Analysis of pulse-width-modulated control systems

Previous work on the analysis and design of pulse-width-modulated control systems is reviewed, and the limitations of some of the earlier contributions are discussed. A mathematical development of an orderly and relatively simple method for the exact determination of the response of closed-loop pulse-width-modulated control systems to arbitrary input is then presented. Through the use of difference equations and the separation of linear and nonlinear terms, the output at the sampling instants is expressed as a function of the sampled error, and
z
-transform theory is then employed to obtain an exact solution for the error at the sampling instants. A technique for studying the stability and other performance characteristics of pulse-width-modulated feedback systems is next presented. The exact method of analysis developed earlier and a modified describing-function technique are utilized together to investigate stability without overlooking pulse-width saturation. Three illustrative examples are also presented to demonstrate the relative simplicity of the methods described in the paper as well as the accuracy of the results obtained by the use of these methods.