Model reference robust control of systems with significant unmodelled dynamics

In this paper, a recently proposed control design technique, model reference robust control (MRRC),(1) is generalized to provide input-output robust control for a much wider class of SISO systems. A system under consideration may contain not only parametric uncertainties, disturbances, uncertain high-order nonlinearities associated with system output (including stable unmodelled dynamics of the output), but also multiplicative unmodelled dynamics of the input of the system. Input unmodelled dynamics may be unstable and of infinite dimension. Common assumptions such as the order of the system, or bounds on system parameters, or coefficients in size-bounding functions on uncertainties and unmodelled dynamics are not needed in this paper. The a priori information required to apply the proposed design procedure includes the relative degree of the overall system, closed-form expressions of bounding functions, and, for arbitrarily small error in tracking the output of any given reference model, the minimum phase condition. Under the proposed control, the output tracking error can be made arbitrarily small to achieve any specified tracking accuracy. The distinct feature of MRRC is that neither uncertainties nor unmodelled dynamics are required to be small. (C) 1997 by John Wiley & Sons, Ltd