Hysteresis Characteristic Of Piezoelectric Actuator Research Articles

Parameter Identification of Model for Piezoelectric Actuators.

Piezoelectric actuators are widely used in high-precision positioning systems. The nonlinear characteristics of piezoelectric actuators, such as multi-valued mapping and frequency-dependent hysteresis, severely limit the advancement of the positioning system's accuracy. Therefore, a particle swarm genetic hybrid parameter identification method is proposed by combining the directivity of the particle swarm optimization algorithm and the genetic random characteristics of the genetic algorithm. Thus, the global search and optimization abilities of the parameter identification approach are improved, and the problems, including the genetic algorithm's poor local search capability and the particle swarm optimization algorithm's ease of falling into local optimal solutions, are resolved. The nonlinear hysteretic model of piezoelectric actuators is established based on the hybrid parameter identification algorithm proposed in this paper. The output of the model of the piezoelectric actuator is in accordance with the real output obtained from the experiments, and the root mean square error is only 0.029423 μm. The experimental and simulation results show that the model of piezoelectric actuators established by the proposed identification method can describe the multi-valued mapping and frequency-dependent nonlinear hysteresis characteristics of piezoelectric actuators.

Modeling and control of rate-dependent hysteresis characteristics of piezoelectric actuators based on analog filters

The hysteresis nonlinearity and rate dependence of piezoelectric actuators seriously affect their positioning accuracy in precise positioning. Proper compensation needs to be given to improve the positioning accuracy of the actuator. In this paper, the static hysteresis characteristics are described by improving the BP neural network model based on the adaptive particle swarm optimization algorithm, and the PI model is used as the hysteresis factor by the extended space method to realize the multi-valued mapping of hysteresis nonlinearity. And input three types of voltage signals, compare and analyze the experimental data and model prediction output, and use the maximum relative error and root mean square error as the evaluation indicators to prove the accuracy of the built model. Based on the improved BP neural network model, a second-order low-pass analog filter is introduced to construct a rate-dependent hysteresis model. Comparing and analyzing the rate-dependent hysteresis model and the static hysteresis model, the experimental results show that when the signal frequency is 10 Hz, 40 Hz, and 100 Hz, the predicted output of the rate-dependent hysteresis model is compared with that of the static hysteresis model, and the root mean square error decreases by 46.3%. %, 59.6%, and 65.1%, the model can more accurately describe the hysteresis characteristics of piezoelectric actuators. Finally, a rate-dependent hysteresis inverse model is established, and the rate-dependent hysteresis inverse model is used as a feedforward combined with a single neuron network PID control to form a composite controller, and the experimental verification is carried out. The results show that the maximum error between the composite controller and the actual expectation is only 2.15%. Therefore, the established model can accurately express the rate-dependent hysteresis characteristics of piezoelectric actuators, and the use of a composite controller can effectively reduce the accuracy error caused by the hysteresis nonlinear characteristics of piezoelectric actuators.

Fractional-order control for nano-positioning of piezoelectric actuators

Piezoelectric actuators are widely used in the field of high-precision positioning control. However, due to the inherent hysteresis nonlinearity of piezoelectric actuators, it can seriously affect their accuracy in tracking and positioning systems, and even cause system instability. In order to suppress the hysteresis characteristics of piezoelectric, based on the analysis of piezoelectric characteristics and the characteristics of classical Bouc–Wen model, a Bouc–Wen model is adopted to describe the hysteresis characteristics of piezoelectric actuators, an artificial bee colony (ABC) algorithm is used to identify Bouc–Wen. The maximum error of the model is 2.49%. According to the established hysteresis model, its inverse model is obtained as the feedforward controller, and the inverse model compensation method is used to realize the open-loop control of the system. Since the feedforward controller based on the inverse model cannot eliminate the modeling errors and external disturbances of the inverse model, a fractional-order controller is designed on the basis of inverse compensation, and a compound control method combining feedforward control and feedback control is adopted. Experiments show that the fractional-order control system has fast response speed, small steady-state error and simple structure compared with other nonlinear controllers, positioning error is about 3%.

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.

Angle hybrid control for a two-axis piezo-positioning system and its application

The hysteresis characteristics of piezoelectric actuators and the residual vibration in the rapid positioning process will greatly affect the positioning accuracy and speed of a piezo-driven positioning system (PPS). In order to improve the positioning accuracy and to restrain the residual vibration of a two-axis PPS, a hybrid controller is proposed and explored based on a comprehensive model by combining the proposed feedforward linearization, the zero vibration and derivative shaping, and the linear-quadratic Gaussian feedback control for the PPS. The experimental results show that the proposed hybrid control significantly improves the positioning accuracy and suppresses the residual vibration of the PPS. Its application shows that the PPS proposed herein can effectively enhance the astronomical telescope’s star tracking and pointing performance.

Identification of micropositioning stage with piezoelectric actuators

In this paper, a two-step identification method for a micropositioning stage with piezoelectric actuator is proposed. It is noted that one of the difficulties encountered in identification is that both input and output of the actuator embedded in the stage cannot be measured directly. Moreover, hysteresis existing in piezoelectric actuators is a non-smooth complex nonlinearity. In the proposed modeling method, a sandwich model with hysteresis is used to describe the performance of the micropositioning stage with piezoelectric actuator. In this modeling architecture, the input linear submodel is utilized to describe the behavior of preceded amplifier with filtering circuit, which provides electrical voltage to the piezoactuator, and the output linear submodel is employed to depict the flexural hinge with load, respectively, while a Duhem function embedded in between the input and output linear submodels is employed to describe the hysteresis characteristic of piezoelectric actuator in the stage. At the first step of the identification procedure, a special excitation input is implemented to excite the stage to decompose the hysteresis into a monotonic polynomial within a certain region. Then, the parameters of linear submodels are separated and estimated. Subsequently, at the second step, an input signal that can fully excite the system within the operation region is implemented to excite the stage. Based on the previously estimated linear submodels, both input and output of the piezoactuator are estimated. Then, in terms of the estimated input and output of the piezoactuator, the parameters of the hysteresis submodel are estimated. Finally, experimental results are presented to verify the proposed method.

Hysteresis Neural Network Modeling and Compensation of Piezoelectric Actuator

By studying on the nonlinear hysteresis characteristics of piezoelectric actuators,this paper proposes a neural network modeling method based on polynomial fitting algorithm and a compound control method for compensation of the hysteresis.Simulation shows that the fitting error of neural network model is 1.42%. According to the developed hysteretic model,PID and feed-forward control methods are applied to the system.The result is that the tracking relative error of control system is 1.59%,so the tracking precision of system is improved significantly.This indicates that the neural network model reflects the hysteresis characteristics of piezoelectric actuators accurately,and this control method is an effective compensation control for hysteresis in piezoelectric actuators.

Fuzzy PID Feedback Control of Piezoelectric Actuator with Feedforward Compensation

Piezoelectric actuator is widely used in the field of micro/nanopositioning. However, piezoelectric hysteresis introduces nonlinearity to the system, which is the major obstacle to achieve a precise positioning. In this paper, the Preisach model is employed to describe the hysteresis characteristic of piezoelectric actuator and an inverse Preisach model is developed to construct a feedforward controller. Considering that the analytical expression of inverse Preisach model is difficult to derive and not suitable for practical application, a digital inverse model is established based on the input and output data of a piezoelectric actuator. Moreover, to mitigate the compensation error of the feedforward control, a feedback control scheme is implemented using different types of control algorithms in terms of PID control, fuzzy control, and fuzzy PID control. Extensive simulation studies are carried out using the three kinds of control systems. Comparative investigation reveals that the fuzzy PID control system with feedforward compensation is capable of providing quicker response and better control accuracy than the other two ones. It provides a promising way of precision control for piezoelectric actuator.