Adaptive internal model control: Design and stability analysis

Abstract

This paper shows how adaptation can be combined with an internal model control structure to obtain an adaptive internal model control scheme possessing theoretically provable guarantees of stability. The internal model controller structure is first reviewed in the context of the YJBK parametrization of all stabilizing controllers, and its appropriateness for the control of open-loop stable plants is discussed. Using a series-parallel identification model, it is then shown how, for a stable plant, one can adapt the internal model on-line and guarantee stability and asymptotic performance in the ideal case i.e. in the absence of modelling errors. This is achieved without having to check any strictly positive real conditions or requiring any persistent excitation. By robustifying the adaptive law using standard approaches from the robust adaptive control literature, the robustness of the scheme to the presence of modelling errors, such as unmodelled dynamics, is also established. The theoretical developments here complement the reported industrial successes of internal model control schemes.