Problem Of Exact Model Matching Research Articles

Structure at infinity and defect of transfer matrices with time-varying coefficients, with application to exact model-matching

We study the structure at infinity of transfer matrices with time-varying coefficients. Such transfer matrices have their entries in a skew field F of rational fractions, i.e. of quotients of skew polynomials. Any skew rational fraction is the quotient of two proper ones, the latter forming a ring Fpr (a subring of F) on which a “valuation at infinity” is defined. A transfer matrix G has both a “generalized degree” and a valuation at infinity, the sum of which is the opposite of the “defect” of G. The latter was first defined by Forney in the time-invariant case to be the difference between the total number of poles and the total number of zeros of G (poles and zeros at infinity included and multiplicities accounted for). In our framework, which covers both continuous- and discrete-time systems, the classic relation between the defect and Forney's left- and right-minimal indices is extended to the time-varying case. The exact model-matching problem is also completely solved. These results are illustrated through an example belonging to the area of power systems.

Simultaneous exact model matching with stability by output feedback

AbstractIn this paper, is studied the problem of simultaneous exact model matching by dynamic output feedback for square and invertible linear time invariant systems. In particular, explicit necessary and sufficient conditions are established which guarantee the solvability of the problem with stability and a procedure is given for the computation of dynamic controller which solves the problem.

Youla-Like Parametrizations Subject to QI Subspace Constraints

Consider that a linear time-invariant (LTI) plant is given and that we wish to design a stabilizing controller for it. Admissible controllers are LTI and must belong to a pre-selected subspace that may impose structural restrictions, such as sparsity constraints. The subspace is assumed to be quadratically invariant (QI) with respect to the plant, which, from prior results, guarantees that there is a convex parametrization of all admissible stabilizing controllers provided that an initial admissible stable stabilizing controller is provided. This paper addresses the previously unsolved problem of extending Youla's classical parametrization so that it admits QI subspace constraints on the controller. In contrast with prior parametrizations, the one proposed here does not require initialization and it does not require the existence of a stable stabilizing controller. The main idea is to cast the stabilizability constraint as an exact model-matching problem with stability restrictions, which can be tackled using existing methods. Furthermore, we show that, when it exists, the solution of the exact model-matching problem can be used to compute an admissible stabilizing controller. Applications of the proposed parametrization on the design of norm-optimal controllers via convex methods are also explored. An illustrative example is provided, and a special case is discussed for which the exact model matching problem has a unique and easily computable solution.

Model Matching Via Stabilizing Static State Feedback

The problem of stable exact model matching of linear systems by static state feedback is considered. Based on the effect that a static state feedback produces on the unobservable/controllable part of the closed-loop system, we provide the set of all static state feedback control laws that solve the exact model matching. Moreover, necessary and sufficient conditions for the existence of static state feedback that solves the model matching with stability are presented, along with a method to determine such a required state feedback law.

Exact model matching of left invertible neutral time delay systems

The problem of Exact Model Matching (EMM) for general left invertible neutral multidelay systems, via proportional realisable state and output feedback, is extensively solved. The necessary and sufficient conditions for the problem to have a realisable solution are established. The general analytical expression of the controllers, solving the problem, is derived. The present results are rather useful to adaptive control of distributed industrial processes described by neutral time delay models.

The exact model-matching problem for linear time-varying systems: an algebraic approach

The exact model-matching problem is formulated and solved for linear time-varying systems. The condition for the existence of a proper solution, which is well known in the time-invariant case, is proven here to still be valid in the time-varying case. The properness is characterized using the Smith-MacMillan form at infinity, recently defined by the authors for the transfer matrices with time-varying coefficients.

Exact model matching of generalized state space systems

The problem of exact model matching for generalized state space (GSS) systems via pure proportional state and output feedback is studied. The following two major issues are resolved here for the first time: The necessary and sufficient conditions for the problem to have a solution and the general analytical expressions for the exact modelmatching controller matrices. The important case of left invertible systems is treated separately wherein simple solutions are established for the above two major issues and results on structural properties of the closed-loop system are reported. Known results on model matching of regular systems are derived as a special case of the GSS systems results, thus unifying the solution of the exact model-matching problem of regular and singular systems.

Uniform exact model matching for a class of linear time-varying analytic systems

The problem of uniform exact model matching is studied via state and output feedback, for a class of linear time-varying analytic systems. The following two major issues are resolved: The nessecary and sufficient conditions for the problems to have a solution and the general analytical expressions for the controller matrices. A major feature of the proposed approach, is that it reduces the uniform exact model matching problem to that of solving a linear nonhomogeneous algebraic matrix equation.

Exact model-matching of 2-D systems via input-output feedback method

In this paper we examine the exact model-matching problem for multiple-input, multiple-output 2-D (two-dimensional) linear systems using a transfer function technique. The system configuration described here is an observer-based feedback configuration, and the feedback compensator is of the form similar to the PID type for analog systems. An example is given to illustrate the feasibility of this approach.

Exact model-matching control of linear discrete-time systems by periodic state or output feedback

The paper considers an exact modelmatching control problem via periodic stateoutput feedback for discrete-time systems. A frequency-domain approach is employed in which the prototype system (model) is given by the transfer function Gm(Z). The approach is based on equating the closed-loop transfer function Gc(Z) to Gm(Z) and solving the resulting equation for the required feedback again. The solvability of this equation leads to the sufficient condition for the exact model-matching problem to have a solution. An example illustrates the proposed method

A New Approach to the Exact Model-Matching Problem

A new approach to the exact model matching problem (EMMP) which plays an important role in linear system theory and has previously been solved in many different ways [1, 6, 7], is presented in this paper. The novel method employs the algebraic ideas centering around module theory, the co-prime factorizations of rational transfer functions and Fuhrmann s algebraic realization theory to offer a new insight into EMMP. It is for the first time in this paper that a set-theoretic interpretation for the solutions of EMM problem is given. Moreover, the proposed method can parametrize all the sets of solutions of an EMM problem and determine a stable solution if one such exists.

Proper rational matrix diophantine equations and the exact model matching problem

Relying on the theory behind the Smith-MacMillan form of a rational matrix at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s = \infty</tex> , a necessary and sufficient condition is derived from the solvability of matrix Diophantine equations of the form <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A(s)X(s)+B(s)Y(s) = M(s)</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A(s), B(s)</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M(s)</tex> are given proper rational matrices and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X(s)</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y(s)</tex> are unknown proper rational matrices. It is shown that the above result can be used in order to resolve in a new illuminating way the exact model matching problem (EMMP). If a solution to EMMP exists, then the family of all solutions is parametrized.

Decoupling controller design via exact model-matching techniques

This paper presents a new method for synthesising decoupling controllers for linear time-invariant multivariable systems. The novel approach proposed is based on the idea of formulating, and subsequently solving, the decoupling problem as an exact model-matching problem. This, in effect, results in reducing the decoupling problem to one of solving a linear system of equations.

The problem of exact model matching by the use of external description

This paper deals with the problem of exact model matching in multivariable systems. The problem is presented using exclusively a transfer matrix for the description of tho system. A solution is obtained by the use of the minimal bases of rational vector spaces.