Non-Minimum-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 to low closed-loop bandwidths due to their lightly damped resonance behavior. Active damping controllers (ADCs) have been widely employed to suppress the dominant first mode and enable higher bandwidths; however, their performance is severely degraded in the presence of delay, while significant higher-order modes often remain unaddressed, further restricting precision. This paper proposes a simple loop-shaping methodology that incorporates a non-minimum-phase (NMP) filter in series with a linear damping controller to restore sufficient phase margins at open-loop crossover frequencies, 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 25.5 dB attenuation of higher-order resonances under significant delay. In conjunction with a standard proportional–integral (PI) motion controller and a non-minimum-phase resonant controller (NRC) targeting the first mode, the overall control architecture extends the closed-loop bandwidth to 435 Hz, surpassing the system’s first resonance frequency, without compromising low-frequency dynamics.