Decentralized Motion and Resonant Damping Control for High-Bandwidth and Cross-Coupling Reduction in MIMO Nanopositioners

TL;DR

The paper tackles the challenge of achieving high-bandwidth, disturbance-resilient motion in MIMO nanopositioners plagued by lightly damped resonances and cross-axis coupling. It develops a decentralized dual-loop framework with an inner non-minimum-phase resonant damping controller for each axis and an outer tracking controller, enabling bandwidth beyond the first structural mode. A parallel band-pass damping path is added (Case B) to target a cross-coupling resonance, yielding substantial reductions in cross-axis coupling (up to ~11.5 dB in Δ(jω)) while preserving tracking performance. Experimental validation on a two-axis piezoelectric nanopositioner confirms improved damping, disturbance rejection, and cross-axis isolation, demonstrating the practicality of targeted band-pass damping for high-bandwidth MIMO nanopositioning systems. The work advances robust, scalable control of precision nanopositioners in applications such as AFM, optical alignment, and micro-manufacturing by enabling high-speed, accurate, and decoupled multi-axis motion.

Abstract

Piezoelectric nanopositioning systems are widely used in precision applications that require nanometer accuracy and high-speed motion; however, lightly damped resonances and pronounced cross-axis coupling severely limit bandwidth and disturbance rejection. This paper presents a decentralized dual-loop control strategy for a two-axis nanopositioner, combining an inner non-minimum-phase resonant damping controller with an outer motion controller on each axis. The dominant diagonal resonance is actively damped to enable closed-loop bandwidths beyond the first structural mode, while a parallel band-pass damping path is specifically tuned to a higher-order resonance that predominantly affects the cross-coupling channels. Experimental results demonstrate that this targeted band-pass damping substantially reduces cross-axis coupling and enhances disturbance rejection, without compromising tracking accuracy.

Figures (7)

• Figure 1: Experimental setup with P-562.2CD PIMars nanopositioning stage.
• Figure 2: Dual closed-loop architecture incorporating damping controller $\boldsymbol{C_d}(s)$ and tracking controller $\boldsymbol{C_t}(s)$.
• Figure 3: Experimental frequency response plots showing the identified MIMO system $\boldsymbol{G}(s)$ (); closed-loop tracking sensitivities $\boldsymbol{T}^{(A)}(s)$ () and $\boldsymbol{T}^{(B)}(s)$ () for Cases (A) and (B), respectively; and closed-loop process sensitivities $\boldsymbol{PS}^{(A)}(s)$ () and $\boldsymbol{PS}^{(B)}(s)$ () for Cases (A) and (B), respectively.
• Figure 4: Nyquist loci of closed-loop eigenvalues for Case (A): $\mu_1(j\omega)$ (), $\mu_2(j\omega)$ (), and Case (B): $\mu_1(j\omega)$ (), $\mu_2(j\omega)$ ().
• Figure 5: Magnitude of the cross-coupling reduction factor for Case (A), $|\Delta^{(A)}(s)|$ (), and Case (B), $|\Delta^{(B)}(s)|$ (), together with their ratio $|\Delta^{(A)}(s)|/|\Delta^{(B)}(s)|$ ().