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 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.

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.

Reset control systems (RCSs) can achieve performance beyond that of conventional linear time-invariant (LTI) controllers, while also allowing analysis directly in the frequency domain using measured frequency response functions (FRFs). Despite this potential, existing frequency-domain stability approaches are typically restricted to specific RCS architectures and commonly depend on parametric plant models, which limits their applicability in practice. In this paper, a generalized H_β framework is developed for the most comprehensive class of RCS structures, incorporating pre-, post-, and parallel LTI filters, as well as nonzero after-reset values. Based on this formulation, an FRF-based representation corresponding to the H_β transfer function is derived, and frequency-domain sufficient conditions are established to certify the H_β-based quadratic stability criterion. As a result, the proposed framework enables direct FRF-based assessment of quadratic stability and convergence for the considered class of reset control systems, using the measured plant FRF together with the known controller and filter transfer functions, without requiring an explicit parametric plant model. The effectiveness and practical relevance of the method are demonstrated through an illustrative industrial case study.

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.

Loop-shaping is widely used in precision motion control, but conventional approaches — focused on phase margin and open-loop gain — are inadequate for piezo positioning systems where open-loop phase critically affects performance. This paper proposes generalized loop-shaping guidelines tailored for nonlinear piezo-actuated stages. A constant-in-gain lead-in-phase reset controller is developed to implement the guidelines by overcoming waterbed effect in linear control. An intuitive methodology for shaping filter design is presented to ensure reliable reset control implementation. Using (higher-order) sinusoidal input describing functions, nonlinear motion control is designed. Experiments demonstrate closed-loop bandwidth flatness (±[jls-end-space/]1 dB) and enhanced sensitivity function.

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.

In this note, we present an extension of the nonlinear negative imaginary (NI) systems theory to reset systems. We define the reset negative imaginary (RNI) and reset strictly negative imaginary (RSNI) systems and provide a state-space characterization of these systems in terms of linear matrix inequalities. Subsequently, we establish the conditions for the internal stability of a positive feedback interconnection of a (strictly) negative imaginary linear time-invariant plant and a reset (strictly) negative imaginary controller. The applicability of the proposed method is demonstrated in a numerical example of a reset version of a positive position feedback (PPF) controller for a plant with resonance.

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.

This paper explores the combination of a Hybrid Reluctance Actuator (HRA) with a Hybrid Tunable Magnet Actuator (HTMA) to realize a high bandwidth actuator that can generate low-frequency forces with greater efficiently. The HTMA allows desired forces to be sustained without continuous coil heating by manipulating the remnant magnetisation of an AlNiCo magnet. This enables the actuator to exert force through two modes of operation: by magnetisation of the Tunable AlNiCo Magnet (TM) or by inducing a proportionally force-dependent field. The second mode may furthermore be used to compensate for unwanted variations in forces during magnetisation. Although FEM analyses provide an understanding of the actuator behaviour in steady states, it is inefficient to integrate transient FEM models with accurate hysteresis models. Hence, firstly, an analytical framework is presented to determine the transient behaviour and the comparative energy efficiency of the two actuator modes. Then, a control strategy is presented for the operation of the combined actuator to track a reluctance force step reference. An experimental setup is designed and tested to validate the concept and control method.

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.