Phase Loss Mitigation in Rate Limited Actuators Through an Interpretable Proportional and Derivative-Based Approach

This article tackles the problem of designing rate limiting elements, commonly found in feedback loops and used to filter signals before passing them to actuators. Under certain circumstances, these elements can introduce a phase delay, which can ultimately cause instability. For this reason, techniques to understand, analyse, and predict instability due to their phase loss have been proposed. Techniques to limit the rate of change of a signal without introducing the significant phase loss of a standard rate limiter have also been studied. However, said schemes have one or multiple of the following problems: the introduction of bias, the necessity to know the internal signals of actuators, difficult parameter tuning/interpretation, and the need to solve online optimisation problems. This study provides an alternative rate-limiting element that is competitive with state-of-the-art methods in phase-matching performance but avoids the mentioned drawbacks. The newly introduced phase anticipation scheme has been tested in step, sinusoidal, and mixed regimes. It proved able to recover up to 65% of the lost phase without introducing any significant downside. To illustrate its performance in a concrete application, we show its effectiveness in avoiding phase loss-induced limit cycles in an aircraft ground handling task in a high-fidelity simulator.