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.

This paper explores the use of reset control in systems subjected to wide-band disturbances. Such excitation may result in too rare or excessive resetting, leading to deteriorated performance. Moreover, the commonly used Describing Function (DF) approximation for the frequency-domain design of reset systems does not sufficiently represent the reset element’s behavior under such conditions as it is defined for sinusoidal excitation. To address this, we present a design approach based on analyzing the power spectral densities (PSD) of the signals in the system and using the Best Linear Approximations (BLA) of reset elements. In the first step, the dominant components in the PSD of the reset triggering signal are related to the frequency domain properties of the reset element. To benefit from resetting, it should lead to an increase in phase margins near the cross-over frequency. This is the case where the components at the cross-over frequency dominate the reset triggering signal. To ensure this, the use of a bandpass shaping filter is proposed. In the second step, the BLA of the reset element is used to represent its response to the signal with a specific PSD in the frequency domain. This information is used to tune both the reset element and the shaping filter to achieve the desired performance and minimize loss of gain at low frequencies. Closed-loop simulations show the method’s feasibility in achieving the desired behavior of the reset element, leading to improved resonance peak damping in the example studied.

Nanopositioning systems frequently encounter limitations in control bandwidth due to their lightly damped resonance behavior. This paper presents a novel Non-Minimum-Phase Resonant Controller (NRC) aimed at active damping control within dual closed-loop architectures, specifically applied to piezo-actuated nanopositioning systems. The control strategy is structured around formulated objectives for shaping sensitivity functions to meet predetermined system performance criteria. Leveraging non-minimum-phase characteristics, the proposed NRC accomplishes complete damping and the bifurcation of double resonant poles at the primary resonance peak through a constant-gain design accompanied by tunable phase variation. The NRC demonstrates robustness against frequency variations of the resonance arising from load changes and is also capable of damping higher-order flexural modes simultaneously. Furthermore, by establishing high gains at low frequencies within the inner closed-loop and integrating it with a conventional PI tracking controller, the NRC achieves substantial dual closed-loop bandwidths that can exceed the first resonance frequency. Moreover, the NRC significantly diminishes the effect of low-frequency reference signals on real feedback errors while effectively rejecting disturbances proximate to the resonance frequency. All contributions are thoroughly formulated and exemplified mathematically, with the controller's performance confirmed through an experimental setup utilizing an industrial nanopositioning system. The experimental results indicate dual closed-loop bandwidths of 830 Hz and 755 Hz, characterized by $\pm3$ dB and $\pm1$ dB bounds, respectively, that surpass the resonance frequency of 710 Hz.

In nanopositioning systems, the control bandwidth is frequently limited due to the presence of lightly damped resonant dynamics. Active Damping Control is typically integrated with tracking control within an inner-loop configuration to mitigate dominant resonant dynamics and enable higher bandwidths. The paper discusses that, in such architectures, feedforward control based on plant dynamics inversion is insufficient to achieve the intended feedforward objectives. In response to this limitation, the study introduces a delay-based input shaping and feedforward framework combined with a dual closed-loop feedback control system that includes active damping. The feedforward filter, derived from partial inner closed-loop dynamics inversion, facilitates precise, delayed tracking of reference signals. This configuration implements a unity-gain shaping filter, effectively reducing tracking feedback errors caused by reference inputs. Furthermore, the study presents a simulated example employing a simplified dynamic model of an industrial nanopositioning system to demonstrate enhancements in closed-loop periodic tracking performance through the proposed feedforward and input-shaping methodology.

In precision positioning systems, lightly damped higher-order resonance modes can induce undesirable vibrations that degrade system performance and accuracy. These resonances pose additional challenges in non-collocated dual-stage positioning systems, where they significantly limit control bandwidth. Although conventional notch filters are commonly used alongside tracking controllers to enhance bandwidth, they lack robustness when faced with system parameter uncertainties. Moreover, the effects of the delimiting resonance on disturbance rejection remain. Active damping control has been successfully used to mitigate issues related to the primary resonance mode, but its application to higher-order modes has not been explored. This paper introduces a novel control strategy, High-Pass Positive Position Feedback (HP-PPF), inspired by existing methods but designed specifically for active damping of higher-order, non-collocated modes in positioning systems. The proposed method incorporates a second-order high-pass filter within a positive feedback loop, effectively attenuating the delimiting resonance. Integrated with a PID tracking controller in a dual-loop configuration, this method enhances disturbance rejection and robustness against model uncertainties, overcoming limitations of traditional notch filter-based methods while achieving comparable bandwidth improvements. The proposed control architecture is validated through a proof-of-concept experimental setup that demonstrates the effectiveness of the underlying mathematical framework.

Piezoelectric nanopositioning systems exhibit low damping and resonance modes that are highly sensitive to loading conditions, resulting in performance degradation under payload variations. Conventional damping and robust control methods typically address these challenges separately, overlooking the coupling between damping and tracking dynamics as well as the influence of higher-order resonant modes. This paper proposes a dual-loop control framework that integrates active damping with mixed-sensitivity H∞ synthesis to achieve robust reference tracking and disturbance rejection under large resonance frequency variations. A Non-Minimum-Phase Resonant Controller (NRC) is implemented in the inner loop to suppress the dominant resonance and reduce system uncertainty. Generalized plant formulation and systematic weighting design guidelines of arbitrary order are developed to explicitly incorporate higher-order modes in the outer-loop H∞ synthesis. The proposed approach is validated through simulations and experiments on an industrial piezoelectric nanopositioning system, demonstrating improved robustness and precision across the full payload range.

In non-collocated compliant positioning systems, the parasitic resonance peak induces undesirable vibrations, limiting control bandwidth. Despite conventional notch filters being employed alongside PID controllers for improving bandwidth, parasitic resonance effects persist in disturbance rejection. This paper introduces an overactuation-based solution, utilizing additional actuators for active damping control to enhance closed-loop disturbance rejection within a PID-based control architecture. Integrating distributed piezoelectric bender actuator sensor pairs in a collocated configuration further improves damping. A formulated mathematical framework substantiates the benefits, validated by an experimental setup serving as a proof of concept. The proposed solution effectively suppresses parasitic resonance, enhances end-effector disturbance rejection, and achieves higher control bandwidth in the positioning system.