Higher-Order Sinusoidal Input Describing Functions for Open-Loop and Closed-Loop Reset Control with Application to Mechatronics Systems

TL;DR

This paper develops advanced frequency-domain analysis tools for reset control systems in mechatronics, enabling improved design and tuning of controllers with demonstrated superior performance in precision motion applications.

Contribution

It introduces Higher-Order Sinusoidal Input Describing Functions for open- and closed-loop reset control systems and provides a practical MATLAB tool for their analysis.

Findings

Shaped reset controllers outperform PID and reset controllers in precision tracking.

The proposed methods accurately predict system behavior through simulations and experiments.

Case studies show improved tracking and reduced actuation forces with shaped reset control.

Abstract

Reset control enhances the performance of high-precision mechatronics systems. This paper introduces a generalized reset feedback control structure that integrates a single reset-state reset controller, a shaping filter for tuning reset actions, and linear compensators arranged in series and parallel configurations with the reset controller. This structure offers greater tuning flexibility to optimize reset control performance. However, frequency-domain analysis for such systems remains underdeveloped. To address this gap, this study makes three key contributions: (1) developing Higher-Order Sinusoidal Input Describing Functions (HOSIDFs) for open-loop reset control systems; (2) deriving HOSIDFs for closed-loop reset control systems and establishing a connection with open-loop analysis; and (3) creating a MATLAB-based App to implement these methods, providing mechatronics engineers with a practical tool for reset control system design and analysis. The accuracy of the proposed methods is validated through simulations and experiments. Finally, the utility of the proposed methods is demonstrated through case studies that analyze and compare the performance of three controllers: a PID controller, a reset controller, and a shaped reset controller on a precision motion stage. Both analytical and experimental results demonstrate that the shaped reset controller provides higher tracking precision while reducing actuation forces, outperforming both the reset and PID controllers. These findings highlight the effectiveness of the proposed frequency-domain methods in analyzing and optimizing the performance of reset-controlled mechatronics systems.