A New Robust Model Reference Adaptive Control Using Variable Structure Adaptation for Plants with Relative Degree Two

Abstract

Variable structure design (VSD) concept has been shown not only useful in dealing with uncertain systems but also in the adaptive context. Motivated by the recent work [13], a robust model reference adaptive control scheme for (single-input single-output) linear plants with relative degree two is developed in this paper. The scheme applies the VSD concept both to the plant input formation and to parameter adaptation. A similar result can be obtained which shows that the global stability of the overall system is achieved under no assumption of persistency of excitation (PE) even in the presence of unmodelled dynamics and bounded disturbances. The tracking errors will converge to a residual set whose size can be directly related to the size of unmodelled dynamics and of bounded output disturbances. In the ideal case, the residual set degenerates to a single null point and the exponential convergence is acquired regardless of the absence of PE. A practical implementation of the scheme is discussed where a trade-off appears in "control-performance vs. control-effort".