This paper presents an experimental framework for inducing and tuning vibration bandgaps in digitally controlled mechatronic metamaterials. A slender-beam structure instrumented with collocated piezoelectric sensor-actuator pairs distributed periodically along the length is used as the host medium, with decentralized second-order low-pass resonant filter with negative position feedback controllers implemented in real time on an FPGA platform. Unlike conventional approaches that assess bandgap formation through tip displacement, this study relies on bending strain minimization of piezoelectric sensors as the principal indicator of control-induced bandgaps. This reflects more accurately the moment-based phase cancellation dynamics similar to resonator behavior. We derive analytical expressions for transmissibility in an n x n decentralized feedback architecture and verify them experimentally using a 7 x 7 unit-cell configuration. The findings show that resonant controllers with negative feedback applied at the unit-cell level can be systematically tuned through controller gain and damping to open targeted low-frequency bandgaps and significantly improve vibration attenuation. By shifting the focus to localized dynamics, this work deepens the understanding of how control-induced bandgaps emerge and demonstrates a scalable pathway for designing programmable mechatronic metamaterials based on unconventional resonator behavior.

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.

The sinusoidal input describing function (SIDF) is a powerful tool for control system analysis and design, with its reliability directly impacting the performance of the designed control systems. This study improves both the accuracy of SIDF analysis and the performance of closed-loop reset feedback systems through two main contributions. First, it introduces a method to identify frequency ranges where SIDF analysis becomes inaccurate. Second, these identified ranges correlate with dominated high-order harmonics that can degrade system performance. To address this, a shaped reset control strategy is proposed, incorporating a shaping filter that tunes reset actions to suppress these harmonics. A frequency-domain design procedure for the shaped reset control system is then demonstrated in a case study, where a proportional–integral–derivative (PID)-based shaping filter effectively reduces high-order harmonics and eliminates limit cycles issues under step inputs. Finally, simulations and experiments on a precision motion stage validate the shaped reset control, confirming improved SIDF analysis accuracy, enhanced steady-state performance over linear and reset controllers, and the elimination of limit cycles under step inputs.

AbstractPiezoelectric 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.

This study introduces a modified version of the constant-in-gain, lead-in-phase (CgLp) filter, which incorporates a feedthrough term in the first-order reset element (FORE) to reduce the undesirable nonlinearities and achieve an almost constant gain across all frequencies. A backward calculation approach is proposed to derive the additional parameter introduced by the feedthrough term, enabling designers to easily tune the filter to generate the required phase. This article also presents an add-on filter structure that can enhance the performance of an existing LTI controller without altering its robustness margins. A sensitivity improvement indicator is proposed to guide the tuning process, enabling designers to visualize the improvements in closed-loop performance. The proposed methodology is demonstrated through a case study of an industrial wire bonder machine, showcasing its effectiveness in addressing low-frequency vibrations and improving overall control performance.

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.

This paper proposes a novel discrete-time (DT) implementation of the generalized Clegg integrator (GCI), which is an integrator that resets its state to a fraction of the original state when its input is equal to zero. The implementation is derived by discretizing a continuous-time (CT) GCI using the Tustin discretization method. By means of a numerical validation it is shown that the state of the DT GCI is identical to its CT counterpart when both are subject to an input which is linearly interpolated between samples, as expected when using this discretization method. For a general CT input which is not linearly interpolated between samples, a numerical comparison is made between the state of the novel DT GCI and the CT GCI. At samples with linear behaviour, the state mismatch is equivalent to the one observed between their linear counterparts. At samples with resetting behaviour, the mismatch even reduces compared to previous samples, as a consequence of (partially) resetting the state mismatch.

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  ± 3 dB and  ± 1 dB bounds, respectively, that surpass the resonance frequency of 710 Hz.

Most systems exhibit significant variability in their dynamics, including variations in system parameters and large high-frequency dynamic uncertainties. Traditional uncertainty modelling techniques consolidate all such variations into a single uncertainty block, often yielding overly conservative representations of the true plant behaviour. This paper introduces an uncertainty modelling framework that employs multiple structured and unstructured uncertainty blocks to reduce this conservatism. The methodology is evaluated for an industrial piezoelectric nanopositioner subject to payload-induced variations, using uncertainty models of differing complexity. A bandpass controller is synthesised via structured mixed-μ synthesis, and the resulting designs are compared in terms of conservatism of the uncertainty model, robust performance, and computational effort.

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.

We introduce a fractional-order generalization of the hybrid integrator-gain system (HIGS) with memory reset of the fractional-order operator when re-enter the integration mode. We compute the describing function for rational orders in terms of Mittag-Leffler functions. The concepts also allow for the evaluation of the higher-order harmonics. For the implementation we represent higher-order approximations by combining first-order reset elements with an integrator. The fractional-order extension without memory reset can also be approximated using the same framework. Finally we show how the approximation affects the describing function.

Lightly damped structural resonances limit the performance of high-precision mechatronic systems and flexible structures. Conventional active damping schemes, such as positive and negative position feedback, provide moderate damping at the targeted mode but often suffer from spillover at low and high frequencies, especially in systems with closely spaced modes or high noise sensitivity. This paper presents a generalized higher-order bandpass active damping framework that enhances modal selectivity and stability for narrowband damping. Analytical formulations establish relationships between controller order, bandpass slope characteristics, and stability margins, enabling systematic design with high phase robustness. A non-minimum-phase filter is incorporated to compensate for delay-induced phase degradation, while a tunable damping coefficient increases design flexibility. Simulation studies on identified collocated and non-collocated systems demonstrate that the proposed controller achieves sharp resonance suppression, improved noise attenuation, and reduced spillover compared with conventional active damping schemes.

This article introduces output prediction methods for two types of systems containing sinusoidal-input uniformly convergent (SIUC) elements. The first method considers these elements in combination with single-input single-output linear time-invariant (LTI) systems before, after, and in parallel to them. The second method considers a multiple-input multiple-output LTI system where each input is controlled by an SIUC element. The output prediction only requires frequency-response functions of the LTI elements and is fully accurate for sinusoidal inputs.

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.

Contactless handling systems for substrates hold significant potential in enhancing chip manufacturing yields by allowing the use of thinner and larger substrates, eliminating the risks associated with physical contact. This article introduces a novel contactless force actuator, employing the active air-bearing working principle, designed with a compact structure to effectively actuate substrates. The actuator features a continuous deformable air-bearing surface composed of compliant-based actuation unit cells, ensuring ease of fabrication to meet tight air-bearing tolerances. A modular design with seven unit cells is designed and manufactured to validate the performance. The results confirm that the proposed contactless actuator can be used to levitate and actuate the substrate simultaneously, in which case the maximum actuation force in the x -axis is determined to be 90 mN and a 42.5- μ m fly height in the z -axis is achieved.

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.

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.

This study presents a shaped reset feedback control strategy to enhance the performance of precision motion systems. The approach utilizes a phase-lead compensator as a shaping filter to tune the phase of reset instants, thereby shaping the nonlinearity in the first-order reset control. The design achieves either an increased phase margin while maintaining gain properties or improved gain without sacrificing phase margin, compared to reset control without the shaping filter. Then, frequency-domain design procedures are provided for both Clegg Integrator (CI)-based and First-Order Reset Element (FORE)-based reset control systems. Finally, the effectiveness of the proposed strategy is demonstrated through two experimental case studies on a precision motion stage. In the first case, the shaped reset control leverages phase-lead benefits to achieve zero overshoot in the transient response. In the second case, the shaped reset control strategy enhances the gain advantages of the previous reset element, resulting in improved steady-state performance, including better tracking precision and disturbance rejection, while reducing overshoot for an improved transient response.

In this paper, a robust nonlinear control scheme is designed for the motion control of a class of piezo-actuated nano-positioning systems using frequency-domain analysis. The hysteresis, the nonlinearity in the piezoelectric material, degrades the precision in tracking references with high frequency contents and different travel ranges. The hysteresis compensation by the inverse model, as the state-of-the-art solution, is not reliable alone. Therefore, a control framework with robustness against the remaining nonlinearity is needed. It is shown that there is an unavoidable limitation in robust linear control design to improve the performance. A robust control methodology based on a complex-order element is established to relax the limitation. Then, a constant-in-gain-lead-in-phase (CgLp) reset controller is utilized to realize the complex-order control. The control design is based on the sinusoidal input describing function (SIDF) and the higher-order SIDF (HOSIDF) tools. A constrained optimization problem is provided to tune the control parameters. The achieved improvements by the CgLp control is validated by the simulation.