Hysteresis Of Actuator Research Articles

Inverse feedforward control of piezoelectric actuators using optimized composite neural network-based Hammerstein model

This paper utilizes the optimized composite neural network (OCNN)-Hammerstein model to directly identify the dynamic inverse hysteresis effect, employing it as a feedforward controller to compensate for the rate-dependent and amplitude-dependent dynamic hysteresis of the piezoelectric actuator. The OCNN-Hammerstein model consists of an optimized composite neural network and an auto-regressive exogenous model in series. The OCNN comprises convolutional neural network layer and radial basis function neural network layer, with its hyperparameters optimized using a modified grey wolf optimizer algorithm. Compared to the existing dynamic Prandtl-Ishlinskii-Hammerstein and dynamic Bouc-Wen-Hammerstein models in the literature, the feedforward controller based on the proposed model in this paper demonstrates superior performance, with an RSME below 0.45 μm and a 74.5% reduction in relative hysteresis at the condition of 300 Hz and maximum amplitude. The feedforward controller exhibits universality across all amplitude ranges and within the 50–300 Hz frequency range, while also providing predictive compensation for dynamic hysteresis at 300–400 Hz. The feedforward controller based on the OCNN-Hammerstein model in this paper provides a crucial methodology for open-loop control of piezoelectric actuators.

Modelling and compensation of rate‐dependent hysteresis in piezoelectric actuators based on a modified Madelung model

AbstractBased on the principle of weight superposition, a modified Madelung model is proposed. By combining the signal delay response characteristics (SDRC), a dynamic model and its inverse model are established to describe and compensate for the rate‐dependent hysteresis phenomenon of the piezoelectric actuators (PEAs). The effectiveness of the proposed method is verified by experiments, and the results show that the hysteresis nonlinearity of the PEA is basically eliminated, with the normalized root‐mean‐square error of 0.64% under the excitation of multi‐frequency superposition signal.

Finite-time prescribed performance tracking control for nonlinear time-delay systems with state constraints and actuator hysteresis

In this paper, the problem of adaptive neural network prescribed performance tracking control for a class of non-strict feedback time-delay systems constrained by full-state is studied. Radial basis function (RBF) neural networks (NNs) are integrated into the backstepping medium to deal with the uncertain functions and the barrier Lyapunov function (BLF) technique ensures that the state of the system does not exceed its limits. Subsequently, integrated with the Lyapunov–Krasovskii functional, the proposed control scheme makes the tracking errors converge to the preset region while the state constraint is not violated. Finally, the effectiveness of the scheme is supported by two simulation experiments.

Innovative Skin Structures: Synthesis, Void Analysis, and Hysteresis Modeling of Zero Poisson’s Ratio Skin for Span Morphing Wing

This paper explores the use of carbon fiber-reinforced elastomeric skins for advancing flexible morphing wing technologies, highlighting exceptional 1D morphing capabilities. The study focuses on synthesizing a specially engineered elastomer-based skin with a zero Poisson’s ratio, achieved through precise formulation and fabrication onto unidirectional carbon fiber. Poisson’s ratio of the 1D skin is confirmed to be zero via image analysis. Micro-CT tomography evaluates carbon fiber quality and voids under varied prestretch conditions, revealing proportional increases in void sizes. X-ray tomography also provides insights into void distribution and morphology during pre- and post-cyclic stretching. The innovative approach enables seamless 1D morphing, achieving an impressive 200% stretch with a slight increase in actuation force and hysteresis loss percentage. Inspired by continuum mechanics, the proposed “Exp-ln-ln” framework accurately models the loading–unloading stretching of the skin. An extensive parametric investigation assesses key parameters, advancing fiber-reinforced elastomeric materials for aerospace morphing skins.

Coupled hysteresis and resonance control of three-degree-of-freedom tip-tilt-piston piezoelectric stage

In order to solve the coupled hysteresis and resonance problems in three-degree-of-freedom tip-tilt-piston piezoelectric stage, a coupled hysteresis model and a coupled integral resonance compensation model are designed. The inverse coupled hysteresis feedforward control combined multi-axis coupled resonance control and high-gain integral tracking controller are used to improve the tracking speed and positioning accuracy of the stage. Firstly, a kinematic model of the stage is built to translate the three-degree-of-freedom motion of the end-effector into the outputs of three piezoelectric actuators. Then, a coupled hysteresis model based on the rate-dependent Prandtl–Ishlinskii model is established and parameterized to simultaneously compensate for the hysteresis of a single piezoelectric actuator and the coupled hysteresis between multiple piezoelectric actuators. The effectiveness of the model is verified by open-loop and closed-loop inverse model feedforward control experiments. Afterwards, a coupled integral resonance compensation model is also established and parameterized to suppresses the resonance and expand the system bandwidth. Finally, the proposed controller is used to conduct tracking experiments on a composite signal, and the results show that the accuracy and speed of trajectory tracking are further improved, and the mechanical coupling between axes are significantly reduced.

Model of Shape Memory Alloy Actuator with the Usage of LSTM Neural Network.

Shape Memory Alloys (SMAs) are used to design actuators, which are one of the most fascinating applications of SMA. Usually, they are on-off actuators because, in the case of continuous actuators, the nonlinearity of their characteristics is the problem. The main problem, especially in control systems in these actuators, is a hysteretic loop. There are many models of hysteresis, but from a control theory point of view, they are not helpful. This study used an artificial neural network (ANN) to model the SMA actuator hysteresis. The ANN structure and training method are presented in the paper. Data were generated from the Preisach model for training. This approach allowed for quick and controllable data generation, making experiments thoroughly planned and repeatable. The advantage and disadvantage of this approach is the lack of disturbances. The paper's main goal is to model an SMA actuator. Additionally, it explores whether and how an ANN can describe and model the hysteresis loop. A literature review shows that ANNs are used to model hysteresis, but to a limited extent; this means that the hysteresis loop was modelled with a hysteretic element.

Modeling and parameter identification of rate-dependent hysteresis behavior based on modified-generalized Prandtl–Ishlinskii model

The intrinsic characteristic of piezoelectric actuators (PEA), known as hysteresis, has been demonstrated to diminish the capability and stability of the system significantly. This paper proposes a modified-generalized Prandtl–Ishlinskii (MGPI) model to describe the rate-dependent hysteresis in piezoelectric actuators. The developed model incorporates a voltage change rate function to replace the first part of the generalized Prandtl–Ishlinskii (GPI) model. Additionally, the model integrates the cubic polynomial into the envelope function, along with the dynamic thresholds and weights. When describing the hysteresis of the piezoelectric actuator (PEA), the model parameters are identified using the Improved Grey Wolf Optimizer (IGWO) algorithm. To prevent the algorithm from getting trapped in local optima, the cubic chaotic mapping is utilized for population initialization, as well as a nonlinear convergence factor, and the Levy flight strategy factor is introduced to update the Wolf pack’s position. The rate-dependent hysteresis behavior of a PEA under excitation in the 1–200 Hz frequency range was experimentally measured. The measured data were used to demonstrate the validity of the proposed MGPI model. The relative root-mean-square error and the relative maximum error of the MGPI model are 1.41% and 6.00%, respectively, which are lower than those of the GPI model, which are 3.15% and 10.58%. Under the composite frequency driving, the outputs of the GPI model and MGPI model were compared with the measured data of the PEA, the results suggest that the MGPI model and the IGWO algorithm can more accurately describe the rate-dependent hysteresis of the piezoelectric actuators.

Neural Network Based Iterative Learning Control for Dynamic Hysteresis and Uncertainties in Magnetic Shape Memory Alloy Actuator

Neural Network Based Iterative Learning Control for Dynamic Hysteresis and Uncertainties in Magnetic Shape Memory Alloy Actuator

Comprehensive compensation of dynamic hysteresis and creep for piezoelectric actuator

This paper addresses the modeling of dynamic hysteresis and creep in piezoelectric actuators, and employs feedforward open-loop control based on inverse models to compensate for hysteresis and creep phenomena. The comprehensive model consists of quasi-dynamic and dynamic components. The quasi-dynamic model combines the quasi-dynamic Prandtl–Ishlinskii (PI) model with an PI-based linear time-invariant model, while the dynamic part utilizes the auto-regressive exogenous model. The model accurately describes creep and dynamic hysteresis with modeling errors of less than 0.01 μm and 0.14 μm, respectively. The inversion of the comprehensive model has been proven to exhibit unique convergence. Under inverse feedforward control, the improvement in dynamic hysteresis and hysteresis with creep can be achieved at 94% and 83%, respectively. The comprehensive model proposed in this paper accurately describes the dynamic hysteresis and creep phenomena in piezoelectric actuators and realizes open-loop compensation control, achieving precise actuation of piezoelectric actuators.

Adaptive Backstepping Time Delay Control for Precision Positioning Stage with Unknown Hysteresis

Piezoelectric-actuated precision positioning stages are widely used in high-precision instruments and high-end equipment due to their advantages of high resolution, fast response, and compact size. However, due to the strong nonlinearity of hysteresis, the presence of hysteresis in piezoelectric actuators seriously affects the positioning accuracy of the system. In addition, it is challenging to identify the model parameters for hysteresis. In this paper, an adaptive backstepping time delay control method is proposed for piezoelectric devices system with unknown hysteresis. Firstly, the Bouc–Wen model is used to describe the hysteresis characteristics, and the model is interpreted as a linear term and a bounded uncertain hysteresis term. Then, the time delay estimation technique is used to estimate the hysteresis term of the Bouc–Wen model online, and the unknown parameters of the system and hysteresis model are obtained through adaptive updating laws. Furthermore, the stability of the control scheme is proved based on Lyapunov stability theory. Finally, the effectiveness and superiority of the proposed control scheme are demonstrated by comparing it with two typical hysteresis compensation control algorithms through three different sets of input signals.

Energy-based modeling of rate-independent hysteresis and viscoelastic effects in dielectric elastomer actuators

Dielectric elastomer (DE) transducers are known to exhibit a rate-dependent hysteresis in their force-displacement response, which is commonly attributed to the viscoelastic behavior of elastomer materials and compliant electrodes. In the case of DE materials characterized by low mechanical losses, such as silicone, the mechanical hysteresis often turns out to be practically rate-independent in the low frequency range (sub-Hz), whereas rate-dependent hysteretic effects only become relevant at higher deformation rates. Most of the existing literature focuses on describing DE hysteretic losses using viscoelasticity theory. This approach results in relatively simple dynamic models, which are not capable of describing rate-independent hysteretic behaviors. In this work, we propose a control-oriented modeling framework for both rate-dependent and rate-dependent hysteresis occurring in uniaxially loaded DE actuators. To this end, classic thermodinamically-consistent modeling approaches for DEs are combined with a new energy-based Maxwell-Lion formalization of the hysteretic losses. The resulting dynamic model comprises a set of nonlinear ordinary differential equations, and is capable of simultaneously describe geometric dependencies, large deformation nonlinearities, electro-mechanical coupling, and rate-independent and rate-dependent hysteretic effects. To deal with the large number of involved parameters, a novel systematic identification algorithm based on quadratic programming is also proposed. After presenting the theory, the model is validated based on experiments conducted on a silicone-based rolled DE actuator. Its superiority compared to classic DE viscoelastic models is quantitatively assessed.

Reinforcement Learning-Based Adaptive Optimal Control for Nonlinear Systems With Asymmetric Hysteresis.

This article investigates the adaptive optimal tracking problem for a class of nonlinear affine systems with asymmetric Prandtl-Ishlinskii (PI) hysteresis nonlinearities based on actor-critic (A-C) learning mechanisms. Considering the huge obstacles arising from the uncertainty of hysteresis nonlinearity in actuators, we develop a scheme for the conflict between the construction of Hamilton functions and hysteresis nonlinearity. The actuator hysteresis forces the input into a hysteresis delay, thus preventing the Hamilton function from getting the current moment's input instantly and thus making optimization impossible. In the first step, an inverse model is constructed to compensate for the hysteresis model with a shift factor. In the second step, we compensate for the control input by designing a feedback controller and incorporating the estimation and approximation errors into the Hamilton error. Optimal control, the other part of the actual control input, is obtained by taking partial derivatives of the Hamiltonian function after the nonlinearities have been circumvented. At the end, a simulation is given to validate the developed solution.

Command filter‐based adaptive fixed‐time fault‐tolerant control for stochastic nonlinear systems with actuator hysteresis

AbstractIn this paper, an adaptive fault‐tolerant fixed‐time control problem is considered via command‐filter technique for stochastic nonlinear systems with sensor fault and actuator hysteresis. With the application of command‐filtering technique, a novel command‐filter compensate mechanism is designed, which implies that the improved control scheme not only eliminates “the explosion of complexity” but also realizes the compensate signal is bounded within fixed‐time interval. The unavailability of state variables caused by sensor fault is solved by applying parameter separation and regrouping approach. Meanwhile, an adaptive auxiliary signal is designed to cope with the backlash‐like hysteresis phenomenon, which can avoid singularity, reduce chattering, and facilitate controller design. Combining backstepping technique and Lyapunov stability theorem, an adaptive fault‐tolerant control approach is developed, which can guarantee all closed‐loop signals remain semi‐globally practical fixed‐time stable (SGPFS) in probability. The validity of the proposed strategy is illustrated by simulation examples.

Review on the Nonlinear Modeling of Hysteresis in Piezoelectric Ceramic Actuators

Piezoelectric ceramic actuators have the advantages of fast response speed and high positioning accuracy and are widely used in micro-machinery, aerospace, precision machining machinery, and other precision positioning fields. However, hysteretic nonlinearity has a great influence on the positioning accuracy of piezoelectric ceramic actuators, so it is necessary to establish a hysteretic model to solve this problem. In this paper, the principles of the Preisach model, the Prandtl Ishilinskii (PI) model, the Maxwell model, the Duhem model, the Bouc–Wen model, and the Hammerstein model and their application and development in piezoelectric hysteresis modeling are described in detail. At the same time, the classical model, the asymmetric model and the rate-dependent model of these models are described in detail, and the application of the inverse model corresponding to these models in the feedforward compensation is explained in detail. At the end of the paper, the methods of inverse model acquisition and control frequency of these models are compared. In addition, the future research trend of the hysteresis model is also prospected. The ideas and suggestions highlighted in this paper will guide the development of piezoelectric hysteresis models.

New phase diagram for low hysteresis response of a coiled shape memory alloy actuator

We demonstrate a new phase diagram describing the responses of shape memory alloy (SMA) spring actuators. The SMA spring actuator has a wide range of temperatures for phase transitions and responses with low hysteresis. To describe these specific responses of the SMA spring actuator, a new phase diagram with an overlapping layer is proposed. In the overlapping layer, even if it changes from a heating phase to a cooling phase or vice versa, a phase transition occurs whenever the temperature of the SMA changes. Because there is no region in which only the temperature changes without a force changes, the hysteresis is reduced. The overlapping layer is formed by changing the properties of the SMA when fabricating the spring actuator. One of the properties that change in the SMA is the amount of latent heat when the phase transition occurs. The latent heat of the SMA spring is significantly low compared to that of the SMA wire due to the plasticity produced by the stress applied to form the spring shape. Therefore, there will be a tradeoff between the amount of the phase transition and the hysteresis of the SMA actuator.

Adaptive Saturated Path Following Control of Underactuated AUV With Unmodeled Dynamics and Unknown Actuator Hysteresis

This article addresses the three-dimensional (3-D) path-following problem of underactuated autonomous underwater vehicles (AUVs) in the presence of multiple uncertainties and nonlinearities, including unmodeled dynamics, actuator hysteresis, input saturation, and oceanic disturbance. First, the AUV kinetic model is reconstructed as a second-order nonlinear system by coupling the smooth saturation function and hysteresis dynamics of actuators. Second, the 3-D tracking error is derived in a simplified manner based on the relative motion theory. Then the approach angle-based symmetrical hyperbolic-tangent line-of-sight (SHLOS) guidance and kinematic control scheme are designed to ensure the global asymptotic stability of the kinematic system. Third, two sets of kinetic control schemes are designed without prior knowledge of AUV dynamics and disturbance, where the Nussbaum gain technique is applied to deal with the unknown hysteresis parameter. The application of the reconstructed kinetic model avoids the degraded performance caused by actuator nonlinearities. The first scheme is improved by adaptively estimating the bound of the generalized disturbance-like term which lumps the unmodeled dynamics, external disturbance, and saturation approximation error. The improved scheme guarantees the global stability of the system and transient tracking performance. Finally, comparative simulation studies under dynamic oceanic environments prove the effectiveness and robustness of the proposed control schemes.

Model-based and model-free collision detection and identification for a parallel Delta robot with uncertainties

This paper presents two methods for human collision detection and identification for a parallel Delta robot considering uncertainties. In the model-based, a generalized momentum observer based on the explicit model of the Delta robot is used to estimate a proposed uncertainty model without collision. A linear regression algorithm is approached to recognize actuator hysteresis friction models and modeling error parameters, constructing the uncertainty model. The boundary and convergence of the identification parameters are guaranteed based on a least square method. Then, the estimated uncertainty is compared with the generalized momentum observer to detect and identify collision impacts as external torques. In the model-free, the neural network model for actuated torque prediction controlling the Delta robot is developed based on a model-driven and data-driven approach. The training procedure of the proposed network only uses no collision datasets. The model-free method uses a neural network to provide detection signals and external torques identified by comparing its conservative predictions to the measured torques when a collision occurs. In this work, only low-cost current sensors and low-resolution encoders are attached to the Delta robot system for generating the datasets. Finally, the identification capacity of the proposed methods is also compared with a force sensor to verify the effectiveness in real-time implementation.

Neural Network Adaptive Control of Magnetic Shape Memory Alloy Actuator With Time Delay Based on Composite NARMAX Model

Magnetic shape memory alloy (MSMA) based actuator plays an important role in the field of micro and nano-fabrication due to its large stroke. However, the inherent hysteresis of MSMA seriously affects the application prospects of MSMA-based actuator in the field of precision positioning. In this study, a composite model is proposed for hysteresis in the MSMA-based actuator by coupling an improved fractional-order Bouc-Wen model to a nonlinear auto-regressive moving average with exogenous inputs (NARMAX) model. Based on the proposed model, a neural network adaptive control method is then used to control the MSMA-based actuator, and the controller design takes into account the effect of time delay on the system performance to improve the positioning accuracy of the MSMA-based actuator. First, we fuse the composite NARMAX model with the canonical form of the nonlinear system to describe the MSMA-based actuator. Then, a control strategy is developed to address the impact of the unknown time delay for controller design and achieve the satisfactory positioning accuracy of the MSMA-based actuator. By using Lyapunov theory, the tracking error is proven to be asymptotic convergence. Experimental studies are provided to validate the effectiveness of the proposed modeling and control schemes.

Self‐Powered Piezoelectric Actuation Systems Based on Triboelectric Nanogenerator

AbstractSustainable power supply via triboelectric nanogenerator (TENG) is attractive for self‐powered actuation systems in the era of the Internet of Things (IoTs). Herein, a low‐power actuation scheme enabled by the multilayered TENG for piezoelectric actuators, including the stack, unimorph, and micro‐fiber composite (MFC) actuator, is reported. The working principles of TENG‐powered piezoelectric actuators and their displacement characteristics in direct current (DC) and alternating current (AC) modes are theoretically investigated. Compared with conventional high‐voltage power sources, the multilayered TENG delivers a maximum power of only 10.17 mW, providing a low‐power alternative for piezoelectric actuator with self‐powered capability and operational safety. Meanwhile, the hysteresis of the stack actuator that is critical in precise positioning control is reduced by 58.1%. A precise positioning system is demonstrated by utilizing the TENG‐powered stack actuator as an object stage for microscope focusing applications. The feasibility of vibration control with a 76.7% reduction in vibration amplitude is also verified via two TENG‐powered MFC actuators. A rectifying control circuit comprising the rectifier and gas discharging tube is established to implement AC–DC conversion and discharging control, achieving a larger displacement of the unimorph actuator. The TENG‐powered piezoelectric micropump demonstrates its potential application in liquid transport through straightforward operation.

Echo State Network-Based Adaptive Event-Triggered Control for Stochastic Nonaffine Systems with Actuator Hysteresis

This paper studies the problem of the event-triggered control of nonaffine stochastic nonlinear systems with actuator hysteresis. The echo state network (ESN) is introduced to approximate an unknown nonlinear function. The command filtering technology is used to avoid the derivation of the virtual controller in the controller design process and tries to solve the problem of complexity explosion in the traditional method. Based on Lyapunov’s finite-time stability theory, the proposed method verifies the stability of non-affine stochastic nonlinear systems. It is proved that the proposed controller method can guarantee that all of the signals in the closed-loop system are bounded, and the tracking error can converge to a minimal neighborhood of zero even if there exists an actuator hysteresis. The effectiveness of the proposed method is demonstrated by the simulation example. The simulation results show that the proposed method is effective.