Adaptive Control of Multivariable Systems via Pole Assignment

Abstract

<p>The adaptive control of linear discrete time multivariable systems is considered. A unifying survey of a number of adaptive control strategies is presented. The various algorithms are shown to be special cases of a more general algorithm. The state space design of self-tuning controllers is considered in detail. Two new algorithms for state space pole assignment self-tuning control are proposed. The first algorithm follows an explicit approach, thus a modification of the bootstrap estimator was used for joint parameter and state estimation of an innovations model. The resulting self-tuning controller is more efficient computationally than the methods based on block canonical forms since a minimal realization can be adopted. The second algorithm may be regarded as an implicit pole assignment controller. The recursive prediction error algorithm is used for joint parameter and state estimation in the controller canonical form. The main contribution of this approach is that on-line computation of transformation matrices is avoided. The subsequent computation of controller parameters is trivial, and the resulting self-tuning controller is robust to over-parameterization. To demonstrate a practical application, the second algorithm was used to design a robust autopilot for a simulated nonlinear model of a Royal Navy frigate subjected to sea disturbances. The autopilot was found to perform well for both the course keeping and course changing modes.</p>