Loop-shaping for non-minimum phase systems using Contoured Robust Bode plots

In this paper, loop-shaping controller design using the Contoured Robust Controller Bode (CRCBode) plot is for the first time demonstrated for a non-minimum phase SISO system. It is shown that minimizing the robust metric in this process can lead to destabilizing controllers. To address this fundamental ambiguity, a new design tool, the Contoured Robust Q Bode (CRQBode) plot is introduced in which the Youla parameterization, Q(s), of all stabilizing controllers is shaped directly. The compensators designed using C and Q loop-shaping are compared, and the effect of certain algebraic and analytic design constraints on the “forbidden regions” of the Contoured Robust Bode plots are discussed.