Singular Perturbation Approach to Pulse-Width Modulated Control in Nonlinear Dynamical Systems

Abstract-The problem of robust controller design under PWM feedback is discussed in terms of Filippov's average model where control variable is a duty ratio function. The proposed controller is an extension of PI/PID control scheme under PWM feedback. The presented design methodology guarantees desired output transient performance indices by inducing of two-timescale motions in the closed-loop system. Stability conditions imposed on the fast and slow modes and sufficiently large mode separation rate between fast and slow modes can ensure that the full-order closed-loop nonlinear system achieves the desired properties in such a way that the output transient performances are desired and insensitive to external disturbances and plant's parameter variations. The method of singular perturbations is used throughout the paper in order to get explicit expressions for evaluation of the controller parameters. Simulation results of tracking control for magnetic levitation system are presented as an example of the application for the discussed PWM control design methodology