Piezoelectric stage has become promising actuator for wide applications of micro-/nano-positioning systems represented mathematically with Bouc–Wen hysteresis model to examine the efficiency. In this investigation, the numerical study of piezostage actuator based on nonlinear Bouc–Wen hysteresis model is presented by neurocomputing intelligence via Levenberg–Marquardt backpropagated neural networks (LMB-NNs). Numerical computing strength of Adams method is implemented to generate a dataset of LMB-NNs for training, testing and validation process based on different scenarios of input voltage signals to piezostage actuator model. The performance of LMB-NNs of nano-positioning system model is validated through accuracy measures on means square error,
 histogram illustrations and regression analysis.

Neuro-intelligent networks for Bouc–Wen hysteresis model for piezostage actuator

Piezoelectric actuators are widely used in the field of micro- and nanopositioning due to their high frequency response, high stiffness, and high resolution. However, piezoelectric actuators have hysteresis nonlinearity, which severely affects their positioning accuracy. As the driving frequency increases, the performance of piezoelectric actuators further degrades. In addition, the impact of force on piezoelectric actuators cannot be ignored in practical applications. Dynamic hysteresis with force-voltage coupling makes the hysteresis phenomenon more complicated when force and driving voltage are both applied to the piezoelectric actuator. Existing hysteresis models are complicated, or inaccurate in describing dynamic hysteresis with force-voltage coupling. To solve this problem, a force-voltage-coupled Prandtl–Ishlinskii (FVPI) model is proposed in this paper. First, the influence of driving frequency and dynamic force on the output displacement of the piezoelectric actuators are analyzed. Then, the accuracy of the FVPI model is verified through experiments. Finally, a force integrated direct inverse (F-DI) compensator based on the FVPI model is designed. The experimental results from this study show that the F-DI compensator can effectively suppress dynamic hysteresis with force-voltage coupling of piezoelectric actuators. This model can improve the positioning accuracy of piezoelectric actuators, thereby improving the working accuracy of the micro- or nano-operating system.

Modeling and Compensation of Dynamic Hysteresis with Force-Voltage Coupling for Piezoelectric Actuators.

As a flexible bionic actuator, pneumatic artificial muscle (PAM) has been widely utilized in robotics. However, due to its strong creep and hysteresis nonlinearities, it is difficult to precisely control its output force and displacement. In order to attenuate the influence of the PAM's hysteresis, this paper proposes the integration of the inverse Prandtl-Ishlinskii (PI) model and the adaptive projection (AP) algorithm such that the model parameters can be identified online. This helps to compensate for the PAM's hysteresis without any offline identification. Finally, the performance of the proposed method is experimentally verified on an in-house built 2-DOF Delta mechanism. Both the angle tracking performance of the joints and the trajectory tracking performance of the end effector are tested. Experimental results demonstrate the effectiveness of the proposed controller.

Closed-loop Control of a Pneumatic Artificial Muscle Actuated 2-DOF Delta Mechanism with Adaptive Hysteresis Compensation

Fast steering mirrors (FSMs), driven by piezoelectric ceramics, are usually used as actuators for high-precision beam control. A FSM generally contains four ceramics that are distributed in a crisscross pattern. The cooperative movement of the two ceramics along one radial direction generates the deflection of the FSM in the same orientation. Unlike the hysteresis nonlinearity of a single piezoelectric ceramic, which is symmetric or asymmetric, the FSM exhibits complex hysteresis characteristics. In this paper, a systematic way of modeling the hysteresis nonlinearity of FSMs is proposed using a Madelung's rules based symmetric hysteresis operator with a cascaded neural network. The hysteresis operator provides a basic hysteresis motion for the FSM. The neural network modifies the basic hysteresis motion to accurately describe the hysteresis nonlinearity of FSMs. The wiping-out and congruency properties of the proposed method are also analyzed. Moreover, the inverse hysteresis model is constructed to reduce the hysteresis nonlinearity of FSMs. The effectiveness of the presented model is validated by experimental results.

Hysteresis Modeling and Compensation of Fast Steering Mirrors with Hysteresis Operator Based Back Propagation Neural Networks.

Piezoelectric actuated models are promising high-performance precision positioning devices used for broad applications in the field of precision machines and nano/micro manufacturing. Piezoelectric actuators involve a nonlinear complex hysteresis that may cause degradation in performance. These hysteresis effects of piezoelectric actuators are mathematically represented as a second-order system using the Dahl hysteresis model. In this paper, artificial intelligence-based neurocomputing feedforward and backpropagation networks of the Levenberg–Marquardt method (LMM-NNs) and Bayesian Regularization method (BRM-NNs) are exploited to examine the numerical behavior of the Dahl hysteresis model representing a piezoelectric actuator, and the Adams numerical scheme is used to create datasets for various cases. The generated datasets were used as input target values to the neural network to obtain approximated solutions and optimize the values by using backpropagation neural networks of LMM-NNs and BRM-NNs. The performance analysis of LMM-NNs and BRM-NNs of the Dahl hysteresis model of the piezoelectric actuator is validated through convergence curves and accuracy measures via mean squared error and regression analysis.

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Intelligent Predictive Solution Dynamics for Dahl Hysteresis Model of Piezoelectric Actuator

Piezoelectric actuators are widely used in micro- and nano-manufacturing and precision machining due to their superior performance. However, there are complex hysteresis nonlinear phenomena in piezoelectric actuators. In particular, the inherent hysteresis can be affected by the input frequency, and it sometimes exhibits asymmetrical characteristic. The existing dynamic hysteresis model is inaccurate in describing hysteresis of piezoelectric actuators at high frequency. In this paper, a Dynamic Delay Prandtl–Ishlinskii (DDPI) model is proposed to describe the asymmetrical and dynamic characteristics of piezoelectric actuators. First, the shape of the Delay Play operator is discussed under two delay coefficients. Then, the accuracy of the DDPI model is verified by experiments. Next, to compensate the asymmetrical and dynamic hysteresis, the compensator is designed based on the Inverse Dynamic Delay Prandtl–Ishlinskii (IDDPI) model. The effectiveness of the inverse compensator was verified by experiments. The results show that the DDPI model can accurately describe the asymmetrical and dynamic hysteresis, and the compensator can effectively suppress the hysteresis of the piezoelectric actuator. This research will be beneficial to extend the application of piezoelectric actuators.

https://www.mdpi.com/2072-666X/12/1/92/pdf

Jiahui Wang

Papers

Modeling and Compensation for Asymmetrical and Dynamic Hysteresis of Piezoelectric Actuators Using a Dynamic Delay Prandtl-Ishlinskii Model.

Modeling and Compensation of Dynamic Hysteresis with Force-Voltage Coupling for Piezoelectric Actuators.