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

TL;DR

The paper tackles the lack of robust frequency-domain tools for reset control in high-precision mechatronics by introducing a generalized reset structure with a single reset-state controller, shaping filter, and configurable linear blocks. It develops open-loop and closed-loop Higher-Order Sinusoidal Input Describing Functions (HOSIDFs) to capture nonlinear harmonics and links the two analyses, validated through simulations and precision-motion experiments. A MATLAB App named 'Reset Far' implements these methods, enabling practitioners to design and analyze reset controllers, including two-reset-per-cycle configurations. Case studies on a precision motion stage demonstrate that the shaped reset (CgLp) controller achieves lower steady-state errors and reduced actuation by suppressing higher-order harmonics, highlighting the practical impact of the proposed frequency-domain framework for reset control in mechatronics.

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.

Figures (18)

• Figure 1: Block diagram of a generalized reset control system, with the resetting action denoted by blue lines.
• Figure 2: The planar precision positioning stage.
• Figure 3: The FRF data from actuator $A_1$ to attached mass $M_1$.
• Figure 4: Block diagram of the open-loop reset control system.
• Figure 5: Block diagram of the open-loop reset control system for HOSIDF analysis.

Theorems & Definitions (10)

• Theorem 1
• proof
• Remark 1
• Theorem 2
• proof
• Corollary 1
• Remark 2
• Remark 3
• proof
• proof