A robust MRAC using variable structure design for multivariable plants

Abstract

It is well known that undesirable transient responses and tracking performances have been frequently observed in traditional model reference adaptive control (MRAC) problems, especially for multivariable plants with unmodeled dynamics and output disturbances. In this paper, a new robust model reference adaptive control using variable structure design (VSD) is proposed to investigate the solution. Based on a definition of generalized relative degree (GRD) for multivariable plants, the general case for plants with arbitrary GRD is completely solved. It is shown that, even when the uncertainties are presnet, global stability and robustness of the closed-loop control system are achieved. Furthermore, without any persistence of excitation, the tracking errors will, at least asymptotically, converge to zero for GRD-one plants and to a small residual set for plants with any higher GRD. With a suitable choice of initial control parameters, the tracking errors can even be driven to zero in finite time for GRD-one plants and to a small residual set exponentially for plants with any higher GRD.