Simplified adaptive control for not ASPR systems

Abstract

Early stability resuIts for the command generator tracker approach to direct model reference adaptive control required that the plant be almost strictly positive real (ASPR). Later, the stability results were extended to the class of not-ASPR plants for which there exists a known dynamic compensator, with transfer matrix H(s), such that the plant in parallel with H(s) is ASPR. In this paper, we propose a modified algorithm for not-ASPR plants which ensures a bounded error without the need for a compensator to be inserted in parallel with the plant. Some special cases are considered for which the sufficient conditions for a bounded error are easily satisfied. An example is shown to illustrate the use of the new algorithm for a SISO plant which is high gain feedback stabilizable.