Parameters Identification for a Composite Piezoelectric Actuator Dynamics

This work presents an approach for identifying the model of a composite piezoelectric (PZT) bimorph actuator dynamics, with the objective of creating a robust model that can be used under various operating conditions. This actuator exhibits nonlinear behavior that can be described using backlash and hysteresis. A linear dynamic model with a damping matrix that incorporates the Bouc–Wen hysteresis model and the backlash operators is developed. This work proposes identifying the actuator’s model parameters using the hybrid master-slave genetic algorithm neural network (HGANN). In this algorithm, the neural network exploits the ability of the genetic algorithm to search globally to optimize its structure, weights, biases and transfer functions to perform time series analysis efficiently. A total of nine datasets (cases) representing three different voltage amplitudes excited at three different frequencies are used to train and validate the model. Four cases are considered for training the NN architecture, connection weights, bias weights and learning rules. The remaining five cases are used to validate the model, which produced results that closely match the experimental ones. The analysis shows that damping parameters are inversely proportional to the excitation frequency. This indicates that the suggested hysteresis model is too general for the PZT model in this work. It also suggests that backlash appears only when dynamic forces become dominant

Application of Laguerre based adaptive predictive control to Shape Memory Alloy (SMA) actuators

This paper discusses the use of an existing adaptive predictive controller to control some Shape Memory Alloy (SMA) linear actuators. The model consists in a truncated linear combination of Laguerre filters identified online. The controller stability is studied in details. It is proven that the tracking error is asymptotically stable under some conditions on the modelling error. Moreover, the tracking error converge toward zero for step references, even if the identified model is inaccurate. Experimentalcresults obtained on two different kind of actuator validate the proposed control. They also show that it is robust with regard to input constraints.ANR MAFESM

Modeling and inverse feedforward control for conducting polymer actuators with hysteresis

Conducting polymer actuators are biocompatible with a small footprint, and operate in air or liquid media under low actuation voltages. This makes them excellent actuators for macro- and micro-manipulation devices, however, their positioning ability or accuracy is adversely affected by their hysteresis non-linearity under open-loop control strategies. In this paper, we establish a hysteresis model for conducting polymer actuators, based on a rate-independent hysteresis model known as the Duhem model. The hysteresis model is experimentally identified and integrated with the linear dynamics of the actuator. This combined model is inverted to control the displacement of the tri-layer actuators considered in this study, without using any external feedback. The inversion requires an inverse hysteresis model which was experimentally identified using an inverse neural network model. Experimental results show that the position tracking errors are reduced by more than 50% when the hysteresis inverse model is incorporated into an inversion-based feedforward controller, indicating the potential of the proposed method in enabling wider use of such smart actuators

Ultraprecise Controller for Piezoelectric Actuators Based on Deep Learning and Model Predictive Control

Piezoelectric actuators (PEA) are high-precision devices used in applications requiring micrometric displacements. However, PEAs present non-linearity phenomena that introduce drawbacks at high precision applications. One of these phenomena is hysteresis, which considerably reduces their performance. The introduction of appropriate control strategies may improve the accuracy of the PEAs. This paper presents a high precision control scheme to be used at PEAs based on the model-based predictive control (MPC) scheme. In this work, the model used to feed the MPC controller has been achieved by means of artificial neural networks (ANN). This approach simplifies the obtaining of the model, since the achievement of a precise mathematical model that reproduces the dynamics of the PEA is a complex task. The presented approach has been embedded over the dSPACE control platform and has been tested over a commercial PEA, supplied by Thorlabs, conducting experiments to demonstrate improvements of the MPC. In addition, the results of the MPC controller have been compared with a proportional-integral-derivative (PID) controller. The experimental results show that the MPC control strategy achieves higher accuracy at high precision PEA applications such as tracking periodic reference signals and sudden reference change

Hysteresis Nonlinearity Identification Using New Preisach Model-Based Artificial Neural Network Approach

Preisach model is a well-known hysteresis identification method in which the hysteresis is modeled by linear combination of hysteresis operators. Although Preisach model describes the main features of system with hysteresis behavior, due to its rigorous numerical nature, it is not convenient to use in real-time control applications. Here a novel neural network approach based on the Preisach model is addressed, provides accurate hysteresis nonlinearity modeling in comparison with the classical Preisach model and can be used for many applications such as hysteresis nonlinearity control and identification in SMA and Piezo actuators and performance evaluation in some physical systems such as magnetic materials. To evaluate the proposed approach, an experimental apparatus consisting one-dimensional flexible aluminum beam actuated with an SMA wire is used. It is shown that the proposed ANN-based Preisach model can identify hysteresis nonlinearity more accurately than the classical one. It also has powerful ability to precisely predict the higher-order hysteresis minor loops behavior even though only the first-order reversal data are in use. It is also shown that to get the same precise results in the classical Preisach model, many more data should be used, and this directly increases the experimental cost

MODELING, ANALYSIS AND CONTROL OF FLEXIBLE SOLID-STATE HYSTERETIC ACTUATORS

A distributed parameters modeling and control framework for flexible solid-state hysteretic actuator is presented in this work. For the simplicity of analysis, the actuator dynamic behavior is decoupled and treated separately from the hysteresis nonlinearity. To include the effects of widely-used flexural mechanisms, a mass-spring-damper boundary condition is considered for system. Moreover, the effect of electromechanical actuation is included as a concentrate force at the boundary. The problem is then divided into two parts: first part deals with free motion analysis of system in order to obtain eigenvalues and eigenfunctions using the expansion theorem and a standard eigenvalue problem procedure. The effects of different boundary mass and spring values on the natural frequencies and mode shapes are demonstrated, which indicate their significant contribution to system performance. In the second part, forced motion analysis of system and its state-space representation are presented. A frequency based control strategy utilizing widely used Lyapunov theorem is designed to obtain an accurate control over the actuator motion. A robust variable structure control is incorporated into the developed controller for compensation of ever-present plant structural uncertainties. A full order state feedback observer is designed to accurately mimic the states of an unobservable plant. An optimization algorithm is developed to compute the optimal observer gain matrix. Various frequency tracking simulations are performed using feedback controller-observer model to observe the effect of modes deficiency on the tracking frequency bandwidth of the controller. Finally, for the accurate prediction of nonlinear multi-loop hysteresis effect, a major source of inaccuracies at quasi-static frequency, a recently developed hysteresis model based on three hysteric properties of piezoelectric material namely targeting of turning points, curve alignment and the wiping-out effect is used. Initially, the hysteresis nonlinearity is decoupled from the looping effect and modeled separately using an exponential function. The obtained exponential function is then utilized in a nonlinear mapping procedure, where it is mapped between consequent turning points recorded in model memory unit. This mapping also uses four constant shaping parameters - two for the ascending and two for the descending hysteresis trajectories. A proportional integral (PI) controller is used for the compensation of hysteresis nonlinearity. Performance of PI controller is validated using several numerical simulations. Finally, the method of combining robust feedback control strategy with the feedforward hysteresis compensation technique is presented to accomplish the precise control over actuator motion

Modeling the Vibrational Dynamics of Piezoelectric Actuator by System Identification Technique

Actuators based on smart materials such as piezoelectric actuators (PEAs) are widely used in many applications to transform electrical signal to mechanical signal and vice versa. However, the major drawbacks for these smart actuators are hysteresis nonlinear, creep and residual vibration. In this paper, PEAs are used for active vibration application. Therefore, a model of PEA must be established to control the vibration that occurs in the system. The frequencies of 1 Hz, 20 Hz and 50 Hz were tested on the PEAs. The results obtained from the experimental were used to develop transfer function model by employing system identification technique. Meanwhile, the model validation was based on level of models fitness to estimation data, mean squared error (MSE), final prediction error (FPE) and correlation test. The experimental result showed that the displacement of the actuator is inversely proportional to the frequency. The following consequences caused the time response criteria at 50 Hz achieved smallest overshoot and fastest response of rise time and settling time

From model-driven to data-driven : a review of hysteresis modeling in structural and mechanical systems

Hysteresis is a natural phenomenon that widely exists in structural and mechanical systems. The characteristics of structural hysteretic behaviors are complicated. Therefore, numerous methods have been developed to describe hysteresis. In this paper, a review of the available hysteretic modeling methods is carried out. Such methods are divided into: a) model-driven and b) datadriven methods. The model-driven method uses parameter identification to determine parameters. Three types of parametric models are introduced including polynomial models, differential based models, and operator based models. Four algorithms as least mean square error algorithm, Kalman filter algorithm, metaheuristic algorithms, and Bayesian estimation are presented to realize parameter identification. The data-driven method utilizes universal mathematical models to describe hysteretic behavior. Regression model, artificial neural network, least square support vector machine, and deep learning are introduced in turn as the classical data-driven methods. Model-data driven hybrid methods are also discussed to make up for the shortcomings of the two methods. Based on a multi-dimensional evaluation, the existing problems and open challenges of different hysteresis modeling methods are discussed. Some possible research directions about hysteresis description are given in the final section

Plurilinear Modeling and discrete μ-Synthesis Control of a Hysteretic and Creeped Unimorph Piezoelectric Cantilever.

International audienceFirst, we present a survey on modeling and control of bending piezoelectric microactuators. Second, a simple model for nonlinear piezoelectric actuators (hysteresis and creep) is presented. It is based on the multilinear approximation. This model requires low computing power and is well adapted for embedded systems. Finally, a μ-synthesis controller is implemented. Experiments show that the obtained performances are compatible with the requirements of micromanipulation tasks