This paper is concerned with the analysis of the tracking capability of Relay Feedback Control Systems (RFCS). The envisioned application is the generation of Pulse-Width-Modulation (PWM) with variable duty-cycle and frequency known also as Duty-Cycle Modulation. In general, two main issues have to be solved with RFCS when used for regulation and tracking. The first issue concerns the determination of autonomous self-oscillations which are generated by the closed loop. The second issue concerns the determination of the relationship between the reference and the output signals. However, if the first issue has beneficiated from different approaches and has been solved particularly in case of zero reference signal, the second issue has got insufficient theoretical results because of mathematical difficulties for obtaining analytical expressions. Considering these reasons, a deep analysis of RFCS constituted of a hysteretic relay and linear systems of first order is presented. Analytical expressions relating self-oscillations and output mean values with respect to the reference signals are obtained. The analysis of these relationships led to infer some conditions under which the relay feedback control can generate commands for regulating and tracking reference signals. It highlights also the key role played by the hysteresis band width for applications based on RFCS. Our analysis, exploiting the analytical expressions, can be used to achieve a complete design for power converters. Moreover, simulation and experiments have confirmed our results.
- Relay feedback
- On/Off control