Guaranteed robustness with fast adaptation advances in design. The optimal control approach to robust control design differs from conventional direct approaches to robust control that are more commonly discussed by. Polynomial approach for design and robust analysis of. 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. Robust control design deals with the question of how to develop such. Fidan abstractthis paper presents a scheme to design a tracking controller for a class of uncertain nonlinear systems using a robust feedback linearization approach. Moreover, the solution of pnc is transformed into solvable lmis. The solution of stochastic and robust optimal control problems is. We propose an optimal control approach to robust control design. Graduate course on polynomial methods for robust control didier henrion. Robust control design deals with the question of how to develop such controllers for system models with uncertainty. Robust control methods seek to bound the uncertainty rather than express it in the form of a distribution. Robust control methods are designed to function properly provided that uncertain parameters or disturbances are found within some typically compact set.
To overcome limitation of the existing approaches, we introduce additional variables that separate the system matrices and the lyapunov matrices. The solution of stochastic and robust optimal control problems is considered. Using a nonquadratic lyapunov function, two stability conditions were derived in the form of sumofsquares sos. N obviously can be taken as the numerator polynomial and d as the. 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 scenario approach to robust control design abstract. 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. Robust performance is imposed in the nmb control design in order to perform appropriate responses on the model database. Robust control of static var compensatorbased power. The proposed ppdc control design can greatly reduce the number of adjustable parameters involved in the original pdc and separate them from the. Read robust control of electricallystimulated muscle using polynomial h. 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.
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. An optimal control approach to robust control design. Accompanying software xvi 1 introduction to optimal robust control 1 1. This paper focuses on this challenge and proposes a novel simple approach, namely, polynomial nonlinear control, to design a nonlinear h. Robust industrial control systems wiley online books. A polynomial chaos approach to robust multiobjective optimization. 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 linear modelbased polynomial approach to control system design is utilized together with robust tuning of some of the closedloop poles. 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. 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. Robust control of uncertain dynamic systems springerlink. 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.
A nonlinear dobc approach article pdf available in journal of dynamic systems measurement and control 87 march 2016 with 3 reads. A mean value theorem approach to robust control design for. Given a bound on the uncertainty, the control can deliver results that meet the control system requirements in all cases. Proportional pdc designbased robust stabilization and. Polynomial chaos based design of robust input shapers. 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. This paper proposes a noniterative state feedback design approach for polynomial systems using polynomial lyapunov function based on the sum of squares sos decomposition. The solution of stochastic and robust optimal control problems is considered, building up from singleinput problems and gradually. Polynomial design methods, international journal of robust. Quadratic robust tracking control a polynomial matrix approach.
The proposed method, based on using homogeneous polynomially parameterdependent matrices of arbitrary degree, is less conservative than previous ones in the literature. Theodore e djaferis our heavy dependence on systems that are automatically controlled is undeniable. Provides connections between lyapunovbased matrix approach and the transfer function based polynomial approaches. 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. Sename state feedback control pole placement control. 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. 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. The paper deals with a new design procedure connecting the algebraic polynomial approach to control design and the internal model control imc method. 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. Theodore e djaferis to a large extent, our lives on this earth depend on systems that operate auto matically. Robustness, robust control, stability, parametric approach.
Polynomial approach for design and robust analysis of lateral missile control. Therefore, parameterization of the statefeedback controllers is independent of the lyapunov matrices. Therefore robust control theory might be stated as a worstcase analysis method rather than a typical case method. Pdf polynomial and statespace based hinfinity robust. Provides an introduction to the design of industrial control systems using the polynomial systems design approach. Because the uncertainty bound is reflected in the cost, the solution to the optimal control problem is a solution to the robust control problem. Manysuchsystems can be found in nature and others are man made. 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. A noniterative sosbased approach for guaranteed cost. Grimble matlab toolbox provided by dimos fragopoulos by kind permission of the university of strathclyde.
This book presents advances in the theory and design of robust nonlinear control systems. Robust industrial control optimal design approach for polynomial systems michael j. 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. This paper presents a novel approach to statefeedback stabilization of polynomial systems with bounded actuators. Robust control systems may successfully be designed by optimization, in particular, by reformulating the design problem as a mixed sensitivity problem. General introduction linear systems, polynomial methods lmis and robust control i robust stability analysis i. Iterative lmi approach to robust statefeedback control of. The characteristic polynomial of a closedloop control system containing a plant with. The scenario approach to robust control design ieee. 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 investigation is concerned with robust analysis and control of uncertain nonlinear systems with parametric uncertainties. Robust control design a polynomial approach theodore e.
Nonlinear control of an uncertain hypersonic aircraft model. 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. This book presents new methods or controller design. Polynomial chaos expansions are used to approximate uncertain system states and cost functions in the stochastic space. In control theory, robust control is an approach to controller design that explicitly deals with uncertainty. 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. 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.
Robust control design rsp series in control theory and applications series editor. Lmibased robust control of uncertain nonlinear systems. Robust performance is imposed in the nmb control design in order to. This paper presents a new approach to design a robust proportionalintegral pi controller for stabilizing power system oscillations. 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. A primary component of such systems is a device or. The question of how to construct a noniterative analytical solution for nonlinear h. Optimal design approach for polynomial systems prentice.
Robust methods aim to achieve robust performance andor stability in the presence of bounded modelling errors. The approach followed relies on the design of poleplacement controllers using inputoutput models and polynomial techniques. 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. This paper exploits a relatively simple framework for robust control of unstable single input single output processes. This method was created for the practical reason that uncertainty in parameters tends to be inherent in system models. Students and researchers in the field will also find it an excellent reference tool. 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. In this paper, we are especially interested in the bene. The methodology is illustrated on the task of magnetic system. Use features like bookmarks, note taking and highlighting while reading robust industrial control systems. Lmis in systems control robust control design polynomial methods. Robust control of uncertain dynamic systems a linear.
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 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. Polynomial approach to robust control of unstable processes. Tadeo, lmi conditions for robust stability of 2d linear discretetime systems, mathematical problems in engineering, vol. 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. Polynomial chaosbased adaptive control for nonlinear systems. Thus, whereas in part i the theory of the robust control procedures is outlined, in this. In this paper, a robust governor design using a multivariablecascade control approach is proposed for hydro turbine speed controls. Pdf robust control design with matlab boubaker krim.