Frequency Response Analysis of Pulse Width Modulated Control System with Higher Type Transfer Functions

Abstract

This paper extends the frequency response approach to the analysis of PWM system with a linear transfer function having distinct and repeated poles at the origin. With the pulse width modulator having linear or nonlinear characteristics, the scheme is always equivalent to a multi nonlinear sampled data system with interaction from several channel inputs determining the state vectors. The nonlinearity in each channel can only be approximated by straight line segments for type zero to type three transfer function. For higher type transfer functions or system with repeated distinct poles such approximations are not easy and harmonic linearisation by digital computer must be resorted to. The open loop frequency response of type two and type three systems with several steady state sinusoidal input magnitudes have been obtained and the most unstable frequency response locus determined for each case. Based on this information, system compensation and possibility of harmonic oscillations can be studied. It is also shown that the extent of harmonics in the output of open loop system can be considerable.