Control Of Piezoelectric Actuators Research Articles

Non-singular fast terminal sliding mode trajectory tracking control of cantilever piezo-electric stack actuator based on asymmetric hysteresis compensation

Abstract Piezoelectric actuators are widely employed in micro-precision applications due to their fast response and high resolution. This paper investigates the trajectory tracking control of a cantilever piezoelectric stack actuator (CPSA) under external perturbations and hysteresis. A control scheme is proposed that effectively compensates for hysteresis by employing an asymmetric Bouc-Wen (ABW) model, integrated with a non-singular fast terminal sliding mode control (NFTSMC) featuring a variable convergence law. This methodology guarantees finite-time convergence and robustness, thereby enhancing the overall control performance of the CPSA. Experimental results reveal that the proposed control algorithm significantly improves control accuracy and speed, achieving stable closed-loop system performance and maintaining bounded closed-loop signals within a finite time frame. The effectiveness and superiority of the NFTSMC method are validated through comprehensive experimental studies.

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.

High-Bandwidth Repetitive Trajectory Tracking Control of Piezoelectric Actuators via Phase-Hysteresis Hybrid Compensation and Feedforward-Feedback Combined Control.

Piezoelectric actuators (PEAs) are widely used in many nano-resolution manipulations. A PEA's hysteresis becomes the main factor limiting its motion accuracy. The distinctive feature of a PEA's hysteresis is the interdependence between the width of the hysteresis loop and the frequency or rate of the control voltage. Generally, the control voltage is first amplified using a voltage amplifier (VA) and then exerted on the PEA. In this VA-PEA module, the linear dynamics of the VA and the nonlinearities of the PEA are coupled. In this paper, it is found that the phase lag of the VA also contributes to the rate dependence of the VA-PEA module. If only the PEA's hysteresis is considered, it will be difficult to achieve high-frequency modeling and control. Consequently, great difficulties arise in high-frequency hysteresis compensation and trajectory tracking, e.g., in the fast scanning of atomic force microscopes. In this paper, the VA-PEA module is modeled to be the series connection of a linear subsystem and a nonlinear subsystem. Subsequently, a feedforward phase-dynamics compensator is proposed to compensate for both the PEA's hysteresis and the phase lag of the VA. Further, an unscented Kalman-filter-based proportional-integral-derivative controller is adopted as the feedback controller. Under this feedforward-feedback combined control scheme, high-bandwidth hysteresis compensation and trajectory tracking are achieved. The trajectory tracking results show that the closed-loop trajectory tracking bandwidth has been increased to the range of 0-1500 Hz, exhibiting excellent performance for fast scanning applications.

Model-Free Adaptive Positioning Control of the Bidirectional Stick-Slip Piezoelectric Actuator with Coupled Asymmetric Flexure-Hinge Mechanisms.

A model-free adaptive positioning control strategy for piezoelectric stick-slip actuators (PSSAs) with uncertain disturbance is proposed. The designed controller consists of a data-driven self-learning feedforward controller and a model-free adaptive feedback controller with a radial basis function neural network (RBFNN)-based observer. Unlike the traditional model-based control methods, the model-free adaptive control (MFAC) strategy avoids the complicated modeling process. First, the nonlinear system of the PSSA is dynamically linearized into a data model. Then, the model-free adaptive feedback controller based on a data model is designed to avoid the complicated modeling process and enhance the robustness of the control system. Simultaneously, the data-driven self-learning feedforward controller is improved to realize the high-precision control performance. Additionally, the convergence of the tracking error and the boundedness of the control output signal are proved. Finally, the experimentally obtained results illustrate the advantages and effectiveness of the developed control methodology on the bidirectional stick-slip piezoelectric actuator with coupled asymmetric flexure-hinge mechanisms. The positioning error through the proposed controller reaches 30 nm under the low-frequency condition and 200 nm under the high-frequency condition when the target position is set to 100 μm. In addition, the target position can be accurately tracked in less than 0.5 s in the presence of a 100 Hz frequency.

Multi-agent reinforcement learning vibration control and trajectory planning of a double flexible beam coupling system

A multi-agent reinforcement learning vibration controller is designed for active vibration suppression of a movable double piezoelectric flexible beam coupling system, and the motion trajectory is optimized to minimize vibration excitation during motion and residual vibration after motion. The finite element method is used to model the system dynamics, then, the actual model parameters are identified by combining wavelet and intelligent optimization algorithm. The corrected piezoelectric driving model is used to train the counterfactual multi-agent reinforcement learning (COMARL) algorithm, and an excellent nonlinear controller for vibration control of piezoelectric actuators is obtained. The motion trajectory of the double flexible beam coupling system is designed by using the corrected motor-driven model. The optimal vibration suppression trajectory is obtained by using tabu search algorithm. The simulation and experimental results show that the optimized trajectory greatly reduces the vibration excitation. The controller trained by the COMARL algorithm fully considers the influence of either beam in the system, and infers the contribution of piezoelectric actuators to the completion of the overall task through counterfactual thinking. The control effect is better than that of PD control, especially the small-amplitude vibration suppression. The effectiveness of the COMARL controller is further verified by simultaneous piezoelectric control during trajectory motion. Vibrations during translational motion and at the end of motion are suppressed quickly.

Charge Estimation of Piezoelectric Actuators: A Comparative Study

This article first reviews the position control of piezoelectric actuators, particularly charge-based sensorless control systems, which often include a charge estimator as a key component. The rest of the paper is about charge estimators for piezoelectric actuators. Two of the most recent/effective types of these estimators utilise either a sensing capacitor (type I in this paper) or a sensing resistor (type II); the latter (and the newer) type is broadly known as a digital charge estimator. Some experimental results in the literature show that, with the same loss in excitation voltage, a considerably higher amount of charge can be estimated with a type II estimator in comparison with a type I estimator; therefore, the superiority of type II estimators was acknowledged. In order to re-assess this conclusion, this paper equitably compares type I and II estimators through analytical modelling and experimentation. The results indicate that type II estimators have only a slight advantage in estimating higher amounts of charge, if both type I and II estimators are designed appropriately. At the same time, type II estimators have disadvantages; e.g., the resistance of type II estimators has to be tuned to suit different excitation frequencies. This research concludes that capacitor-based (type I) charge estimators for piezoelectric actuators, with pertinent design and implementation, can be still the prime solution for many charge estimation problems despite claims in the literature in the last decade.

Third‐order integral sliding mode control of piezoelectric actuators based on rate‐amplitude‐dependent Prandtl‐Ishlinskii model

AbstractAiming at trajectory tracking control of piezoelectric actuators (PEAs), this article proposes a third‐order integral sliding mode control (3‐ISMC) based on rate‐amplitude‐dependent Prandtl‐Ishlinskii (PI) inverse model feedforward (3‐RAPI) scheme, which can achieve finite time convergence and avoid singular problems, while ensuring the continuity of the control signal. In this control scheme, a rate‐amplitude‐dependent PI (RAPI) model is proposed to describe the hysteresis characteristics of PEA, and the RAPI hysteresis inverse model is used to realize the feedforward control. The simulation results verify the improvement of the modeling accuracy of the RAPI model compared with the traditional PI model. In order to reduce the influence of modeling error and improve the robustness of the system, a 3‐ISMC scheme based on integral non‐singular fast terminal sliding mode surface is proposed. Simulation and experimental results demonstrate that the tracking performance of 3‐ISMC is improved compared with the existing third‐order integral terminal sliding model control (3‐ITSMC). Finally, the composite control algorithm is realized by combining the RAPI hysteresis inverse model feedforward with the 3‐ISMC algorithm. The experimental results further show that the control algorithm can track the input signal in a wide range of rate and amplitude.

Sampled-Data Model-Free Adaptive Sliding Mode Control for Piezoelectric Actuators Subject to Time Delay

This paper proposes a model-free sampled-data sliding mode control of piezoelectric actuators considering time delay. As time delay is a challenging subject in controller design, we try to eradicate its effect on the tracking performance of the control system as much as possible. For this goal, an equivalent sampled-data data-based model from the continuous-time nonlinear system of a piezoelectric actuator is first derived. Then, we include the delay of the control system into the sliding surface to enrich the controller performance. Next, the sliding mode controller is designed using the equivalent model and the delayed sliding surface. No observer is used to compensate for the total disturbances. Thus, the scheme is easy to design and implement. The stability of the closed-loop system is theoretically studied, and the controller performance is confirmed through comparative experimental tests. Based on the experimental results, the proposed controller successfully obtains control objectives.

Application of Least-Squares Support-Vector Machine Based on Hysteresis Operators and Particle Swarm Optimization for Modeling and Control of Hysteresis in Piezoelectric Actuators

Nanopositioning systems driven by piezoelectric actuators are widely used in different fields. However, the hysteresis phenomenon is a major factor in reducing the positioning accuracy of piezoelectric actuators. This effect makes the task of accurate modeling and position control of piezoelectric actuators challenging. In this paper, the learning and generalization capabilities of the model are efficiently enhanced to describe and compensate for the rate-independent and rate-dependent hysteresis using a kernel-based learning method. The proposed model is inspired by the classical Preisach hysteresis model, in which a set of hysteresis operators is used to address the problem of mapping, and then least-squares support-vector machines (LSSVM) combined with a particle swarm optimization (PSO) algorithm are used for identification. Two control schemes are proposed for hysteresis compensation, and their performance is evaluated through real-time experiments on a nanopositioning platform. First, an inverse model-based feedforward controller is designed based on the LSSVM model, and then a combined feedback/feedforward control scheme is designed using a classical control strategy (PID) to further enhance the tracking performance. For performance evaluation, different datasets with a variety of hysteresis loops are used during the simulation and experimental procedures. The results show that the proposed method is successful in enhancing the generalization capabilities of LSSVM training and achieving the best tracking performance based on the combination of feedforward control and PID feedback control. The proposed control scheme outperformed the inverse Preisach model-based control scheme in terms of both positioning accuracy and execution time. The control scheme that uses the LSSVM based on nonlinear autoregressive exogenous (NARX) models has significantly less computational complexity compared to our control scheme but at the expense of accuracy.

Robust Control of a Bimorph Piezoelectric Robotic Manipulator Considering Ellipsoidal-Type State Restrictions

The current study presents an adaptive control approach to solve the tracking trajectory problem for a robotic manipulator that uses a gripper based on bimorph piezoelectric actuators. The development of an adaptive gain state feedback form that considers the state restrictions is proposed using a novel class of barrier Lyapunov function that drives the effective control of joints and piezoelectric actuators. The proposed method allows for the inclusion of complex combinations of state restrictions in the Lyapunov function, yielding the construction of differential forms for the gains in the controller that can handle the evolution of trajectories of the robotic arm inside the restricted region. The proposed control design successfully tracks reference trajectories for both joints of the robotic arm as well as the motion of the piezoelectric device during several operative scenarios. A comprehensive experimental study evaluates the effect of introducing state-dependent gain considering state restrictions of the ellipsoidal type. The comparison of the mean square error confirms the contributions of the developed control action, showing better tracking quality for less control power with the same evaluation, which is a desirable characteristic in the controlled motion of micromanipulators. The proposed controller solves the tracking trajectory problem for the micromanipulation system, satisfies the motion restrictions, and allows better tracking performance to be enforced. Furthermore, comparison of the obtained trajectories seems to validate the proposed controller’s contribution concerning a feedback form with fixed gains.

Feedforward Control of Piezoelectric Ceramic Actuators Based on PEA-RNN.

Multilayer perceptron (MLP) has been demonstrated to implement feedforward control of the piezoelectric actuator (PEA). To further improve the control accuracy of the neural network, reduce the training time, and explore the possibility of online model updating, a novel recurrent neural network named PEA-RNN is established in this paper. PEA-RNN is a three-input, one-output neural network, including one gated recurrent unit (GRU) layer, seven linear layers, and one residual connection in the linear layers. The experimental results show that the displacement linearity error of piezoelectric ceramics reaches 8.96 m in the open-loop condition. After using PEA-RNN compensation, the maximum displacement error of piezoelectric ceramics is reduced to 0.465 m at the operating frequency of 10 Hz, which proves that PEA-RNN can accurately compensate piezoelectric ceramics’ dynamic hysteresis nonlinearity. At the same time, the training epochs of PEA-RNN are only 5% of the MLP, and fewer training epochs provide the possibility to realize online updates of the model in the future.

Memory related predictive compensation control of Piezoelectric actuators based on global linearization Koopman theory

Piezoelectric actuators (PEAs) are widely applied in precision positioning. However, the nonlinear characteristics such as hysteresis and creep limit the ultra-precision applications. This paper proposes a linear model predictive control (MPC) scheme for compensating the nonlinearity of PEA. Firstly, a global linearization predictor is constructed based on Koopman theory to represent the hysteresis behavior of PEA. The high-precision predictor is implemented by a novel memory related neural network (NN), and the prediction error reaches only 0.002 μm. Then the tracking control problem is transformed into a linear MPC optimization problem, thereby avoids the sophisticated nonconvex optimization problem. In practice, the constrained MPC problem is rewritten into a dense form, and solved by quadratic programming technique. Finally, the validity of the proposed scheme is demonstrated by experiments. The short-term steady-state error of the proposed scheme is 0.002 μm, which is far less than that of the inversion method; the long-term steady-state performance also indicates its effectiveness in compensating creep. Further, the excellent frequency-dependent results show that the proposed scheme is superior to the existing control method. Especially, the computational efficiency can be improved by 20%. The proposed predictor and control method are of great significance for the tracking control of PEA.

Characterization and RST control of a nonlinear piezoelectric actuator for a robotic hand

This paper presents the characterization, modeling, and control of piezoelectric actuators of a robotic system by considering the temperature effect. Besides the sensitivity to temperature variation, quite often the behavior of piezoelectric actuators is negatively affected by badly-damped vibrations and nonlinear phenomena such as strong hysteresis and creep. An analysis of the sensitivity of piezoelectric actuators to temperature variations (thermo-mechanical displacement) is first presented and the characterization results are discussed. The effect of the temperature mainly on the hysteresis loops, the creep, and vibrations is presented. Then, a temperature-dependent model of piezoelectric actuators is derived based on the study and characterization results obtained. Finally, the model of piezoelectric actuators obtained is used to design a robust RST (Regulation-Sensitivity-Tracking) controller to improve their behavior and achieve a good quality of positioning tasks. Experimental validation is given to demonstrate the efficacy of the presented modeling and control methods.

Adaptive compound control based on generalized Bouc-Wen inverse hysteresis modeling in piezoelectric actuators.

This paper focuses on the study of the dynamic hysteresis compensation and control of piezoelectric actuators so as to improve the swing accuracy of the piezoelectric fast steering mirror mechanism in the photoelectric compound-axis control system. Moreover, in view of the rate dependence and asymmetry of piezoelectric hysteresis, and the complex inversion process of the generalized Bouc-Wen hysteresis model, the Hammerstein dynamic inverse hysteresis model of the piezoelectric actuator is established. To be specific, the static nonlinearity and rate dependence of the piezoelectric inverse hysteresis are represented by the generalized Bouc-Wen inverse model and the auto-regressive exogenous model, respectively, and the parameters of the model are identified by the adaptive beetle swarm optimization algorithm. In the process of the open-loop feedforward compensation, the dynamic positioning accuracy of the piezoelectric actuator is greatly affected by various disturbances and the uncertainty of the hysteresis compensation model. In this context, a compound control strategy that combines the feedforward compensation with the single-neuron adaptive proportion-integration-differentiation control is proposed based on the Hammerstein dynamic inverse hysteresis model of the piezoelectric actuator. The experimental results verify the effectiveness and superiority of the proposed control strategy.

A neural network-based model predictive controller for displacement tracking of piezoelectric actuator with feedback delays

Piezoelectric actuators are widely used in micro/nanoscale robotic manipulators. Due to its hysteresis and dynamic-related nonlinearity, accurate displacement tracking control of piezoelectric actuator is challenging. Besides, in some low-cost practical systems with low sampling rate, transmission delay causes mismatches between feedback and real displacement, further increasing the challenge in tracking control. In this article, a neural network-based model predictive controller (MPC) is proposed for precise tracking control of piezoelectric actuator’s displacement in situation where feedback is slow and delayed. The prediction model is based on a nonlinear-autoregressive-moving-average-with-exogenous-inputs framework, which outputs entire prediction horizon of future displacement in a single time, and is fulfilled by a multilayer feedforward neural network. An extended Kalman filter-based estimation for displacement is introduced to relieve the influence of feedback delays so as to improve dynamic performance of the controller. Another neural network is trained to provide initial values for MPC to reduce computation costs and improve performance in dynamic tracking. In a series of tracking experiments, the effectiveness of proposed controller is verified.

Long Short-term Memory Neural Network-based System Identification and Augmented Predictive Control of Piezoelectric Actuators for Precise Trajectory Tracking

Long Short-term Memory Neural Network-based System Identification and Augmented Predictive Control of Piezoelectric Actuators for Precise Trajectory Tracking

Simplification of the Model of Piezoelectric Actuator Control Based on Preliminary Measurements

This article describes a mathematical model simplification, designed to automate the iterative process of non-circular drilling with a precise shape. This model has been optimized for systems that already have experimental data for processing and analysis. Additionally, using optimization steps, the model can be used for systems with insufficient experimental data with a self-learning opportunity. The high-end model can be used for drilling systems represented as a “black box” without knowing of any parameters of the system. The simplification and assumptions algorithm is based on controlling the input signal for non-circular drilling in the cylinders of internal combustion engines using a drilling machine controlled by 8 piezoelectric actuators. The total dynamics of this system is unknown and consists of the dynamics of electrical converters, piezo-kinematics, and mechanics. Simplification is carried out starting from the methods of diacoptics for a complex system with different process-flow rates, and ending with one or the sum of linear models valid for a given system of assumptions.

Extended state observer–based fractional order sliding-mode control of piezoelectric actuators

Tracking control of piezoelectric actuators is considered in the article. A Hammerstein model is used to depict the rate-dependent hysteresis characteristics of piezoelectric actuators, in which a Bouc–Wen model is to describe the static hysteresis characteristic, and a linear time-invariant system is to describe its rate-dependent characteristics. An inverse Bouc–Wen model connected in series with the piezoelectric actuator is used to compensate the static hysteresis nonlinearity of piezoelectric actuators. Furthermore, an extended state observer–based fractional order sliding-mode control is designed to deal with higher order unmodelled dynamics and inverse compensation errors. Moreover, the bounds of the estimation error of the extended state observer are estimated, and the convergence of the proposed control strategy is proved. Experimental results show that the proposed scheme can track both single and composite input signals within a certain frequency range. Compared with extended state observer–based conventional sliding-mode controller, the proposed scheme has faster response time and smaller tracking error.

Nonlinear multi-scale dynamics modeling of piezoceramic energy harvesters with ferroelectric and ferroelastic hysteresis

Hysteretic nonlinearities significantly affect the behavior of devices based on piezoelectric materials. The topic has been widely addressed in the actuation framework, as modeling nonlinear effects is crucial for the dynamic control of piezoelectric actuators. Far less studies, however, discuss the role of hysteresis in the dynamic response of piezoelectric energy harvesters, usually adopting phenomenological modeling approaches. In this work, a physics-based model is employed to reproduce—through a probabilistic thermodynamic approach—the process behind hysteresis in piezoceramic transducers, i.e., the switching of dipoles in crystal domains. A multi-scale approach is then adopted in order to comprise hysteretic effects in the dynamic response of a piezoelectric energy harvester, modeled as a SDOF system. Effects of hysteretic nonlinearities on the device behavior are investigated by means of simulations, and a detailed discussion on the role of material parameters is reported. Moreover, a comparison between predictions of two models—with and without hysteresis—is presented.

Simple and efficient inverse hysteretic model and associated experimental procedure for precise piezoelectric actuator control and positioning

This paper exposes inversion techniques of a simple yet efficient system-level approach for modeling quasi-static hysteretic behavior of piezoelectric actuators, allowing the transducer voltage to be properly shaped to get the desired target strain response. The inversion principles lie in considering a coefficient relating the voltage derivative to the target strain derivative through a simple formulation using a function of the input strain, combined with equivalent strain cancellation and inversion when the desired target strain derivative crosses zero value. Conceptual and theoretical developments are validated through experimental measurements that show good control capabilities of the quasi-static strain. Hence, the proposed concept provides a lightweight yet efficient approach for embedded control systems.