Enhancing the Reliability of Closed-Loop Describing Function Analysis for Reset Control Applied to Precision Motion Systems

Abstract

The sinusoidal input describing function (SIDF) is a powerful tool for control system analysis and design, with its reliability directly impacting the performance of the designed control systems. This study improves both the accuracy of SIDF analysis and the performance of closed-loop reset feedback systems through two main contributions. First, it introduces a method to identify frequency ranges where SIDF analysis becomes inaccurate. Second, these identified ranges correlate with dominated high-order harmonics that can degrade system performance. To address this, a shaped reset control strategy is proposed, incorporating a shaping filter that tunes reset actions to suppress these harmonics. A frequency-domain design procedure for the shaped reset control system is then demonstrated in a case study, where a proportional–integral–derivative (PID)-based shaping filter effectively reduces high-order harmonics and eliminates limit cycles issues under step inputs. Finally, simulations and experiments on a precision motion stage validate the shaped reset control, confirming improved SIDF analysis accuracy, enhanced steady-state performance over linear and reset controllers, and the elimination of limit cycles under step inputs.