| The main purpose of this dissertation is to present a coherent study of adaptive control algorithms for multi-input multi-output (MIMO) systems using pole placement approach. Both direct and indirect algorithms are discussed here and the associated global stability issues are resolved using a novel block processing technique. Also for the sake of completeness, this study covers both continuous time as well as discrete time systems in a unified manner.; The direct adaptive pole placement algorithm presented here is the only one of its kind reported in the literature till this date. The only a priori knowledge about the system, necessary for implementation of this algorithm, consists of the system controllability indices and an upper bound on its observability index. The only drawback of this algorithm lies in the fact that a fairly high order estimation problem needs to be solved in real time. As a step toward resolving this problem, this thesis also presents a reduced order pole assignment algorithm which causes a significant reduction in the dimension of the parameter space. The only a priori knowledge required by the later consists of an upper bound on the observability index of the system.; The standard techniques of indirect adaptive pole assignment involve inversion of a generalized Sylvester resultant matrix which, because of its large dimension, poses a significant problem of numerical stability particularly for implementation on a microprocessor. The algorithm presented here is vastly superior in this regard because it involves inversion of a (n x n) matrix alone, where n denotes the order of the system.; The interactor matrix of a system provides the designer information about the relative degrees (continuous time case) or delays (discrete time case) associated with the system transfer matrix. Thus, a priori knowledge of the system interactor matrix, which plays a major role in the design of model-matching adaptive controllers for MIMO minimum phase systems, requires considerable information about the system transfer matrix itself. As a step toward reduction of this a priori information, this thesis presents a scheme for estimation of the nondiagonal entries of the system interactor matrix from knowledge of the degrees of its diagonal entries alone. This is believed to be a significant improvement over other similar algorithms reported in the literature till this date.; For the purpose of demonstration of performance, simulation examples are presented for all the algorithms discussed here. |
