Robust control of uncertain dynamic systems springerlink. Moreover, the solution of pnc is transformed into solvable lmis. Robust industrial control systems optimal approach for polynomial systems this text provides a comprehensive introduction to the use of frequency domain and polynomial system design techniques for a range of industrial control and signal processing applications. In this paper, we present a robust sosrobust lmi method to design a nonlinear controller for longitudinal dynamics of a hypersonic aircraft model with parametric uncertainties. Polynomial chaos based design of robust input shapers. The proposed method, based on using homogeneous polynomially parameterdependent matrices of arbitrary degree, is less conservative than previous ones in the literature. This paper presents a new approach to design a robust proportionalintegral pi controller for stabilizing power system oscillations. The question of how to construct a noniterative analytical solution for nonlinear h. Quadratic robust tracking control a polynomial matrix approach. This investigation is concerned with robust analysis and control of uncertain nonlinear systems with parametric uncertainties.
N obviously can be taken as the numerator polynomial and d as the. Robust control design deals with the question of how to develop such. Therefore, parameterization of the statefeedback controllers is independent of the lyapunov matrices. Sename state feedback control pole placement control. To overcome limitation of the existing approaches, we introduce additional variables that separate the system matrices and the lyapunov matrices. It utilises state space techniques by transforming the system to state space form, performing the design and transforming the resulting controller back to polynomial form. Manysuchsystems can be found in nature and others are man made. In control theory, robust control is an approach to controller design that explicitly deals with uncertainty. Theodore e djaferis to a large extent, our lives on this earth depend on systems that operate auto matically.
An optimal control approach to robust control design. A linear state space approach is an ideal book for first year graduate students taking a course in robust control in aerospace, mechanical, or electrical engineering. Therefore robust control theory might be stated as a worstcase analysis method rather than a typical case method. The characteristic polynomial of a closedloop control system containing a plant with. Polynomial design methods, international journal of robust. Pdf download robust control design with matlab download. In this paper we focus on this source of uncertainty and propose an approach based on polynomial chaos expansions to quantify and control uncertainty during the optimization process. Thus, whereas in part i the theory of the robust control procedures is outlined, in this. Grimble matlab toolbox provided by dimos fragopoulos by kind permission of the university of strathclyde. Pdf polynomial and statespace based hinfinity robust. Robust control methods are designed to function properly provided that uncertain parameters or disturbances are found within some typically compact set. Given a bound on the uncertainty, the control can deliver results that meet the control system requirements in all cases. The optimal control approach to robust control design differs from conventional direct approaches to robust control that are more commonly discussed by. In the first part of the book, the authors provide a unified framework for statespace and lyapunov techniques by combining concepts from setvalued analysis, lyapunov stability theory, and game theory.
Provides connections between lyapunovbased matrix approach and the transfer function based polynomial approaches. This paper proposes a new probabilistic solution framework for robust control analysis and synthesis problems that can be expressed in the form of minimization of a linear objective subject to convex constraints parameterized by uncertainty terms. Robust control methods seek to bound the uncertainty rather than express it in the form of a distribution. Applications chapters provide a range of realistic industrial control design studies, and the book is accompanied by a disk that provides a matlab toolbox and program cc macros. Polynomial chaos based design of robust input shapers a probabilistic approach, which exploits the domain and distribution of the uncertain model parameters, has been developed for the design of robust input shapers.
A mean value theorem approach to robust control design for. A polynomial chaos approach to robust multiobjective optimization. Read polynomial design methods, international journal of robust and nonlinear control on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Provides an introduction to the design of industrial control systems using the polynomial systems design approach. General introduction linear systems, polynomial methods lmis and robust control i robust stability analysis i. This book presents advances in the theory and design of robust nonlinear control systems. This paper exploits a relatively simple framework for robust control of unstable single input single output processes. Optimal design approach for polynomial systems prentice. Robust pole placement now assume that the plant transfer function bq a q contains some uncertain parameter q the problem of robust pole placement will then consists in nding a controller y x such that the uncertain closedloop charact. Fidan abstractthis paper presents a scheme to design a tracking controller for a class of uncertain nonlinear systems using a robust feedback linearization approach. Guaranteed robustness with fast adaptation advances in design. Graduate course on polynomial methods for robust control didier henrion.
This paper focuses on this challenge and proposes a novel simple approach, namely, polynomial nonlinear control, to design a nonlinear h. Polynomial approach to robust control of unstable processes. This paper presents a novel approach to statefeedback stabilization of polynomial systems with bounded actuators. Polynomial approach for design and robust analysis of lateral missile control. A nonlinear dobc approach article pdf available in journal of dynamic systems measurement and control 87 march 2016 with 3 reads. Students and researchers in the field will also find it an excellent reference tool. Robust performance is imposed in the nmb control design in order to perform appropriate responses on the model database. Our goal is to design a state feedback to stabilize a system under uncertainty. Optimal design approach for polynomial systems presents a comprehensive introduction to the use of frequency domain and polynomial system design techniques for a range of industrial control and signal processing applications. This book presents new methods or controller design.
Accompanying software xvi 1 introduction to optimal robust control 1 1. Included imc filtering is recognized as a very useful way to regard the mismatch between the model used for control design and the actual process. Robust industrial control optimal design approach for polynomial systems michael j. The scenario approach to robust control design ieee. A noniterative sosbased approach for guaranteed cost. Robust control design rsp series in control theory and applications series editor. The scenario approach to robust control design abstract. Robust methods aim to achieve robust performance andor stability in the presence of bounded modelling errors. The proposed ppdc control design can greatly reduce the number of adjustable parameters involved in the original pdc and separate them from the. Lmibased robust control of uncertain nonlinear systems. Robust industrial control systems wiley online books. A method utilizing h2 control concepts and the numerical method of polynomial chaos was developed in order to create a novel robust probabilistically optimal control approach. Using a nonquadratic lyapunov function, two stability conditions were derived in the form of sumofsquares sos.
Theodore e djaferis our heavy dependence on systems that are automatically controlled is undeniable. Robust control of static var compensatorbased power. Polynomial chaos expansions are used to approximate uncertain system states and cost functions in the stochastic space. Nonlinear control of an uncertain hypersonic aircraft model. Robust control systems may successfully be designed by optimization, in particular, by reformulating the design problem as a mixed sensitivity problem. May 25, 2007 read polynomial design methods, international journal of robust and nonlinear control on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. The solution of stochastic and robust optimal control problems is. The methodology is illustrated on the task of magnetic system. Use features like bookmarks, note taking and highlighting while reading robust industrial control systems. Robust performance is imposed in the nmb control design in order to.
The polynomial lyapunov matrix consists of states of the system leading to the nonconvex problem. The main contribution of this work is the proposal of an alternative approach to the design of robust polynomial control systems. The process ofdeveloping a controller or control strategy can be dramatically improved if one can generate an appropriate dynamic model for the system under consideration. A mean value theorem approach to robust control design for uncertain nonlinear systems obaid ur rehman ian r. We translate this robust control problem into an optimal control problem of minimizing a cost. Optimal design approach for polynomial systems kindle edition by grimble, michael j download it once and read it on your kindle device, pc, phones or tablets. The solution of stochastic and robust optimal control problems is considered, building up from singleinput problems and gradually. Optimal design approach for polynomial systems is essential reading for professional engineers requiring an introduction to optimal control theory and insights into its use in the design of real industrial processes. This paper has studied the robust filtering problem for 2d discrete systems described by roesser statespace model. This paper proposes a noniterative state feedback design approach for polynomial systems using polynomial lyapunov function based on the sum of squares sos decomposition. Because the uncertainty bound is reflected in the cost, the solution to the optimal control problem is a solution to the robust control problem.
Read robust control of electricallystimulated muscle using polynomial h. The paper deals with a new design procedure connecting the algebraic polynomial approach to control design and the internal model control imc method. Proportional pdc designbased robust stabilization and. Robust control design deals with the question of how to develop such controllers for system models with uncertainty. Tadeo, lmi conditions for robust stability of 2d linear discretetime systems, mathematical problems in engineering, vol. Polynomial chaosbased adaptive control for nonlinear systems. A linear modelbased polynomial approach to control system design is utilized together with robust tuning of some of the closedloop poles. Read quadratic robust tracking control a polynomial matrix approach, international journal of robust and nonlinear control on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. We propose an optimal control approach to robust control design. Robustness, robust control, stability, parametric approach.
The solution of stochastic and robust optimal control problems is considered. Comprehensive and accessible guide to the three main approaches to robust control design and its applications optimal control is a mathematical field that is concerned with control policies that can be deduced using optimization algorithms. The approach followed relies on the design of poleplacement controllers using inputoutput models and polynomial techniques. This method was created for the practical reason that uncertainty in parameters tends to be inherent in system models. In this paper, we are especially interested in the bene. In this paper, a robust governor design using a multivariablecascade control approach is proposed for hydro turbine speed controls. The application of robust control theory offers more reliable and robust damping controller to achieve desired damping level considering variations in the operating conditions of power system. Pdf robust control design with matlab boubaker krim. This work addresses the design of robust controllers for the neuromuscular blockade nmb level of patients subject to general anesthesia. Polynomial approach for design and robust analysis of. A primary component of such systems is a device or. In contrast to the methodologies from the field of linear parameter varying systems, which employ convex structures of the state space representation in order to perform analysis and design, the proposed approach makes use of a polytopic form of a.
Lmis in systems control robust control design polynomial methods. This paper presents a proportional parallel distributed compensation ppdc design to the robust stabilization and tracking control of the nonlinear dynamic system, which is described by the uncertain and perturbed takagisugeno ts fuzzy model. Iterative lmi approach to robust statefeedback control of. Robust control of uncertain dynamic systems a linear. Robust control design a polynomial approach theodore e. Robust control design using the algebraic polynomial approach. Request pdf a noniterative sosbased approach for guaranteed cost control design of polynomial systems with input saturation this study proposes a novel sum of squares sos decomposition.
227 161 891 1128 237 1338 101 1275 1230 1171 266 1468 723 317 1544 983 138 287 1090 1654 976 1133 1399 1132 582 1325 836 1452 952 87 168 898 472 263 365 735 483 463 1330