Hysteresis Inversion Research Articles

Dynamic inversion-based hysteresis compensation using extended high-gain observer

We consider the tracking problem for an uncertain nonlinear single-input-single-output system satisfying the minimum-phase assumption, preceded by an unknown hysteresis operator. This is a widely used model for smart material-actuated systems, such as piezo-based nanopositioning systems. Existing hysteresis compensation methods typically require explicit hysteresis models, which tend to be high-dimensional operators and entail significant complexity in model identification and inversion. We propose an output feedback-based hysteresis compensation approach for this class of systems using dynamic inversion and extended high-gain observers. With mild assumptions on the hysteresis nonlinearity properties, the system can be represented as an uncertain, nonaffine, nonlinear system containing a hysteretic perturbation. Dynamic inversion is used to deal with the nonaffine input, uncertainties, and the hysteretic perturbation, where the latter two are estimated using an extended high-gain observer. Analysis of the closed-loop system under output feedback shows that the tracking error converges to a small neighborhood near the origin, which can be made arbitrarily small via a proper choice of time-scale parameters of dynamic inversion and the observer, respectively. Simulation results are presented to show the interplay between these two parameters. Finally, experiments conducted on a commercial nanopositioner confirm the theoretical analysis and demonstrate that the proposed method delivers performance comparable to several competing methods, all of which require an explicit hysteresis inversion operator.

Inversion-Based Hysteresis Compensation Using Adaptive Conditional Servocompensator for Nanopositioning Systems

Abstract Nanopositioning stages are widely used in high-precision positioning applications. However, they suffer from an intrinsic hysteretic behavior, which deteriorates their tracking performance. This study proposes an adaptive conditional servocompensator (ACS) to compensate the effect of the hysteresis when tracking periodic references. The nanopositioning system is modeled as a linear system cascaded with hysteresis at the input side. The hysteresis is modeled with a modified Prandtl–Ishlinskii (MPI) operator. With an approximate inverse MPI operator placed before the system hysteresis operator, the resulting system takes a semi-affine form. The design of the ACS consists of two stages: first, we design a continuously implemented sliding mode control (SMC) law. The hysteresis inversion error is treated as a matched disturbance, and an analytical bound on the inversion error is used to minimize the conservativeness of the SMC design. The second part of the controller is the ACS. Under mild assumptions, we establish the well-posedness and periodic stability of the closed-loop system. In particular, the solution of the closed-loop error system will converge exponentially to a unique periodic solution in the neighborhood of zero. The efficacy of the proposed controller is verified experimentally on a commercial nanopositioning device under different types of periodic reference inputs, via comparison with multiple inversion-based and inversion-free approaches.

Morphological Evolution of Bistable Copper Electrodeposition during Potentiodynamic and Galvanodynamic Measurements on Microelectrodes

Copper electrodeposition from an electrolyte containing a polyether suppressor and chloride exhibits bistable behavior characteristic of s-shaped negative differential (S-NDR) critical systems. The polyether and chloride form a co-adsorbed adlayer on the electrode that inhibits copper electrodeposition by sterically blocking cupric ion from accessing the interface. At sufficiently negative overpotentials, the adlayer is disrupted and copper electrodeposition occurs freely. In cyclic voltammetry (CV) measurements this behavior manifests as large hysteretic windows. The current response is negligible during the forward sweep until potential-dependent breakdown of the suppressor-halide adlayer occurs. The return sweep exhibits elevated current levels until the blocking layer is reformed at potentials 100s of millivolts more positive than the breakdown potential. When operating at a potential within the hysteretic window, and in an electrochemical configuration with sufficient ohmic resistance, copper electrodeposition exhibits bistable, passive – active deposition on the electrode surface. On macroscale planar electrodes this manifests as random Turing patterns whereas on topographically engineered electrodes, common in electronics manufacturing applications, deposition is localized to the most recessed regions of the interface and progresses in a bottom-up manner.The inversion associated with NDR behavior is only apparent in CV measurements after post-experimental correction for the iR-drop in the electrochemical cell. Thus, linear or cyclic galvanodynamic sweeps (GDS) offer an alternative measurement method to capture the overpotential inversion associated with critical systems. Electroanalytical measurements on microelectrodes further offer an avenue for exploring systems without significant iR-drop in solution. In this work, CV and GDS measurements on microdisk electrodes are used to explore the influence of additive (suppressor and chloride) concentration on critical behavior during copper electrodeposition. Further, in-situ optical microscopy during electroanalytical measurements is used to correlate characteristics of global potential/current responses to observations of copper growth dynamics. Continuum simulations capture key characteristics, such as hysteresis and overpotential inversion, of CV and GDS measurements as well as the different deposit growth profiles observed for potentiodynamic versus galvanodynamic operating modes.

Microvibration isolation by adaptive feedforward control with asymmetric hysteresis compensation

Abstract This paper proposes an improved adaptive filtered-x normalized least-mean-square (FxNLMS) algorithm to achieve active microvibration isolation. Physically, microvibration disturbance is attenuated by a custom-developed magnetostrictive-actuated device. Whereas, magnetostrictive materials characterize hysteresis. Particularly, when the amplitude of the input current is large, the hysteresis loop describes strong asymmetry and nonlinearity. To avoid this phenomenon, in some studies, the actuators are limited to move over a small range, and thus the potential range of the isolated microvibration is restrictive. Then Jiles-Atherton model and Bouc-Wen model are utilized to compensate hysteresis, however these models are non-analytical with certain approximation. In order to compensate hysteresis more accurately, Preisach model, a popular operator-based model, is presented. However, due to the double integrals in this model, the hysteresis identification and inversion process is complicated. Therefore, we reduce hysteresis based on a modified Prandtl-Ishlinskii (PI) model which is more simple but effective. This model utilizes the polynomial operators to describe hysteresis asymmetry and nonlinearity. The inverse hysteresis is then applied to compensate the magnetostrictive-induced hysteresis and to alleviate microvibration combining with the conventional FxNLMS algorithm. An experimental setup is fabricated and some experimental investigations are conducted. Experimental results show that the improved FxNLMS algorithm enhances the performance of microvibration isolation effectively—in the presence of single-tone (4 Hz at amplitude of 250 μm) and double tone (2 Hz mixed with 6 Hz at amplitude of 250 μm) excited microvibration, the isolation ratios of the improved FxNLMS controller are 20.79 dB and 15.32 dB respectively, while those of the conventional FxNLMS controller are 13.83 dB and 10.65 dB respectively.

Adaptive hysteresis compensation of piezoelectric actuator using direct inverse modelling approach

Hysteretic non-linearity significantly degrades the motion accuracy of piezoelectric actuators (PEAs). Hysteresis modelling and inversion (MI) is a widely-accepted hysteresis compensation approach. Alternately, direct inverse modelling (DIM) approach has also been proposed to directly identify the inverse hysteresis model. DIM is superior to MI as the inversion calculation has been totally eliminated, making DIM applicable in both rate-independent and rate-dependent hysteretic systems. This work proposes a further development of DIM by integrating adaptive projection (AP) algorithm so that parameters of the inverse hysteresis model can be automatically updated without any off-line identification. This work compares the proposed method with other methods via tracking continuous and discontinuous trajectories. Experimental results show that the integration of DIM and AP is effective in attenuating the hysteretic non-linearity and improving the trajectory tracking performance of the PEA.

Analysis of a displacer-coupled multi-stage thermoacoustic-Stirling engine

A new thermoacoustic-Stirling engine is introduced, composed of a compressor, regenerative assemblies, displacers and an alternator. The regenerative assemblies are coupled to displacers to successively multiply the acoustic power input by the compressor. The amplified acoustic power is converted into electric power in the alternator. This new configuration overcomes the limitations of traditional thermoacoustic or Stirling engines, including losses in long resonant tubes, response hysteresis and current inversion. The design method of the displacers and alternators is presented. Numerical simulations are carried out to investigate the characteristics of this system. Results show that the overall efficiency of this system could reach 47% with heating temperature of 900 K. Changing alternator load is the most plausible factor in piston or displacer exceeding the displacement limit. These parts can be effectively protected as long as the voltage of the compressor can be instantaneously adjusted. The working frequency, charging pressure and mechanical resistance do not substantially influence the efficiency and power capacity, when varied within a limited range. This allows the proposed engine to work stably when these parameters deviate from the design.

Reversible hysteresis inversion in MoS2 field effect transistors

The origin of threshold voltage instability with gate voltage in MoS2 transistors is poorly understood but critical for device reliability and performance. Reversibility of the temperature dependence of hysteresis and its inversion with temperature in MoS2 transistors has not been demonstrated. In this work, we delineate two independent mechanisms responsible for thermally assisted hysteresis inversion in gate transfer characteristics of contact resistance-independent multilayer MoS2 transistors. Variable temperature hysteresis measurements were performed on gated four-terminal van der Pauw and two-terminal devices of MoS2 on SiO2. Additional hysteresis measurements on suspended (~100 nm air gap between MoS2 and SiO2) transistors and under different ambient conditions (vacuum/nitrogen) were used to further isolate the mechanisms. Clockwise hysteresis at room temperature (300 K) that decreases with increasing temperature is shown to result from intrinsic defects/traps in MoS2. At higher temperatures a second, independent mechanism of charge trapping and de-trapping between the oxide and p+ Si gate leads to hysteresis collapse at ~350 K and anti-clockwise hysteresis (inversion) for temperatures >350 K. The intrinsic-oxide trap model has been corroborated through device simulations. Further, pulsed current–voltage (I–V) measurements were carried out to extract the trap time constants at different temperatures. Non-volatile memory and temperature sensor applications exploiting temperature dependent hysteresis inversion and its reversibility in MoS2 transistors have also been demonstrated.

Two-Degree-of-Freedom Hysteresis Compensation for a Dynamic Mirror Actuator

A low-computation, high-bandwidth, inverse-based hysteresis compensation and control strategy, not needing a priori knowledge of the desired trajectory, is presented. The resulting two degree-of-freedom controller is applied to a dynamic mirror with antagonistic piezoelectric stack actuation. Hysteresis compensation is performed by a finite-state machine activating polynomials for hysteresis inversion based on input signal slope. Residual error after hysteresis compensation is corrected by an LQR feedback controller. Experimental results demonstrate effectiveness of the hysteresis compensator and closed-loop system. For the input signal tested, a 91.5% reduction in hysteresis uncertainty is achieved at a 60 kHz sample rate.

Tracking Error Analysis for Feedback Systems With Hysteresis Inversion and Fast Linear Dynamics1

Analysis of closed-loop systems involving hysteresis is important to both the understanding of these systems and the synthesis of control schemes. However, such analysis is challenging due to the nonsmooth nature of hysteresis nonlinearities. In this paper, singular perturbation techniques are employed to derive an analytical approximation to the tracking error for a system consisting of fast linear dynamics preceded by a piecewise linear hysteresis nonlinearity, which is motivated by applications such as piezo-actuated nanopositioning. The control architecture considered combines hysteresis inversion and proportional-integral feedback, with and without a constant feedforward control. The analysis incorporates the effect of uncertainty in the hysteresis model, and offers insight into how the tracking performance depends on the system parameters and the references, thereby offering guidance in the controller design. Simulation and experimental results on a piezo-actuated nanopositioning system are presented to support the analysis. In particular, the control scheme incorporating the feedforward element consistently outperforms the classical PI controller in tracking a variety of references.

Inversion-free stabilization and regulation of systems with hysteresis via integral action

In this paper, we present conditions for the stabilization and regulation of the tracking error for ann-dimensional minimum-phase system preceded by a Prandtl–Ishlinskii hysteresis operator. A general controller structure is considered; however, we assume that an integral action is present. The common Lyapunov function theorem is utilized together with a Linear Matrix Inequality (LMI) condition to show that, under suitable conditions, the tracking error of the system goes to zero exponentially fast when a constant reference is considered. A key feature of this LMI condition is that it does not require the hysteresis effect to be small, meaning that hysteresis inversion is not required. We use this condition together with a periodicity assumption to prove that a servocompensator-based controller can stabilize the system without using hysteresis inversion. Additionally, we draw parallels between our LMI condition and passivity-based results achieved in the literature. We then verify our LMI results in simulation, where we show that the LMI condition can accurately predict the stability margins of a system with hysteresis. Finally, we conduct experiments using a servocompensator-based controller, where we verify the stability of the system and achieve a mean tracking error of 0.5% for a 200 Hz sinusoidal reference.

An indirect adaptive servocompensator for signals of unknown frequencies with application to nanopositioning

We propose an adaptive servocompensator utilizing frequency estimation and slow adaptation for systems subject to inputs of unknown frequencies. We show that the proposed controller can achieve zero tracking error for a class of periodic references and disturbances, including scenarios specifically relevant to piezo-actuated nanopositioning systems. In particular, for the case of a sinusoidal reference input, we establish the exponential stability of the closed-loop system in the presence of harmonic disturbances, under certain conditions on the amplitudes of the reference and disturbances. We also prove exponential stability in the case of sinusoidal reference and disturbance with two distinct frequencies. Additionally, we show that the proposed method, in conjunction with approximate hysteresis inversion, can attenuate the effect of hysteresis nonlinearity preceding linear dynamics and ensure the boundedness of the closed-loop system. Experiments conducted on a commercially available nanopositioner confirm our theoretical analysis and demonstrate the effectiveness of the proposed method as compared to Iterative Learning Control, a competitive technique in nanopositioning for tracking periodic references.

Dual-stage repetitive control with Prandtl–Ishlinskii hysteresis inversion for piezo-based nanopositioning

The positioning performance of piezo-based nanopositioning systems is limited by dynamic and hysteresis effects in the piezoactuator. Herein, a high-performance, dual-stage repetitive controller (dual-RC) with a feedforward hysteresis compensator is proposed for tracking periodic trajectories, such as the scanning-type motion, in nanopositioning systems. Firstly, a discrete-time dual-RC is created by cascading a conventional RC with an odd-harmonic RC. The favorable gain characteristics of the dual-RC coincide with the odd harmonics of the scanning-type periodic reference trajectory, thus offering good robustness and low tracking error. Secondly, a new inverse-hysteresis compensator is developed based on the Prandtl–Ishlinskii hysteresis model. The structure of the inverse model mimics the structure of the forward model, where the parameters of the inverse model can be easily identified from measured input–output data. Finally, the controllers are applied to a custom-designed high-speed nanopositioner, and simulations and experimental results are provided to illustrate the performance improvement of the proposed control scheme compared to industry-standard PID control and conventional RC. High-speed positioning results (tracking of triangle scan trajectories) at rates of 1kHz, 1.5kHz, and 2kHz are shown. Compared to a conventional RC, the tracking error of the dual-RC is 48% lower at 1kHz and 33% lower at 2kHz scanning frequency. It is also shown that by compensating for hysteresis, the performance of the RC system designed based on the linear dynamics can be enhanced.

Multirate Sampled-Data Output Feedback Control With Application to Smart Material Actuated Systems

We consider multirate sampled-data output feedback control of a class of nonlinear systems using high-gain observers where the measurement sampling rate is made faster than the control update rate. We show that, in the presence of bounded disturbances, given a sampled data state feedback controller that achieves stabilization with respect to a closed set, the multirate output feedback controller recovers stabilization of the same set provided the measurement sampling rate is sufficiently fast. As an application we consider the control of smart material actuated systems. This scheme combines a discrete-time high-gain observer with a hysteresis inversion controller where the hysteresis is modeled using a Preisach operator. Experimental results for the control of a shape memory alloy actuated rotary joint are provided.

Improved Equivalent Circuit Model for V-Shaped, Thresholdless Switching Ferroelectric Liquid Crystals

For V-shaped, thresholdless switching ferroelectric liquid crystals (FLCs), the impedance divider induced by the multilayer structure of FLC cells and the drive circuit play an important role in switching characteristics. In this paper, an equivalent circuit model that can be applied to conventional circuit simulators is proposed for the optical response prediction and drive circuit optimization of V-shaped FLCs. The model is improved from the original model of Moore and Travis; however, the impedance divider is taken into account, and both polar and nonpolar surface anchoring energies are considered to make the model more preferable. The model is then utilized to investigate thresholdless switching characteristics. Simulation results show that the hysteresis inversion frequency fi increases more than one thousand fold with the drive circuit and then decreases with REXT following the relation log fi = -alog REXT + b, and a (b) increases from 0.43 to 0.46 (2.46 to 2.66) as the amplitude of triangular voltage increases from 4 to 10 V, agreeing with experimental results. Also, the same optical transmissions are plotted as different coordinates, as a function of voltage dropping on liquid crystal layer and of drive voltage, and the results show that genuine V-shaped switching is only observed when the transmission is plotted as a function of drive voltage, coinciding with the model suggested by Blinov et al.

An improved equivalent circuit model and the dependence of hysteresis inversion frequency on typical parameters of V‐shaped switching SSFLC cells for both bookshelf and chevron structures

An improved equivalent circuit model able to be applied to conventional circuit simulators is presented for optical response prediction and drive circuit design of V‐shaped surface‐stabilised ferroelectric liquid crystal (SSFLC) cells. The model is derived from Moore and Travis' original model. Moreover, the impedance divider induced by the multilayer structure of the liquid‐crystal cells is taken into account, and both polar and non‐polar surface anchoring energy are considered to make the model more preferable. The model is then utilised to investigate the thresholdless switching characteristics for both bookshelf and chevron structures. With the circuit model: (1) the genuine V‐shaped switching occurs only at the hysteresis inversion frequency f i, and below (above) f i an anomalous (normal) hysteresis is observed; (2) the genuine V‐shaped switching is only observed when the transmission is plotted as a function of the total applied voltage; (3) f i increases with increasing conductivity of liquid‐crystal layer (G LC) and the amplitude of applied voltage, and the function of is almost linear; (4) For small spontaneous polarisation p s, f i grows as p s increases, however, on further increasing p s, f i reaches its maxima and then decreases (5) the V‐shaped switching can be observed in both bookshelf and chevron structures, however, f i is higher for the chevron structure. Results obtained from the circuit model compare favourably with the reported experimental and numerical results.

Shift of the Hysteresis Inversion Frequency with Temperature in a Surface Stabilized Ferroelectric Liquid Crystal Cell

The capacitance–voltage (C–V) hysteresis inversion frequency ( fi) of a surface stabilized ferroelectric liquid crystal device (SSFLC) is found to shift to the higher frequency side with increasing temperature. The frequency ( fc) up to which the amount of switchable polarization (ASP) decreases also shifts to the higher value. ASP for a fixed frequency also decreases with increasing temperature. The decrease in the tilt angle, spontaneous polarization and the traversable path of the chiral molecule between two fully switched states on the smectic cone, with increasing temperature causes the decrease in ASP and also shifts fi. Accordingly, temperature dependence of the inversion of the dielectric biaxiality can be determined.

Study of the Hysteretic Behavior in Polymer-Stabilized Ferroelectric Liquid Crystal System

We have studied the hysteresis-free switching behaviors of a polymer-stabilized ferroelectric liquid crystal (PSFLC) as well as a pure ferroelectric liquid crystal (FLC) system and found that they coincided with the model suggested by Blinov et al. [Phys. Rev. E 66 (2002) 021701] The hysteresis inversion frequency was promoted to up to 7000 Hz by connecting an external capacitor and resistor in series. In addition, the influence of temperature on the hysteresis-free switching of the cell could be optimized.

High frequency hysteresis-free switching in thin layers of smectic-C*ferroelectric liquid crystals

The insulating layers used for the alignment of ferroelectric liquid crystals (FLC) in electro-optical cells usually have non-negligible thickness and their capacitance determines the type of the director switching caused by a triangular-form external voltage U(tr) . With decreasing frequency of U(tr) , the hysteresis in a switching direction changes from the normal to the abnormal one at a characteristic hysteresis inversion frequency f(i) . In the vicinity of f(i) , the electro-optical response is thresholdless and the optical transmission manifests the V -shape field dependence. The V -shape regime is very interesting for certain applications, in particular to microdisplays due to a possibility of the gray scale realization. However, f(i) has to be enhanced from the usually observed frequency of a few Hz up to the range of hundreds of Hz. To this effect, a special FLC material has been designed and its basic properties (tilt angle, spontaneous polarization, rotational viscosity, and electric conductivity) have been measured over the entire range of the smectic-C* phase. Upon variation of cell parameters (thickness of both the FLC and alignment layers), temperature, and external voltage, the frequency of the V -shape effect as high as 150-1000 Hz (in the temperature range 30-75 degrees C) has been found experimentally. The operating voltage remains lower than 8 V. A quantitative interpretation of these results has been done using the modeling procedure developed earlier [S.P. Palto, Cryst. Rep. 48, 124 (2003)]. The modeling has been performed with the experimental values of the FLC material and the cell parameters and has shown very good agreement with experiment. The key point of this approach is consideration of the internal voltage on the FLC layer, the sign, amplitude, and form of which differ from U(tr) . The results of the modeling allow further improvement of the performance of electro-optical FLC cells for high frequency V-shape effect.

Vortex imaging and local magnetization studies in HTS by scanning Hall probe microscopy

We have used scanning Hall probe microscopy to correlate vortex images and local magnetisation measurements in two different high temperature superconducting samples. Near the edge of a continuous YBCO thin film we have observed local hysteresis inversion and negative remanent fields, which can be semi-quantitatively explained in terms of a theoretical model of flux penetration in an infinitely long superconducting strip. In a YBCO film containing a regular square array of antidots we have further find that vortices trapped at antidots exhibit an unusual behaviour upon field sweep reversal.

Hall probe imaging of local hysteresis inversion and negative remanent fields near the edge of a YBCO thin film

We report vortex imaging and local magnetometry studies near the edge of a YBCO thin film using scanning Hall probe microscopy (SHPM). Our data show some unusual features, namely local hysteresis inversion and negative remanent fields, which are semi-quantitatively explained in terms of a theoretical model of flux penetration in an infinite-long thin superconducting strip.