Design of robust feedforward compensators for direct model reference adaptive control algorithms

Consideration is given to the problem of designing robust feedforward compensators for an easily implementable Direct Model Reference Adaptive Control (DMRAC) algorithm which ensures asymptotic model following provided that the plant to be controlled is required to satisfy a strictly positive real (SPR) condition. That is, for a plant to be controlled there exists a feedback gain such that the resulting closed-loop system is strictly positive real. The plant satisfying the above condition is called almost strictly positive real (ASPR). However, the fact that the most real systems are not ASPR limits the applicability of the DMRAC algorithm. One way to alleviate the ASPR conditions is to augment the plant, in parallel, with a feedforward compensator.; Although various augmentation schemes have been developed to alleviate this ASPR condition, a systematic procedure to design the necessary feedforward compensator to satisfy the ASPR conditions for plants with plant uncertainties has not been proposed. Recently proposed feedforward compensator design methods are applicable only to minimum phase systems. In those design procedures, variations in plant parameters are not considered explicitly. Feedforward compensator design methods, using the frequency domain design techniques, have also been proposed for plants represented with a nominal transfer function and a norm bounded perturbation. However, a systematic procedure to find such a feedforward compensator that satisfies the design conditions has not been proposed. Furthermore, these design methods are restricted to minimum phase nominal plants.; Thus, in this research, design conditions for robust feedforward compensators are developed for both single-input single-output (SISO) and multi-input multi-output (MIMO) plants, so that the alignmented plant will satisfy the ASPR conditions in the presence of plant uncertainties which are modeled as either parametric uncertainty or a norm bounded plant perturbation in the transfer function. Representing the plant uncertainty by the variations in the plant parameters, an optimization based robust stability analysis is developed for determining the necessary feedforward compensator. Transforming the variations of the plant parameters into norm bounded plant perturbations (an additive or a multiplicative perturbation in the transfer function), robust feedforward compensator design conditions utilizing an optimization method are developed in the frequency domain. Design conditions for a feedforward compensator are also developed using the so-called Q parameterization method. This design method in fact simplified the problem significantly.; Illustrative examples and case studies are given to validate the proposed design methods. The resulted robust feedforward compensator design procedures from this research, in conjunction with the DMRAC algorithm result in easily implementable procedures for designing and synthesizing robust SISO and MIMO direct adaptive controllers that are applicable to many systems with significant uncertainty.