Asymptotically Stable Multiple Input-Multiple Output Direct Model Reference Adaptive Controllers for Processes Not Necessarily Satisfying a Positive Real Constraint

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A modification is proposed that should, for a very large class of processes, guarantee asymptotic output model following for a very easily implementable direct adaptive control algorithm that can be applied to multiple input multiple output systems. This algorithm in order to satisfy a positive real constraint, has had to incorporate supplementary feedforward dynamics, thus resulting in stability but not perfect asymptotic tracking. The new modification by incorporating part of the feedforward dynamics into the model is such that perfect tracking of the augmented plant and model outputs implies perfect tracking of the original outputs. The proposed research involves the stability proof of the new modified algorithm, a study of procedures for designing robust feedforward dynamics, and an experimental validation study.