Geometric statespace theory in linear multivariable control. Linear multivariable control stochastic modelling and. Linear and nonlinear multivariable feedback control. The maximum principle and dynamic programming are the two most commonly used approaches in solving optimal control problems. In fact, solving the lq regulator problem is equivalent to keep the output of the related hamiltonian system identically zero. For such systems, one can study structural properties, i. Krishnaprasad for contributions to geometric and nonlinear control and to engineering education 1991. Emphasis will be placed on designanalysis tools and their use in solving realworld control problems. We revisit the classical geometric theory in the context of.
Stabilization of solutions of boundary value problems for a second order parabolic equation with one space variable. A novel scheme for an upgrade of a linear control algorithm to a nonlinear one is developed based on the concepts of a generalized homogeneity and an implicit homogeneous feedback design. Control theory for linear systems university of groningen. Polynomial equation approach to exact model matching problem in multivariable linear systems, international journal of control 363. Geometric statespace theory in linear multivariable control a status report 7 play a basic role are the a,binvariant sub spaces and the a,bcontrollability subspaces. A geometric approach to structural model matching by output.
Xue, dingyu, chen, yangquan, and atherton, derek p. A geometric approach book in wntmg this monograph my aim has been to present a geometric approach to the structural synthesis of multivariable control systems that are linear, timeinvariant and of finite dynamic order. The control input to stabilize the system described in state space is achieved by the state feedback ufx 4 if the system is stabilizable. First and obviously, the setting is linear state space and the mathematics chiefly linear algebra in abstract geometric style. Krener for contributions to the control and estimation of nonlinear and causal systems 1990. In the theory of isolated dynamical systems flows on mani in the late 70s and in. Ici bucharest, computer process control laboratory.
Krishnaprasad for contributions to geometric and nonlinear control and. For these systems, the entries of the statespace model matrices are supposed to be either fixed zeros or free independent parameters. Part i linear multivariable control systems 1 canonical representations and stability analysis of linear mimo systems 3 1. The label geometric in the title is applied for several reasons. In keeping with the spirit of this book we emphasize the geometric content of the mathematical foundations, laying stress on the presentation of results in terms of vector spaces and their subspaces. Using an approach that is conceptually similar to the geometric approach developed for. Morse, decoupling and pole assignment in linear multivariable systems.
Despite the extensive literature certain fundamental matters are not well understood. Popescu 1976 sipac a computer prosram package for system identlfication and control system design, rep. Complicated dynamics of scalar reaction diffusion equations. A generalized framework of linear multivariable control 1st. The solution to the system of linear inequalities is the region that satisifies all of the inequalities and is called the feasible region. Iv versus control functions most models that are linear are estimated using standard iv methods. Sontag considered the deterministic analogue of kalman. A typical multivariable control problem requires the design of dynamic. Controlled and conditioned invariants in linear system theory. An alternative, the control function cf approach, relies on the same kinds of identification conditions. The history of the emergence of multivariable linear control systems theory is written nicely in pearson 1991 describing how kalmans state space approach appeared after freeman and kavanaghs multivariable control. Structured systems described by statespace models are considered. The importance of linear multivariable control systems is evidencedbythelarge numberofpapers 112 publishedinrecentyears. This is confirmed by numerous inaccurate stability analyses, erroneous statements about the existence of stable control, and overly.
A central role in this theory is played by the geometric i. At the beginning of the seventies wonham and morse independently in troduced. Multivariable calculus a geometric approach download pdf. As most control systems are conceived to be digitally implemented in a computerbased system, the use of process models is generalised and the control design approach is based on a model of the process. A geometric approach find, read and cite all the research you need on researchgate. Office of control theory and application, nasa electronics research center. The quantity to be maximized or minimized translates to some linear combinations of. Program package for process identification and control system. List of fellows of ieee control systems society wikipedia. This type of analysis is called sensitivity analysis. For contributions to the theory of robust linear multivariable control systems 1990. The goal of this course is to give graduate students and practicing engineers a thorough exposure to the stateoftheart in multivariable control system design methodolgies.
Morse n the theory of isolated dynamical systems flows on mani folds, etc. On another hand, though or maybe even because of the importance of digital control in practical realizations, it is essential to be at ease with these control or estimation methods, both in continuous and in discrete. The book is ad dressed to graduate students specializing in control, to engineering scientists involved in control systems research and development, and to mathemati cians interested in systems control theory. The geometric aspect is reinforced by a lot of this work having strong connections with the geometric theory of linear systems wonham, 1979. We assume that the beam is driven by a control torque at one of its ends, and the other end carries a rigid body as a load. Hirschorn, invertibility of control systems on lie groups, siam j. Algebraic notions and modules remain a suitable and effective tool for analysis and control design of mimo systems. Stabilization and observability of a rotating timoshenko beam. Vii control of linear multivariable systems katsuhisa furuta encyclopedia of life support systems eolss 1963, popov 1972. Mouktonglang y abstract we relate a deterministic kalman. In wntmg this monograph my aim has been to present a geometric approach to the structural synthesis of multivariable control systems that are linear, timeinvariant and of finite dynamic order. Reprinted with permission from siam journal on control, w. Linear, parametervarying control and its application to aerospace systems y x1.
He dealt with multivariable geometric control theory, stochastic control and stochastic filters, and more recently the control of discrete event systems from the standpoint of mathematical logic and formal languages. Linear multivariable control, a geometric approach, springerverlag. Purchase a generalized framework of linear multivariable control 1st edition. The solution lies on a controlled invariant subspace whose dimension is characterized in terms of the minimal conditioned invariant of the. Volume 101 of lecture notes in economics and mathematical systems. The quantity to be maximized or minimized translates to some linear combinations of the variables called an objective function. The theme of this book is to unify these two approaches, and to demonstrate that the viscosity solution theory provides the framework to unify them. These approaches have been developed independently. Murray wonham and others published linear multivariable controll. So, scalar polynomials describing single input output linear systems are replaced by polynomial matrices. A control system describing the dynamics of a rotating timoshenko beam is considered. Around 1980, a complete theory on the disturbance decoupling problem by dynamic measurement feedback became available.
A geometric approach in addition to constraints, linear programming problems usually involve some quantity to maximize or minimize such as pro ts or costs. In writing this monograph my objective is to present arecent, geometrie approach to the structural synthesis of multivariable control systems that are linear, timeinvariant, and of finite dynamic order. All content in this area was uploaded by walter wonham on dec 10, 2014. A geometric approach to multivariable control system design of a.
This linearisation retains the feedbackinvariant character of the tautological control systems framework and so permits, for example, a welldefined notion of linearisation of a system about an equilibrium point, something which has surprisingly been missing up to now. Multivariable control systems electrical engineering and. The basic ideas are the familiar system concepts of controllability and observability, thought of as geometric properties of distinguished state subspaces. Here, the linearisation of tautological control systems is described. The book is ad dressed to graduate students specializing in control, to engineering scientists involved in control systems research and development. The course covers roughly the first seven chapters of the book by wonham. Deis,universityofbologna,italy dii,universityofsiena,italy references wonham linearmultivariablecontrolageometricapproach, 3rdedition,springerverlag,1985. Suboptimality bounds for linear quadratic problems in hybrid linear systems, 20 european control conference, z. Modeling, analysis, and computation michiels, wim and niculescu, silviuiulian, stability and stabilization of timedelay systems.
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