Design of Nonlinear H∞ Controllers Using Describing Functions

A systematic procedure for design of nonlinear Hinf controllers for nonlinear plants, whose dynamic and static behavior are highly sensitive to the amplitude level of excitation, is presented. The procedure is based on describing function concepts involving sinusoidal input describing function models of the nonlinear plant and application of an inverse describing function technique to arrive at nonlinear gains of the Hinf controller. The procedure is applied to a servomechanism problem to demonstrate the typical results that may be achieved.