Previous work on the analysis and design of pulsewidth-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-widthmodulated control systems to arbitrary input is then presented.Through the use of difference equations and the separation of linear and nonlinear terms, the output a t the sampling instants is expressed a s 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.
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