Modelling linear systems for pulsewidth-modulated control

An approximate linear model is developed for a linear process in which the control signal can assume only two values, and , and which is controlled by varying the fraction δnof a sampling cycle of duration that the control is at . The dynamic equations are of the form where wnis related to the average state xnover one cycle, and where δsis the steady-state value of δnrequired to maintain a desired average state xd. The system error at sampling intervals is related to these variables by an equation of the form , where is a bias vector. These relations may be used to design a linear control system by well-known techniques for discrete-time systems. The method is illustrated by the design of a third-order process which could represent a temperature control problem. Simulation results are given for a design that includes a Kalman filter for estimating the inaccessible states.