Controller design for nonlinear systems using the robust controller bode (RCBode) plot

In this paper, we develop a controller design method for nonlinear systems using the Robust Controller Bode (RCBode) plot. A robust performance criterion defines allowed and forbidden regions for the controller frequency response on the RCBode plot. The nonlinear system is linearized about a finite set of operating points which are considered to be a set of structured uncertainties. The union of the forbidden regions of each linearized system then defines the RCBode plot of the nonlinear system. We apply an iterative loop shaping technique to eliminate the intersections between the forbidden regions of the RCBode plot and the frequency response of the controller. We demonstrate the effectiveness of this technique for the design of a flow-rate controller for a dynamic nonlinear butterfly valve system. We show that this design is less conservative than a design satisfying the Circle Criterion. Finally, simulations are presented which verify the performance of the compensated system.