Model Reference Robust Control of SISO Systems with Significant Unmodelled Dyamics

In this paper, a recently proposed control design technique, model reference robust control (MRRC) [10], is generalised to provide input-output robust control for much wider class of SISO systems. A system under consideration may contain not only parametric uncertainties, disturbances, uncertain high-order nonlinearities associated with output, but also unmodelled dynamics associated both input and output of the system. Unmodelled dynamics may be unstable and of infinite dimension. Common assumptions such as the order of nominal system, or bounds on system parameters, or coefficients in sise-bounding functions on uncertainties and unmodelled dynamics are not needed in this paper. The apriori information required to apply the proposed design procedure includes relative degree of the nominal system, closed-form expression of bounding functions, and, for arbitrarily small tracking error of reference model output, 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.