are sufficient to guarantee offset-free control in the m controlled variables. We show this idea is incorrect and present general conditions that allow zero steady-state offset. In particular, a number of integrating disturbances equal to the number of measured variables are shown to be sufficient to guarantee zero offset in the controlled variables. These results apply to square and nonsquare, open-loop stable, integrating and unstable systems.
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01 Dec 2004TL;DR: This paper recalls a few past achievements in Model Predictive Control, gives an overview of some current developments and suggests a few avenues for future research.
Abstract: This paper recalls a few past achievements in Model Predictive Control, gives an overview of some current developments and suggests a few avenues for future research.
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Book•
27 Jul 2017TL;DR: Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.
Abstract: Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control.
1,142 citations
Cites background or methods from "Disturbance models for offset‐free ..."
...Several disturbance models have been presented in the literature [13, 205, 193, 226, 225, 294]....
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...4 was proven in [226] by using a different approach....
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...Here we follow [226] and use the form: x(t+ 1) = Ax(t) + Bu(t) +Bdd(t) d(t+ 1) = d(t) y(t) = Cx(t) + Cdd(t) (12....
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...Extensive treatment of reference tracking for RHC can be found in in [13, 218, 225, 226, 198]....
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TL;DR: It is proved that error free output estimation and error free nominal tracking imply offset-free Model Predictive Control.
327 citations
Cites background or methods from "Disturbance models for offset‐free ..."
...Simply adding an integrator to the plant may not even remove offset as illustrated by Pannocchia and Rawlings (2003)....
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...This work presents a generalization of the concepts in Muske and Badgwell (2002), Pannocchia and Rawlings (2003) andMaeder et al. (2009) to nonlinear MPC, and at the same time offers a much simpler exposition of the ideas behind offset-free linear MPC....
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...…same system (42) is controlled by using a model of (38) linearized at the origin, as proposed in Maeder et al. (2009), Maeder and Morari (2008), Muske and Badgwell (2002), Pannocchia and Bemporad (2007), Pannocchia and Kerrigan (2003), Pannocchia and Rawlings (2003), and Qin and Badgwell (2003)....
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...We briefly recall the main results for linear models given in Muske and Badgwell (2002), Pannocchia and Rawlings (2003) and Maeder et al. (2009)....
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...In Muske and Rawlings (1993) and Pannocchia and Rawlings (2003) it is suggested to solve an additional optimization problem to determine the target independently from the MPC....
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TL;DR: This paper proposes using a hybrid configuration, in which a bank of ultracapacitors supplements the polymer electrolyte membrane fuel cell during fast current transients, to avoid fuel cell oxygen starvation, prevent air compressor surge and choke, and simultaneously match an arbitrary level of current demand
Abstract: The problem of oxygen starvation in fuel cells coupled with air compressor saturation limits, is addressed in this paper. We propose using a hybrid configuration, in which a bank of ultracapacitors supplements the polymer electrolyte membrane fuel cell during fast current transients. Our objective is to avoid fuel cell oxygen starvation, prevent air compressor surge and choke, and simultaneously match an arbitrary level of current demand. We formulate the distribution of current demand between the fuel cell and the bank of ultracapacitors in a model predictive control framework, which can handle multiple constraints of the hybrid system. Simulation results show that reactant deficit during sudden increase in stack current is reduced from 50% in stand-alone architecture to less than 1% in the hybrid configuration. In addition, the explicit constraint handling capability of the current management scheme prevents compressor surge and choke and maintains the state-of-charge of the ultracapacitor within feasible bounds
279 citations
Cites background from "Disturbance models for offset‐free ..."
...An interested reader can find more details about other possible disturbance models in [30] and [31]....
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TL;DR: This paper provides a unified framework for model predictive building control technology with focus on the real-world applications and presents the essential components of a practical implementation of MPC such as different control architectures and nuances of communication infrastructures within supervisory control and data acquisition (SCADA) systems.
276 citations
References
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01 Jan 1996
TL;DR: This book presents a rigorous, yet easily readable, introduction to the analysis and design of robust multivariable control systems and provides the reader with insights into the opportunities and limitations of feedback control.
Abstract: From the Publisher:
This is a book on practical feedback control and not on system theory in general. Feedback is used in control systems to change the dynamics of the system and to reduce the sensitivity of the system to both signal and model uncertainty. The book presents a rigorous, yet easily readable, introduction to the analysis and design of robust multivariable control systems. It provides the reader with insights into the opportunities and limitations of feedback control. Its objective is to enable the engineer to design real control systems. Important topics are: extensions and classical frequency-domain methods to multivariable systems, analysis of directions using the singular value decomposition, performance limitations and input-output controllability analysis, model uncertainty and robustness including the structured singular value, control structure design, and methods for controller synthesis and model reduction. Numerous worked examples, exercises and case studies, which make frequent use of MATLAB, are included. MATLAB files for examples and figures, solutions to selected exercises, extra problems and linear state-space models for the case studies are available on the Internet.
6,279 citations
Book•
01 Oct 1972
TL;DR: In this article, the authors provide an excellent introduction to feedback control system design, including a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems.
Abstract: Linear Optimal Control SystemsFeedback Control TheoryOptimal ControlLinear Optimal ControlOptimal Control SystemsThe Zeros of Linear Optimal Control Systems and Their Role in High Feedback Gain Stability DesignOptimal ControlLinear State-Space Control SystemsOptimal Control of Dynamic Systems Driven by Vector MeasuresApplied Linear Optimal Control Paperback with CD-ROMNonlinear and Optimal Control SystemsLinear SystemsLinear Control TheoryLinear Systems and Optimal ControlOptimal Control Methods for Linear Discrete-Time Economic SystemsOptimal Control Theory for Infinite Dimensional SystemsInfinite Dimensional Linear Control SystemsStochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop SolutionsApplications of Optimal Control Theory to Computer Controller DesignSwitching and Learning in Feedback SystemsContinuous Time Dynamical SystemsNew Trends in Optimal Filtering and Control for Polynomial and Time-Delay SystemsThe Theory and Application of Linear Optimal ControlTurnpike Theory of Continuous-Time Linear Optimal Control ProblemsLinear Optimal Control SystemsLinear Control TheoryCalculus of Variations and Optimal Control TheoryOptimal ControlNonlinear Controllability and Optimal ControlOptimal Control TheoryOptimal Control Of Singularly Perturbed Linear Systems And ApplicationsOptimal Control SystemsDesign criterion for improving the sensitivity of linear optimal control systemsLinear Stochastic Control SystemsConstrained Optimal Control of Linear and Hybrid SystemsOptimal Control Of Singularly Perturbed Linear Systems And ApplicationsPredictive Control for Linear and Hybrid SystemsOptimal ControlOptimal Control Theory with Applications in EconomicsNonlinear Optimal Control Theory Successfully classroom-tested at the graduate level, Linear Control Theory: Structure, Robustness, and Optimization covers three major areas of control engineering (PID control, robust control, and optimal control). It provides balanced coverage of elegant mathematical theory and useful engineering-oriented results. The first part of the book develops results relating to the design of PID and first-order controllers for continuous and discrete-time linear systems with possible delays. The second section deals with the robust stability and performance of systems under parametric and unstructured uncertainty. This section describes several elegant and sharp results, such as Kharitonov’s theorem and its extensions, the edge theorem, and the mapping theorem. Focusing on the optimal control of linear systems, the third part discusses the standard theories of the linear quadratic regulator, Hinfinity and l1 optimal control, and associated results. Written by recognized leaders in the field, this book explains how control theory can be applied to the design of real-world systems. It shows that the techniques of three term controllers, along with the results on robust and optimal control, are invaluable to developing and solving research problems in many areas of engineering.An excellent introduction to feedback control system design, this book offers a theoretical approach that captures the essential issues and can be applied to a wide range of practical problems. Its explorations of recent developments in the field emphasize the relationship of new procedures to classical control theory, with a focus on single input and output systems that keeps concepts accessible to students with limited backgrounds. The text is geared toward a single-semester senior course or a graduate-level class for students of electrical engineering. The opening chapters constitute a basic treatment of feedback design. Topics include a detailed formulation of the control design program, the fundamental issue of performance/stability robustness tradeoff, and the graphical design technique of loopshaping. Subsequent chapters extend the discussion of the loopshaping technique and connect it with notions of optimality. Concluding chapters examine controller design via optimization, offering a mathematical approach that is useful for multivariable systems.Upper-level undergraduate text introduces aspects of optimal control theory: dynamic programming, Pontryagin's minimum principle, and numerical techniques for trajectory optimization. Numerous figures, tables. Solution guide available upon request. 1970 edition.Infinite dimensional systems can be used to describe many phenomena in the real world. As is well known, heat conduction, properties of elastic plastic material, fluid dynamics, diffusion-reaction processes, etc., all lie within this area. The object that we are studying (temperature, displace ment, concentration, velocity, etc.) is usually referred to as the state. We are interested in the case where the state satisfies proper differential equa tions that are derived from certain physical laws, such as Newton's law, Fourier's law etc. The space in which the state exists is called the state space, and the equation that the state satisfies is called the state equation. By an infinite dimensional system we mean one whose corresponding state space is infinite dimensional. In particular, we are interested in the case where the state equation is one of the following types: partial differential equation, functional differential equation, integro-differential equation, or abstract evolution equation. The case in which the state equation is being a stochastic differential equation is also an infinite dimensional problem, but we will not discuss such a case in this book.For more than forty years, the equation y’(t) = Ay(t) + u(t) in Banach spaces has been used as model for optimal control processes described by partial differential equations, in particular heat and diffusion processes. Many of the outstanding open problems, however, have remained open until recently, and some have never been solved. This book is a survey of all results know to the author, with emphasis on very recent results (1999 to date). The book is restricted to linear equations and two particular problems (the time optimal problem, the norm optimal problem) which results in a more focused and concrete treatment. As experience shows, results on linear equations are the basis for the treatment of their semilinear counterparts, and techniques for the time and norm optimal problems can often be generalized to more general cost functionals. The main object of this book is to be a state-of-the-art monograph on the theory of the time and norm optimal controls for y’(t) = Ay(t) + u(t) that ends at the very latest frontier of research, with open problems and indications for future research. Key features: · Applications to optimal diffusion processes. · Applications to optimal heat propagation processes. · Modelling of optimal processes governed by partial differential equations. · Complete bibliography. · Includes the latest research on the subject. · Does not assume anything from the reader except basic functional analysis. · Accessible to researchers and advanced graduate students alike · Applications to optimal diffusion processes. · Applications to optimal heat propagation processes. · Modelling of optimal processes governed by partial differential equations. · Complete bibliography. · Includes the latest research on the subject. · Does not assume anything from the reader except basic functional analysis. · Accessible to researchers and advanced graduate students alikeLinear Stochastic Control Systems presents a thorough description of the mathematical theory and fundamental principles of linear stochastic control systems. Both continuous-time and discrete-time systems are thoroughly covered. Reviews of the modern probability and random processes theories and the Itô stochastic differential equations are provided. Discrete-time stochastic systems theory, optimal estimation and Kalman filtering, and optimal stochastic control theory are studied in detail. A modern treatment of these same topics for continuous-time stochastic control systems is included. The text is written in an easy-to-understand style, and the reader needs only to have a background of elementary real analysis and linear deterministic systems theory to comprehend the subject matter. This graduate textbook is also suitable for self-study, professional training, and as a handy research reference. Linear Stochastic Control Systems is self-contained and provides a step-by-step development of the theory, with many illustrative examples, exercises, and engineering applications.This outstanding reference presents current, state-of-the-art research on importantproblems of finite-dimensional nonlinear optimal control and controllability theory. Itpresents an overview of a broad variety of new techniques useful in solving classicalcontrol theory problems.Written and edited by renowned mathematicians at the forefront of research in thisevolving field, Nonlinear Controllability and Optimal Control providesdetailed coverage of the construction of solutions of differential inclusions by means ofdirectionally continuous sections Lie algebraic conditions for local controllability the use of the Campbell-Hausdorff series to derive properties of optimal trajectories the Fuller phenomenon the theory of orbits and more.Containing more than 1,300 display equations, this exemplary, instructive reference is aninvaluable source for mathematical researchers and applied mathematicians, electrical andelectronics, aerospace, mechanical, control, systems, and computer engineers, and graduatestudents in these disciplines .This book is based on lectures from a one-year course at the Far Eastern Federal University (Vladivostok, Russia) as well as on workshops on optimal control offered to students at various mathematical departments at the university level. The main themes of the theory of linear and nonlinear systems are considered, including the basic problem of establishing the necessary and sufficient conditions of optimal processes. In the
4,294 citations
TL;DR: A novel method—generalized predictive control or GPC—is developed which is shown by simulation studies to be superior to accepted techniques such as generalized minimum-variance and pole-placement and to be a contender for general self-tuning applications.
3,576 citations
"Disturbance models for offset‐free ..." refers methods in this paper
...Ž .dictive control GPC Clarke et al., 1987a,b , instead, used autoregressive models....
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Book•
01 Jan 1988
TL;DR: A state-of-the-art study of computerized control of chemical processes used in industry is presented in this article for chemical engineering and industrial chemistry students involved in learning the micro-macro design of chemical process systems.
Abstract: A state-of-the-art study of computerized control of chemical processes used in industry, this book is for chemical engineering and industrial chemistry students involved in learning the micro-macro design of chemical process systems.
2,689 citations