Abstract
In most of the studies of Model Reference Adaptive Control (MRAC), the controlled systems are confined to minimum phase systems, since the MRAC techniques utilize the control laws involving cancellations of zeros of the systems. It makes the scope of application of MRAC too restrictive, for non-minimum phase discrete-time systems can often appear. For example, when continuous-time systems with relative degree greater than 2, are sampled at a fast rate, those give rise to non-minimum phase discrete-time systems. Hence, the study of MRAC for non-minimum phase systems is of great importance.
In the present paper, we propose a design method of MRAC for non-minimum phase systems. The poles and zeros of the controlled systems are relocated by the periodic time-varying feedback control with multirate sampling, and no cancellation of zeros occurs in our method. It is shown that even if unstable zeros exist, the output error converges to zero asymptotically, while the control input remains uniformly bounded. Finally, some simulation results for the non-minimum phase system also show the effectiveness of the proposed method.
