Interplay Between Control Law Selection and Closed Loop Adaptation

Abstract

Adaptive control methods combine parametrized controller computation with a closed loop system parameter identifier. This cont rol law design is typically carried out as a parametric version of a standard nona.daptive design. IV hich possesses desirable stability. performance and robustness properties. Similarly. the identifier usually is identical to that used for open loop parameter estimation. Our subject here is to investigate the interconnection between the selection of the control law and the consequent achieved closed loop input signal spectrum presented to the plant. According to the recent theory of Ljung. this signal spectrum plus the measnrement noise process spectrum dictate the frequency weighting implicit in the identified parametric plant model. In turn. this identi fied pla.nt model affects the controlled plant's stability through the robust ness of the control law at this nominal value. We shall present results demonstrating the potential coincidence of the control law's robustness perturbations to the plant and the implied closed loop identification frequency weighting.