PWM Motor Control: Model and Servo Analysis

The pulse width modulated (PWM) motor amplifier performs an important function in the direct current (dc) servo system by boosting the low level command signal to the high voltage and current levels required by the motor. The power gain associated with the PWM amplifiers is ideally constant over all frequencies; but in practice, the gain is frequency dependent and this affects the closed loop system dynamics. The amplifier gain and phase relationships (as functions of frequency), noise, and dc offsets must be known to the servo designer to properly design the motor control system. The switching effects of the PWM amplifier may result in making the overall system unstable if the system bandwidth is kept high with respect to the PWM switching frequency. Since the standard servo design techniques utilize linear system modeling, analysis, and compensation, it would be very advantageous to the design engineer to have a linear model which best approximates the true nonlinear PWM amplifier. The present work considers the output response of the PWM amplifier within a closed loop positioning system with respect to the overall stability and output ripple. A linear model is developed which accurately represents the stability and ripple behavior in a position control servo system over a wide range of frequencies. The present work extends the application of "The Principle of Equivalent Areas" [10] developed by Andeen in the early sixties to bipolar PWM systems. It is then combined with a detailed analysis of the PWM waveform by Double Fourier Transform to yield the unique PWM switching results in a position control servo system. Theoretical results predicted by employing the developed linear model are verified by computer simulation. It is hoped that the results of this work will give the practicing engineer a much needed accurate linear model for the PWM controller.