Loop-shaping controller design for nonlinear systems using the Contoured Robust Controller Bode (CRCBode) plot

In this paper we introduce the Contoured Robust Controller Bode (CRCBode) plot and demonstrate how it can be used for frequency domain controller design for nonlinear systems. The CRCBode plot is based on a standard robust performance criteria which is mapped onto the controller Bode magnitude and phase plots. The contours indicate level sets of a robust performance index and define allowable and forbidden regions for the controller frequency response. We apply an iterative loop-shaping technique to design a compensator which avoids the areas of the CRCBode plot with performance index greater than zero, and we demonstrate the effectiveness of this technique for flow-rate control of a dynamic nonlinear butterfly valve system. Finally we verify the performance of the compensated system via simulation.