A frequency-domain approach to fix the commutation frequency in relay control systems: A DC motor case-study

Control of commuting devices can be naturally achieved by switching mechanisms, designed through relay control systems and sliding-mode control, for example. Consequently, a robust operation is guaranteed but the resulting operating switching frequency is normally high and varying. Such behavior is undesired in power electronics as it implies an increase in commutation losses, devices heating, and a reduction of their life-span. Despite many modulation techniques are currently available, they commonly preclude the natural interaction between switching devices and the designed controller, making the resulting behavior of the system to be unforeseeable. In this work, a novel technique to fix the steady-state operating frequency of a relay controller is introduced. This is achieved by cascading a simple all-pass filter whose resulting steady oscillation can be predicted through the Describing Function (DF) approach. The augmented relay makes possible to identify oscillations for systems with relative degree 1 unlike the classical hysteresis approach, which requires relative degrees of 2 if using DF. As validation, simulated results are shown considering standard problem settings, as well as a co-simulated DC motor controller.