Performance Assessment of Model Reference Adaptive Control – a Benchmark Based Comparison among Techniques

The main objective of adaptive control schemes is to produces reliable controllers under plant uncertainties, non-linearity and time varying parameters. Adaptation schemes are designed to cope with slow parameter changes; in addition, input signals are assumed to have frequency spectrum restricted to low frequency. In model reference adaptive control (MRAC) schemes, however, perfect model tracking depends on some conditions that usually are too restrictive for the class of plants under consideration. The derivations of control laws for MRAC are usually based on Lyapunov’s and Popov's theorems, some basic assumptions appear in almost every variation of those approaches; the most restrictive one is that the plant must remain strictly positive real (SPR) for all time. Alsol, to avoid dimensionality problems, MRAC schemes are implemented based only on output measurements. The discussions here are based on some of the main contributions in the area of model reference adaptive control, such as, the command generator tracking (CGT) technique and on the dynamic model reduction adaptive control (DMR-AC) approach. This work considers adaptive control applied to plants with time varying parameters and time delays. The results are given for the case in which the plant, defined by [A, B, C, D] and the reference model [Am, Bm, Cm, Dm], do not share the same state space realization. Simulation results are presented for a time-varyng non-strictly positive real linear model with time delay. They show and compare the performance degradation of the adaptive controllers when the plant parameters drift from their nominal values.