Nonlinear Controller Design by an Inverse Random Input Describing Function Method

An interactive Inverse Random Input Describing Function method is developed which is able to find an approximate nonlinear function from given Random Input Describing Function data. Using this technique, a nonlinear controller design method for nonlinear systems with random inputs is presented that keeps the transient and r.m.s. error response insensitive to the input r.m.s. value. The method is then applied to a second order servo system with actuator saturation. The analytical results show the advantage of the nonlinear controller over the linear one and these results are verified through Monte Carlo simulations.