Loop Shaping with the Circle Criterion-Bode Plot with Application to Active Tape Steering

A drawback of the circle criterion for controller design for systems with memory-less nonlinearities is that it employs the Nyquist plot, for which frequency is an implicit variable. This paper presents a method for translating the circle criterion into allowable and forbidden regions on the Bode plot of a single-input/single-output system. This circle criterion-bode plot facilitates controller synthesis with loop shaping. The design concept is to shape the open loop response to avoid intersections between the forbidden regions and the magnitude and phase graphs. An application to the design of the controller for a lateral tape motion compensation system shows the utility of the plot.