Aditya Natu
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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.
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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.
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.
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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.
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.
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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.
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.
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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.
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.
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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.
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.
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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.
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.
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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.
Passive elastic metamaterials offer effective vibration attenuation through locally resonant bandgaps, but suffer from fundamental limitations in real-time tunability, narrow operational bandwidth, and non-adaptive behavior. This work 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 more accurately reflects the moment-based phase cancellation dynamics underlying resonant actuation. Closed-form analytical expressions for transmissibility in a general $n \times n$ decentralized feedback architecture are derived via block elimination and experimentally validated using the $7\times 7$ unit-cell configuration. The results demonstrate that targeted low-frequency bandgaps in the range of 20–100 Hz can be systematically induced and reshaped through programmable tuning of controller gain and damping ratio, significantly improving 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 based on digitally synthesized resonator dynamics.
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Passive elastic metamaterials offer effective vibration attenuation through locally resonant bandgaps, but suffer from fundamental limitations in real-time tunability, narrow operational bandwidth, and non-adaptive behavior. This work 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 more accurately reflects the moment-based phase cancellation dynamics underlying resonant actuation. Closed-form analytical expressions for transmissibility in a general $n \times n$ decentralized feedback architecture are derived via block elimination and experimentally validated using the $7\times 7$ unit-cell configuration. The results demonstrate that targeted low-frequency bandgaps in the range of 20–100 Hz can be systematically induced and reshaped through programmable tuning of controller gain and damping ratio, significantly improving 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 based on digitally synthesized resonator dynamics.
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.
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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.
Active damping control of higher-order resonance mode in positioning systems
Application to prototype compliant dual positioning stage
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.
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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.
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.
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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.
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.
...
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.
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.
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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.
...
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 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.
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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.