Loop Gain-Phase Shaping Design of SISO Robust Controllers Having Mixed Uncertainty

This paper discusses the extension of the loop gain-phase shaping (LGPS) techniques of QFT to SISO robust controller design for mixed uncertainty situations: that is, processes having both parametric and non-parametric uncertainty. The mixed uncertainty problem leads to a set of frequency dependent high frequency stability boundaries replacing the traditional (single) universal high frequency boundary considered in [1]. In the presence of these new frequency dependent, high frequency boundaries the existence of a LGPS solution becomes problematical - even in the case of minimum phase stable plants. We will outline the modified LGPS problem, describe new CAD software for its formalation and solution and present a simple test that can be used to indicate the existence of solutions to the fitting problem. An example demonstrates the application of these tools and techniques in the design of a robust controller for a motion control systems with uncertain resonances.