Controller gain bounding in the minimal control synthesis algorithm

Abstract

The minimal controller synthesis (MCS) algorithm is an extension of the class of model reference adaptive control (MRAC) algorithms that requires neither plant model identification nor linear controller synthesis. Various theoretical and experimental studies have shown it to possess the stability and robustness features essential to any successful adaptive control scheme. However, due to its high responsiveness to plant parameter variations and external disturbances, it can occasionally suffer from the long-term effects of measurement errors resulting in gain wind-up, closed-loop signal aliasing and hence instability. To counteract this effect, we propose an algorithm that extends MCS in such a way as to confine its adaptive gain evolutions by using automatically adjusting bounding corridors. The gain corridors MCS (GCMCS) algorithm that results does not suffer from error-boundedness or gain decay problems. Its name describes the controller's graphic functionality. In this paper, we extend the normal Popov criterion based stability proofs of MCS by including the consideration of plants with measurement or state errors, which had hitherto not been included. By working through this proof for single input single output (SISO) phase-variable plant structures, we show that the new algorithm retains the asymptotic properties of basic MCS and satisfies Popov's inequality under the assumed conditions of slower plant parameter variations relative to the controller bandwidth.