Nonminimum-Phase-Based Loop Shaping for Multimode Active Damping Control: Application to Piezoelectric Nanopositioning System

Abstract

Piezoelectric nanopositioning systems, typically guided by flexure mechanisms, are limited by lightly damped resonances, which constrain achievable closed-loop bandwidth. Active damping controllers (ADCs) are widely employed to suppress the dominant first mode and increase bandwidth; however, their effectiveness degrades significantly in the presence of delay, and dominant higher-order modes often remain insufficiently attenuated, further restricting precision. This article proposes a simple loop-shaping methodology that incorporates a constant-gain nonminimum-phase (NMP) filter in series with a linear damping controller. The NMP filter is tuned using two open-loop crossover frequencies to enforce sufficiently large and approximately symmetric phase margins, thereby mitigating delay-induced degradation in closed-loop damping performance. The methodology is further extended to a parallel damping control structure that enables simultaneous suppression of both the first dominant and higher-order modes. Experimental validation on a piezoelectric nanopositioner demonstrates the effectiveness of the proposed strategy, achieving up to 13.7 dB attenuation of higher-order resonances under significant delay. In combination with a standard proportional-integral (PI) motion controller and a nonminimum-phase resonant controller (NRC) targeting the first mode, the overall control architecture extends the closed-loop bandwidth to 760 Hz, surpassing the system’s first resonance frequency without compromising low-frequency dynamics.