Effects of finite switching frequency and delay on PWM controlled systems

The paper examines the effects of (low) switching frequency and delays on a closed loop system with pulse-width modulated (PWM) components. A modeling procedure is described together with analytical formulas. Deviations from standard (idealized) models which replace a PWM unit with a fixed gain are quantified. Low switching frequency reduces the effective PWM gain, and delays make the gain larger than the idealized one at low voltages. The necessary and sufficient condition for existence of a T-periodic stable equilibrium in the closed loop linear system with a PWM is obtained. This result is based on an analysis of a piecewise affine discrete-time map under the assumption of linear-ripple approximation. Experimental results are provided for a PWM controlled dc servo motor, while analytical results are presented for certain examples from the power electronics literature.