Enhancing Reset Control Phase with Lead Shaping Filters: Applications to Precision Motion Systems

TL;DR

The paper addresses the limitations of linear precision-motion controllers by introducing shaped reset control, where a phase-lead shaping filter tunes the phase of reset instants to yield either greater phase margin or improved low-frequency gain without sacrificing high-frequency behavior. It develops frequency-domain design procedures for CI- and FORE-based resets, grounded in HOSIDF analysis, and proves conditions (via lemmas and theorems) to realize phase lead while preserving high-order harmonics. Two experimental case studies on a precision motion stage demonstrate a zero-overshoot transient with phase lead (Case Study 1) and enhanced tracking and disturbance rejection with increased bandwidth (Case Study 2). The approach offers practical gains for precision motion systems, with caveats about noise amplification that can be mitigated by filtering, and points to future work in higher-order lead elements and noise-robust extensions.

Abstract

This study presents a shaped reset feedback control strategy to enhance the performance of precision motion systems. The approach utilizes a phase-lead compensator as a shaping filter to tune the phase of reset instants, thereby shaping the nonlinearity in the first-order reset control. {The design achieves either an increased phase margin while maintaining gain properties or improved gain without sacrificing phase margin, compared to reset control without the shaping filter.} Then, frequency-domain design procedures are provided for both Clegg Integrator (CI)-based and First-Order Reset Element (FORE)-based reset control systems. Finally, the effectiveness of the proposed strategy is demonstrated through two experimental case studies on a precision motion stage. In the first case, the shaped reset control leverages phase-lead benefits to achieve zero overshoot in the transient response. In the second case, the shaped reset control strategy enhances the gain advantages of the previous reset element, resulting in improved steady-state performance, including better tracking precision and disturbance rejection, while reducing overshoot for an improved transient response.

Figures (20)

• Figure 1: Block diagram of the closed-loop reset feedback control system, where the blue lines represent the reset action.
• Figure 2: The magnitudes $|\mathcal{C}_1(\omega)|$ and phases $\angle \mathcal{C}_1(\omega)$ of the first-order harmonic, along with the magnitude $|\mathcal{C}_3(\omega)|$of the third-order harmonic, for both the CI and the shaped CI with $\gamma = 0$ considering $\sigma = 0.01, 0.05, 0.1, 0.2$.
• Figure 3: The three bounds, $\eta_1$(), $\eta_2$(), and $\eta_3$(), for $\angle \mathcal{C}_s(\omega)$ are depicted as shaded regions. The constraint on $\angle \mathcal{C}_s(\omega)$ at the bandwidth frequency $\omega_c$ is highlighted with blue double arrows (${\leftrightarrow}$). The desired curve of $\angle \mathcal{C}_s(\omega)$ for the generalized CI is shown in red, adhering to the constraints.
• Figure 4: The four bounds, $\beta_1$(), $\beta_2$(), $\beta_3$(), and $\beta_4$(), for $\angle \mathcal{C}_s(\omega)$ are depicted as shaded regions. The constraint on $\angle \mathcal{C}_s(\omega)$ at the bandwidth frequency $\omega_c$ is highlighted with blue double arrows (${\leftrightarrow}$). The desired curve of $\angle \mathcal{C}_s(\omega)$ for the FORE is shown in red, adhering to the constraints.
• Figure 5: Experimental precision positioning setup.

Theorems & Definitions (17)

• Remark 1
• Remark 2
• Remark 3
• Lemma 1
• proof
• Lemma 2
• proof
• Theorem 1
• proof
• Theorem 2