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