Integrating Active Damping with Shaping-Filtered Reset Tracking Control for Piezo-Actuated Nanopositioning

arXiv:2602.10724 · eess.SY, cs.SY · Submitted 2026-02-11 · Read on arXiv

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Introduction to the show: ident: Robotics Radio. Generated commentary on the latest robotics and control papers.

Rosa: Today's paper: "Integrating Active Damping with Shaping-Filtered Reset Tracking Control for Piezo-Actuated Nanopositioning".

Dev: The gist Piezoelectric nanopositioning systems are often limited by lightly damped structural resonances and the gain–phase constraints of linear feedback,

Rosa: First, who's behind it and why it matters.

Paper summary: Rosa: So we're looking at this paper now called "Integrating Active Damping with Shaping-Filtered Reset Tracking Control for Piezo-Actuated Nanopositioning". Basically, they're tackling the problem that these nanopositioning systems have—they get stuck because of those lightly damped structural resonances and the limits of linear feedback.

Dev: Right, so they’re proposing this dualloop architecture that puts an inner loop on active damping, which uses a non-minimumphase resonant controller to actively dampen those resonances.

Taro: And then on top of that, there's an outer loop for tracking, but they add this constant-gain lead-in-phase element with a reset action to get the phase lead needed at the target crossover without boosting the overall loop gain.

Rosa: What that means in plain terms is they’re trying to get better tracking performance and higher bandwidth while avoiding that problem where pushing for more speed just makes things unstable or causes weird behavior with those resonances.

Dev: They claim this approach lets them operate beyond the first dominant resonance, which is pretty significant because standard linear control gets really restricted by that waterbed effect when you get close to the resonance frequency.

Taro: I'm interested in what happens when things go wrong outside of the lab setting, Rosa. If you're using this on a mobile robot or something where the environment keeps changing, how robust is this whole setup?

Rosa: That’s a big question. The paper shows real-time experiments on an industrial nanopositioner confirming they got about fifty-five hertz improvement in open-loop crossover frequency and about thirty-four hertz increase in closed-loop bandwidth compared to their baseline linear design.

Dev: Those numbers suggest a solid gain, but we have to remember the caveats mentioned in the paper. They also show that aggressive tuning of those constant-gain lead-in-phase designs can introduce pronounced higher-order harmonics, which degrades error sensitivity in specific frequency bands.

Taro: Higher-order harmonics mean what? Does that just make the system noisy or less accurate when it's trying to hold a precise position?

Rosa: Exactly. The paper tackles that by introducing a shaping filter in the reset path. They tune this shaping filter for designs like Case six and Case seven to introduce a phase lag below two hundred hertz, which helps reduce those low-frequency higher-order harmonics while still keeping the phase lead needed at the target crossover frequency.

Dev: So, it’s not just about adding damping; it’s about carefully managing the non-linear reset element so you don't create unwanted noise or multiple resets when you push for that desired tracking speed.

Taro: That shaping filter sounds like a clever way to decouple the phase recovery from the harmonic pollution. But what does this mean for systems where the underlying physics itself is changing, not just a fixed structural resonance?

Paper summary: Rosa: It suggests that combining linear active damping with a carefully shaped nonlinear reset control is a promising strategy for precision motion when you’re dealing with these kinds of resonant dynamics.

Dev: The main thing to keep in mind from this paper, "Integrating Active Damping with Shaping-Filtered Reset Tracking Control for Piezo-Actuated Nanopositioning," is that while they improved bandwidth by about thirty-four hertz, the authors also explicitly state that higher phase-lead designs can amplify measurement noise in the error signal driving the reset action <ref:2602.10724#pg3>.

Taro: That means we have to be careful not to overdo that lead element if we want a system that handles unexpected disturbances well, which is what I’m really interested in for autonomy.

Rosa: So, to summarize this paper on "Integrating Active Damping with Shaping-Filtered Reset Tracking Control for Piezo-Actuated Nanopositioning", the core idea is using a dual-loop system where an inner loop handles structural damping, and the outer loop uses a constant-gain lead-in-phase element coupled with a shaping filter to recover phase without causing high harmonics.

Dev: It’s about getting higher bandwidth by using non-minimumphase resonant control for damping, and then carefully controlling the reset action through that shaping filter to manage those harmonics.

Taro: For someone just listening, this paper shows how you can push the performance of these nanopositioning systems up significantly—about fifty-five hertz in open-loop crossover and thirty-four hertz in closed-loop bandwidth—compared to a simple linear controller.

Rosa: And the implication for me is that if we're building something that needs very high precision movement, this approach gives us a way to achieve that speed without just letting the system get messy with unwanted frequency components.

Dev: The limitation they flag is that aggressively tuned CgLp designs can cause those higher-order harmonics to degrade sensitivity in certain frequency bands, which is why they needed that shaping filter.

Taro: So, the real world application for me is thinking about how this control strategy handles sudden changes in external forces or when the system encounters unexpected dynamics outside of a controlled test bench.

Rosa: That’s where we need more data on how long this setup can maintain those performance gains in a real, messy environment before those higher-order harmonics start causing trouble.

Dev: So, the paper shows a way to combine active damping with nonlinear reset control to get better tracking, and then they showed how shaping filters tame the resulting noise from that control action.

Taro: It’s about finding a balance between aggressive phase lead for speed and keeping the system clean from unwanted harmonics.

Rosa: And that's what this paper demonstrates in "Integrating Active Damping with Shaping-Filtered Reset Tracking Control for Piezo-Actuated Nanopositioning," showing how you can achieve better tracking by integrating damping and reset control smartly.

Conclusion: Rosa: So we’re looking at the conclusion of this paper, "Integrating Active Damping with Shaping-Filtered Reset Tracking Control for Piezo-Actuated Nanopositioning." It basically wraps up how they put together that inner damping loop and the outer tracking loop with that special reset element.

Dev: Yeah, they developed a system that uses non-minimumphase resonant control on the inside to kill those structural vibrations, which then lets the outer tracking controller work much faster than before.

Taro: And they added this constant-gain lead-in-phase element for the tracking part, which helps get the right phase at the crossover point without making your overall system gain way too high.

Rosa: What that means is they managed to push the performance up a lot, getting that bandwidth boost we talked about earlier with both loops working together.

Dev: The results they showed on the industrial nanopositioner were pretty impressive, showing about fifty-five hertz of improvement in open-loop crossover and a thirty-four hertz increase in closed-loop bandwidth compared to just using a simple linear controller.

Taro: But they also had to be careful with that constant-gain element because if you tune the phase lead too aggressively, you start getting these high-order harmonics, which messes up the error sensitivity.

Rosa: That’s where they introduced this shaping filter in the reset path to tame those harmonics without ruining the intended phase recovery at the target frequency.

Dev: The main thing this paper means is that you can get higher speed and better tracking for these tiny actuators by actively fighting their natural resonances, even if you have to add some extra layers of non-linear control.

Taro: So what does this actually change for someone building autonomous systems? It suggests we can design controllers that are more robust against the inherent physics of the machine, not just reacting to external noise.

Rosa: Exactly. It moves us toward designs where the controller itself is designed to handle the physical limitations of how those tiny pieces vibrate and move.

Dev: The challenge for me as an engineer is making sure that this whole structure—the inner loop, the outer loop, and that shaping filter—runs reliably at a high enough rate without introducing too much latency or instability.

Taro: So while they show great performance on a lab bench, the question remains how long this setup stays stable when you throw unexpected forces at it in a real-world scenario.

Rosa: That’s the next big question, right? We need to see if these gains hold up when the environment isn't perfectly controlled.

Delft University of Technology

eess.SY, cs.SY

Submitted: 2026-02-11

Updated: 2026-02-11

Journal ref: 2026 IEEE Conference on Control Technology and Applications (CCTA)

DOI: 10.1109/CCTA62090.2026.11684112

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 90/100

The gist: The gist Piezoelectric nanopositioning systems are often limited by lightly damped structural resonances and the gain–phase constraints of linear feedback, which restrict achievable bandwidth and

Key concepts

Non-Minimumphase Resonant Controller (NRC)
This controller is used in the inner loop to actively damp the system's dominant structural resonances. It allows the control system to operate effectively beyond the first resonance frequency, which is a major limitation of standard linear controllers. This enables a much wider operational bandwidth for nanopositioning systems.
Constant-Gain, Lead-in-Phase (CgLp) Reset Element
This element is part of the outer tracking loop and provides necessary phase lead at the desired crossover point without increasing the overall loop gain. It combines a generalized FORE with a lead–lag filter to achieve this, improving tracking performance while maintaining stability margins.
Shaping Filter ($C_s(s)$)
This filter is placed in the reset path to regulate the action of the CgLp element. Its purpose is twofold: first, to suppress higher-order harmonics generated by aggressive CgLp designs, which can degrade error sensitivity; second, to ensure proper reset timing and phase recovery without altering the fundamental linear loop dynamics.
Dual-Loop Architecture
The control system consists of two interconnected loops. The inner loop uses the NRC to handle physical damping (suppressing resonances), while the outer loop handles tracking performance. This separation allows the outer loop to operate at a higher bandwidth, improving overall system speed and accuracy.

Terminology

Summary

The gist 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 dualloop architecture that combines an inner-loop non-minimumphase 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

System Limitations and Control Strategy

Piezoelectric nanopositioning systems are typically limited by lightly damped resonant modes that fundamentally limit the achievable closedloop bandwidth and disturbance rejection Proportional–integral (PI) controllers remain a common baseline, but the dominant resonance restricts the control bandwidth to a fraction of the resonance frequency To address these limitations, active damping strategies like Positive Position Feedback (PPF) and Integral Resonant Control (IRC) have been proposed More recently, the non-minimumphase resonant controller (NRC) enables substantially higher closed-loop bandwidths, including operation beyond the first dominant resonance Linear control remains fundamentally limited by the waterbed effect and the Bode gain–phase relationship as crossover approaches structural resonance

Dual-Loop Architecture Components

The proposed control architecture in Fig. 2 comprises an inner active damping loop with a linear controller Cd(s) and an outer tracking loop with a linear controller Ct(s) The inner loop attenuates the dominant resonant modes of the plant, enabling the outer loop to operate at a higher closed-loop bandwidth and improve tracking performance The outer control loop incorporates a nonlinear reset element R connected in series with Ct(s) This reset element is driven by the error signal er and generates the reset control signal ur Furthermore, a shaping filter Cs(s) is implemented in the reset path to produce the reset-triggering signal es and to modulate the reset action

Controller Design Details

The NRC damping controller is defined as Cd(s) = k/(s − ωa)/(s + ωa), where k, and ωa denote the controller gain and corner frequency, respectively The tracking controller Ct(s) is designed as a series combination of a PI controller, notch filters targeting the dominant higher-order modes, and a low-pass filter The CgLp element combines a generalized FORE (GFORE) with a linear lead–lag filter to deliver approximately constant gain with phase lead The CgLp is expressed as CgLp(s) = R(s) · kc · Cl(s), where R is the proportional FORE with the state-space defined as Ar = −ωr, Br = 1, Cr = ωr, Dr = ωl/ωf −ωl, Aρ = γr The lead–lag filter Cl(s) is expressed as 1 + s/ωl / 1 + s/ωf

Harmonic Mitigation via Shaping Filter

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 crossoverphase recovery The shaping filter Cs(s) is defined as Cs(s) = Rbl(s) Ns1(s) · Ns2(s) · CL(s) This modification allows the shaping filter to attenuate higher-order harmonics without directly altering the linear loop dynamics The shaping filter parameters are tuned for the 15◦(Case 6) and 20◦(Case 7) CgLp designs to introduce a Fig.8, phase lag below 200 Hz (light-blue region in Fig.7). This additional lag reduces low-frequency higher-order harmonics while preserving the required phase lead at the target crossover frequency and avoiding unintended changes at higher frequencies

Experimental Performance Results

Realtime experiments on an industrial nanopositioner confirmed the effectiveness of the approach, yielding approximately 55 Hz improvement in open-loop crossover frequency and about 34 Hz increase in closed-loop bandwidth compared with a baseline linear design The results show a consistent reduction in RMS error for CgLp-assisted reset cases compared to the baseline linear controller, with improved performance as the designed phase lead increases For higher phase-lead designs, the shaping filter further reduces higher-order harmonic effects and yields an additional reduction in RMS error compared to the corresponding cases without shaping The closed-loop bandwidth ωc, defined by the ±3 dB crossings, improves by about 34 Hz

Conclusion

A dual-loop controller was developed in which an NRCbased inner loop suppresses dominant resonant dynamics, enabling an outer-loop tracking controller with a CgLp reset element to recover phase at the targeted crossover and achieve higher bandwidth without high-frequency gain amplification Higher phase-lead CgLp settings can amplify higher-order harmonics, leading to localized sensitivity degradation and multiple resetting, and we mitigated this effect using a shaping filter placed in the reset-trigger path to regulate reset timing and attenuate harmonic influence Realtime experiments on an industrial nanopositioner confirmed the effectiveness of the approach, yielding approximately 55 Hz improvement in open-loop crossover frequency and about 34 Hz increase in closed-loop bandwidth compared with a baseline linear design, while maintaining the intended robustness margins

Acknowledgments

This work was financed by Physik Instrumente (PI) SE & Co. KG and co-financed by Holland High Tech with PPS Project supplement for research and development in the field of High Tech Systems and Materials

References

[1] A. J. Fleming and K. K. Leang, Design, modeling and control of nanopositioning systems [8] A Al-Mamun, E Keikha, C S Bhatia, and T H Lee, Integral resonant control for suppression of resonance in piezoelectric micro-actuator used in precision servomechanism [13] J C Clegg, A nonlinear integrator for servomechanisms [15] N Saikumar, R K Sinha, and S H HosseinNia, “constant in gain lead in phase” element–application in precision motion control [18] N Karbasizadeh, “Shaping nonlinearity in reset control systems to realize complex-order controllers: Application in precision motion control” [19] N Karbasizadeh and S H HosseinNia, “Continuous reset element: Transient and steady-state analysis for precision motion systems” [21] X Zhang and S H HosseinNia, “Enhancing the reliability of closedloop describing function analysis for reset control applied to precision motion systems” [3] Q Xu and K K Tan, Advanced control of piezoelectric micro-/nanopositioning systems [9] Z Chen, X Zhong, J Shi, and X Zhang, “Damping-enabling technologies for broadband control of piezo-stages: A survey”<ref:2602.

Improvements for AI systems

  1. Bold header: Active Damping Integration for Resonance Suppression

The system can achieve 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 by combining an inner-loop non-minimumphase resonant controller (NRC) for active damping with an outer-loop tracking controller.

  1. Bold header: Higher Bandwidth Tracking via CgLp Reset Control

The improved AI system can operate at higher closed-loop bandwidths and extend the bandwidth further by utilizing a constant-gain, lead-in-phase (CgLp) reset element to provide phase lead at the targeted crossover without increasing loop gain.

  1. Bold header: Harmonic Suppression for Robust Control

The system can maintain high performance in higher phase-lead settings by introducing a shaping filter to suppress the problematic harmonics and prevent excessive resetting, thereby reducing error sensitivity in problematic frequency ranges like 80–160 Hz.

  1. Bold header: Enhanced Tracking Accuracy

The system demonstrates improved tracking accuracy, as evidenced by a consistent reduction in RMS error for CgLp-assisted reset cases compared to the baseline linear controller, leading to better precision in applications like AFM probe positioning and semiconductor alignment.

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