# CRCBode

Controller design for nonlinear systems using the contoured robust controller bode plot. We develop the Contoured Robust Controller Bode (CRCBode) plot and demonstrate its use in the design of robust controllers for nonlinear single-input single-output (SISO) systems. The CRCBode plot shows contours (level sets) of a robust performance quantity on the Bode magnitude and phase plots of the controller. An iterative frequency domain loop-shaping design approach is employed to eliminate all intersections of the controller frequency response with certain ’forbidden regions,’ indicating that a standard SISO robust stability and performance criterion is satisfied. Nonlinearities are accounted for by avoiding the maximum forbidden regions over a structured uncertainty set consisting of linearizations of the system dynamics about several operating points. We demonstrate this technique by designing and experimentally verifying a flow-rate controller for a butterfly-valve based liquid cooling system, which is robust to valve nonlinearities and flow disturbances. Finally, we compare this compensator with one generated using an automated $H_infty$ synthesis algorithm and discuss the advantages of the CRCBode approach.

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