The impact of phase modulation on the performance of pulse-width modulated controls

For resource-intensive processes such as heating and cooling systems that use pulse-width modulated (PWM) controls, the residual of the PWM signal is a significant fraction of the process variance. In this paper, the impact on control performance of continuously modulating the phase of PWM signals in order to minimize the demand for a shared resource such as electric power is analyzed. The variance of the PWM residual for a system with the phase modulated to minimize peak resource demand is compared to the PWM residual from three abstract signals. It is shown that the process variance resulting from demand-optimized phase modulation is bounded by the process variance resulting from a constant-phase PWM signal (no modulation) and alternating-phase PWM signal