Tracking Control Of Piezoelectric Actuators Research Articles

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.

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.

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.

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.

Modeling and tracking control for piezoelectric actuator based on a new asymmetric hysteresis model

This paper presents a new asymmetric hysteresis model and its application in the tracking control of piezoelectric actuators. The proposed model is based on a coupled-play operator which can avoid the conventional Prandtl-Ishlinskii U+0028 CPI U+0029 model U+02BC s defects, i.e., the symmetric property. The high accuracy for modeling asymmetric hysteresis is validated by comparing simulation results with experimental measurements. In order to further evaluate the performance of the proposed model in closed-loop tracking application, two different hybrid control methods which experimentally demonstrate their performance under the same operating conditions, are compared to validate that the hybrid control strategy with proposed hysteresis model can mitigate the hysteresis more effectively and achieve better tracking precision. The experimental results demonstrate that the proposed modeling and tracking control strategy can realize efficient control of piezoelectric actuator.

Tracking Control of Piezoelectric Actuators using PID based Sliding Mode

Tracking Control of Piezoelectric Actuators using PID based Sliding Mode

Dynamic Hysteresis Based Modeling Of Piezoelectric Actuators

Piezoelectric actuators are popularly applied as actuators in high precision systems due to their small displacement resolution, fast response and simple construction. However, the hysteresis nonlinear behavior limits the dynamic modeling and tracking control of piezoelectric actuators. This paper studies a dynamic model of a moving stage driven by piezoelectric stack actuator. The Bouc-Wen model is introduced and analyzed to express the nonlinear hysteresis term. Two triangular actuating voltages with frequency of 1 Hz and amplitudes of 80 V and 90 V are applied to drive the piezoelectric stack actuator. The results demonstrate the existence of the hysteresis phenomenon between the input voltage and the output displacement of the piezoelectric stack actuator, and validate the correctness of the model.

Integrated PID-Based Sliding Mode State Estimation and Control for Piezoelectric Actuators

Tracking control of piezoelectric actuators (PEAs) has stimulated the development of various advanced control schemes that utilize the feedback of PEA system states for improved control performance. Among them, the one based on the concept of sliding mode has been shown promising due to its robustness to matched uncertainties, but leaving the required state estimation to be desired. Previous studies show that the PEA can be modeled as a linear dynamic system with matched uncertainties. On this basis, this paper presents the development of a novel observer based on the concept of proportional-integral-derivative-based (PID-based) sliding mode, in which the switching function is replaced by a PID regulator. The novel observer, referred to as the PID-based sliding mode observer (PIDSMO), relaxes the observer matching condition as required in the use of the unknown-input observers. The PIDSMO is then integrated with the PID-based sliding mode controller (PIDSMC) to form a novel integrated PID-based sliding mode observer-controller (PIDSMOC) for PEA tracking control. Experiments performed on a PEA showed that the PIDSMO can accurately estimate the PEA states and that the integrated PIDSMOC can achieve better tracking control performances as compared to the PIDSMC with α-β filter control scheme.

Precise tracking control of piezoelectric actuators based on a hysteresis observer

In this paper, a precise tracking control method for piezoelectric actuators based on a hysteresis observer is considered. A nonlinear observer to estimate the hysteretic nonlinearity in the piezoelectric actuator is designed, and then the hysteretic nonlinearity is compensated for by a feedforward control. The proposed observer is easy to design and has better performance compared to the previous work presented in the literature. A feedback controller is also designed to track reference signals. A numerical simulation is presented to verify the method proposed.

Hysteresis compensation and high-performance tracking control of piezoelectric actuators

This paper presents a repetitive control-based independent design method for high-performance tracking control of piezoelectric actuators. This work applies an inverse Prandtl–Ishlinskii hysteresis model as a non-linear feedforward compensator to compensate for the hysteresis effect, and validates its inverse model by open-loop compensation. To achieve precision tracking control, the current study designs and implements the feedback control using a prototype repetitive control algorithm, integrating the inverse linear plant model-based feedforward compensation and hysteresis compensation methods to further reduce tracking error. Experimental results and performance analysis demonstrate that using the control structure further improves tracking performance.

Novel models for one-sided hysteresis of piezoelectric actuators

The hysteretic behavior of a plant with a non-negative input, referred to as one-sided hysteresis, is characterized by an initial ascending curve and hysteresis loops. It is observed that the widely-used classical Preisach hysteresis model and its modifications cannot represent such one-sided hysteresis due to the limitation of the Preisach hysteresis operator. To address this issue, a novel hysteresis operator modified from the Preisach hysteresis operator is proposed in this study and on this basis, a rate-independent hysteresis model and a rate-dependent hysteresis model are developed with methods to estimate their parameters. An algorithm to invert the rate-independent hysteresis model and its application to tracking control are also presented. The models and control schemes developed were verified experimentally on a commercially-available piezoelectric actuator. The results obtained show that the models developed are promising to represent the one-sided hysteresis of the piezoelectric actuator and that the inverting algorithm of the rate-independent hysteresis model is effective as applied to the tracking control of piezoelectric actuators.

Tracking Control of Piezoelectric Actuators with Waveshaping Technique

There are many inherent nonlinear characteristics in piezoceramics material, which result in roll off, phase lag and deteriorate the tracking accuracy in dynamic applications. To improve dynamics, a waveshaping technique is put forth, which is based on fast Fourier transform algorithm, and software to shape the control signals. Using information gathered from frequency response and harmonic analysis with the original control signal applied, new track is calculated to compensate for the system nonlinearity. Experimental results indicate that the proposed waveshaping technique is more effective than the traditional control methods.

Tracking Control of Piezoelectric Actuators with Waveshaping Technique

Tracking Control of Piezoelectric Actuators with Waveshaping Technique

Trajectory tracking control of a piezoelectric stage for dynamic load applications

In this paper, a robust control approach using a novel hysteresis observer is developed for precise tracking control of piezoelectric actuators (PEAs). This control methodology considers the problems of unknown or uncertain system parameters, hysteresis non-linearity, and external load disturbances. For representing the behaviour of a PEA, a Bouc–Wen hysteresis model is integrated with a second-order linear dynamic. It is shown that the non-linear response of the model owing to the hysteresis effect acts as a bounded disturbance. Based on this fact a hysteresis observer is proposed to estimate the hysteresis effect. Then for real-time compensation of the observer error, parametric uncertainties, and external disturbances, a sliding mode control strategy with a perturbation estimation function is utilized. By using the proposed control approach the asymptotical stability in displacement tracking and robustness to the dynamic load disturbance can be provided. Finally, the proposed approach and conventional controllers are compared by experiments.

High-speed tracking control of piezoelectric actuators using an ellipse-based hysteresis model

In this paper, an ellipse-based mathematic model is developed to characterize the rate-dependent hysteresis in piezoelectric actuators. Based on the proposed model, an expanded input space is constructed to describe the multivalued hysteresis function H[u](t) by a multiple input single output (MISO) mapping Gamma:R(2)-->R. Subsequently, the inverse MISO mapping Gamma(-1)(H[u](t),H[u](t);u(t)) is proposed for real-time hysteresis compensation. In controller design, a hybrid control strategy combining a model-based feedforward controller and a proportional integral differential (PID) feedback loop is used for high-accuracy and high-speed tracking control of piezoelectric actuators. The real-time feedforward controller is developed to cancel the rate-dependent hysteresis based on the inverse hysteresis model, while the PID controller is used to compensate for the creep, modeling errors, and parameter uncertainties. Finally, experiments with and without hysteresis compensation are conducted and the experimental results are compared. The experimental results show that the hysteresis compensation in the feedforward path can reduce the hysteresis-caused error by up to 88% and the tracking performance of the hybrid controller is greatly improved in high-speed tracking control applications, e.g., the root-mean-square tracking error is reduced to only 0.34% of the displacement range under the input frequency of 100 Hz.

Tracking control of piezoelectric actuator based on a new mathematical model

A major deficiency of piezoelectric actuators is that their open-loop control accuracy is seriously limited by hysteresis. In this paper, a novel mathematical model is proposed to describe hysteresis precisely and a new parameter called turning voltage is introduced. It was found experimentally that the shapes of hysteresis curves are decided by the value of the turning voltage. A computer-based inverse control approach under open-loop operation based on the mathematical model was applied to suppress the inherent hysteresis to within ±1% full span range of a stack piezoelectric actuator and the performance of the piezoelectric actuator is noticeably improved.