© 1995 by Institute of Mathematics and its Applications
An indirect adaptive pole place for MIMO systems based on multirate sampling of the plant output
Division of Computer Science, Department of Electrical and Computer Engineering, National Technical University of Athens Zographou, 157 73, Athens, Greece
The use of multirate-output controllers in order to achieve adaptive pole placement in linear multiple-input multiple-output systems with unknown parameters is investigated for the first time. Multirate-output controllers contain a multirate sampling mechanism with different sampling period at each system output. Such {acute} control allows us to assign the poles of the sampled closed-loop system arbitrarily in desired locations, and does not make assumptions on the plant other than controllability, observability, and the knowledge of two sets of structural indices, namely the controllability and the observability indices. An indirect adaptive control scheme based on these sampled-data controllers is proposed, which estimates the controller parameters on line. Using the proposed adaptive algorithm, the problem of adaptive pole placement is reduced to the determination of a fictitious static state-feedback controller, due to the merits of dynamic multirate-output controllers. Known techniques resort to the direct computation of dynamic controllers. The controller determinations here is based on the transformation of the discrete analogue of the systems under control to a phase-variable canonical form prior to the applications of the control design procedure. The solution of the problem can be obtained by a quite simple utilization of the concept of state similarity transformation, whereas known techniques usually require the solution of matrix polynomial Diophantine equations. Moreover, persistent excitation of the continuous-time plant is provided without assuming any special richness of the reference signals.