Integrating Active Damping with Shaping-Filtered Reset Tracking Control for Piezo-Actuated Nanopositioning

TL;DR

This work tackles bandwidth limits in piezoelectric nanopositioners caused by lightly damped resonances and gain–phase constraints. It introduces a dual-loop scheme with an inner non-minimum-phase resonant controller for active damping and an outer tracking loop that uses a constant-gain, lead-in-phase (CgLp) reset element, augmented by a shaping filter to curb reset-induced harmonics. Simulations and real-time experiments on an industrial nanopositioner show substantial improvements, including $ω_b$ gains of up to roughly $65$ Hz and $ω_c$ gains of about $34$ Hz over a well-tuned linear baseline, with shaping filters mitigating higher-order harmonics and multiple-reset effects. The approach provides a practical pathway to higher-bandwidth, robust nanopositioning performance without increasing linear loop gain, with clear implications for high-precision raster-scanning and related applications.

Abstract

Piezoelectric nanopositioning systems are often limited by lightly damped structural resonances and the gain--phase constraints of linear feedback, which restrict achievable bandwidth and tracking performance. This paper presents a dual-loop architecture that combines an inner-loop non-minimum-phase resonant controller (NRC) for active damping with an outer-loop tracking controller augmented by a constant-gain, lead-in-phase (CgLp) reset element to provide phase lead at the targeted crossover without increasing loop gain. We show that aggressively tuned CgLp designs with larger phase lead can introduce pronounced higher-order harmonics, degrading error sensitivity in specific frequency bands and causing multiple-reset behavior. To address this, a shaping filter is introduced in the reset-trigger path to regulate the reset action and suppress harmonic-induced effects while preserving the desired crossover-phase recovery. The proposed controllers are implemented in real time on an industrial piezo nanopositioner, demonstrating an experimental open-loop crossover increase of approximately 55~Hz and a closed-loop bandwidth improvement of about 34~Hz relative to a well-tuned linear baseline.

Figures (12)

• Figure 1: (a) Experimental setup of a piezo-actuated nanopositioning system, (b) Identified frequency response of the nanopositioning system $G(s)$.
• Figure 2: Dual closed-loop architecture with damping controller $C_d(s)$ and tracking controller $C_t(s)$ incorporating a reset element $\mathcal{R}(s)$.
• Figure 3: Frequency response from HOSIDF analysis of CgLp with phase lead of $5^\circ$ ( ), $10^\circ$ ( ), $15^\circ$ ( ), and $20^\circ$ ( ). Dashed curves indicate the corresponding dominant third-harmonic components.
• Figure 4: Simulated open-loop frequency response for Case 1 ( ), Case 2 ( ), Case 3 ( ), Case 4 ( ), and Case 5 ( ). Dashed curves indicate the corresponding dominant third-harmonic components.
• Figure 5: Simulated closed-loop frequency response $S_{er}(s)$ for Case 1 ( ), Case 2 ( ), Case 3 ( ), Case 4 ( ), Case 5 ( ), Case 6 ( ), and Case 7 ( ).