Model Of Piezoelectric Actuator Research Articles

Hysteresis modeling of piezoelectric actuators based on neural network considering load and environmental stiffness

Hysteresis modeling of piezoelectric actuators based on neural network considering load and environmental stiffness

Modeling and Control of a Linear Piezoelectric Actuator

To improve the output displacement of piezoelectric actuators, a linear piezoelectric actuator based on a multistage amplifying mechanism with a small volume, large thrust, high resolution, high precision, and fast response speed is proposed. However, inherent nonlinear characteristics, such as hysteresis and creep, significantly affect the output accuracy of piezoelectric actuators and may cause system instability. Therefore, a complex nonlinear hysteresis mathematical model with a high degree of fit was established. A Play operator was introduced into the backpropagation neural network, and a genetic algorithm (GA) was used to reduce the probability of the fitting of the neural network model falling into a local minimum. Moreover, simulation and experimental test platforms were constructed. The results showed that the maximum displacement of the actuator was 558.3 μm under a driving voltage of 150 V and a driving frequency of 1 Hz. The complex GA-BP neural network model of the piezoelectric actuator not only exhibited high modeling accuracy but also solved the problems of strong randomness and slow convergence. Compared with other control algorithms, the GA-BP fuzzy PID control exhibited higher control precision.

Fractional-Order Modeling of Piezoelectric Actuators with Coupled Hysteresis and Creep Effects

A novel fractional-order model, incorporating coupled hysteresis and creep effects, is proposed for typical piezoelectric actuators in this study. Throughout the actuation process, various nonlinear behaviors such as piezoelectric hysteresis, non-local memory, peak transition, and creep nonlinearity are accurately characterized by the model. Offering a simpler structure and superior tracking performance compared to conventional models, the proposed fractional-order model parameters are identified using a method that integrates actuator dynamics and employs the particle swarm optimization algorithm. Experimental validation on a piezoelectric actuation platform confirms the model’s superior accuracy and simplified structure, contributing to a deeper understanding of piezoelectric actuation mechanisms and providing an efficient modeling tool for enhanced system performance.

Electro-mechanical transfer matrix modeling of piezoelectric actuators and application for elliptical flexure amplifiers

Mechanically amplified piezoelectric actuators (APAs) can be found in many scenarios of precision engineering and instrumental devices. However, the electro-mechanical design of curvilinear APAs is difficult due to the existence of curved flexure beams and multi-domain electro-elasto dynamics. In this paper, the electro-mechanical behavior of elliptical APAs is studied by exploiting a novel electro-mechanical transfer matrix method. The motivation is to facilitate both the static and dynamic analyses of such a complex APA with curvilinear flexure beams by considering the multi-domain dynamics of piezoelectric stacks and compliant mechanisms from an electro-mechanical viewpoint. To this end, an analytical electro-elasto transfer matrix of piezoelectric stacks operating at the d33 mode is derived in the form of Taylor's series based on Timoshenko beam theory. The dynamic response spectrum of displacement and impedance for elliptical APAs are insightfully captured by such an electro-mechanical model. Different topologies of elliptical APAs are also compared and the optimal configuration is suggested. At last, a proof-of-concept prototype is fabricated and tested with a special focus on experimental evaluation of the electro-mechanical coupling model.

An integrated modeling method for piezo-actuated compliant mechanisms

Piezo-actuated compliant mechanisms are widely employed in precision positioning and micro/nano manipulation due to their advantages of compact structure, high displacement resolution, and fast response. However, it is still challenging to accurately analyze the designed mechanisms due to the complicated coupled electromechanical behaviors of piezoelectric actuators and compliant mechanisms, which prevents further performance improvement by configuration design and optimization. A novel modeling method is developed in this paper for the kinetostatic and dynamic analyses of piezoelectric actuators and their comprised systems with compliant mechanisms. The electromechanical model of piezoelectric actuators is derived from linear piezoelectric vibration theory and further simplified as a practical equivalent model in the form of dynamic stiffness matrices. With the proposed actuator model, an integrated modeling method based on the dynamic stiffness matrix method is proposed for analyses of the piezo-actuated compliant mechanism with complicated configurations of piezoelectric actuators and flexible structures. Two case studies, including a piezoelectric actuator and a fast scanning stage, are analyzed to verify the effectiveness of the proposed approach. Both finite element analysis and experimental results validate that the presented modeling method can be used to resolve the kinetostatics and dynamics of complex piezo-actuated compliant mechanisms efficiently and effectively.

Fractional order neural sliding mode control based on the FO-Hammerstein model of piezoelectric actuator

Piezoelectric actuators (PEA) are extensively utilized in high-precision micro-measurement and operation. However, owing to the rate-dependent nature of its hysteresis, its accuracy in certain applications would suffer significantly, and the system would become unstable. To address this issue, a new method for developing a feedback control system that can reduce the rate-dependent impacts of PEA on the positioning system is provided using PEA as the research object. This strategy is based on the fractional order Hammerstein model (FO-Hammerstein). For the fractional order model, a novel fractional order integral sliding mode surface is proposed here that can accurately delineate the dynamic characteristics of PEA. This sliding mode surface is composed of a fractional polynomial and an integral term, which can better minimize static errors and monitor reference signals, and it is built using a fractional neural sliding mode control (BP-FSMC) method. The control technique can be extensively utilized in various systems, such as FO-Hammerstein and those described by the fractional transfer function. The research introduces a neural network and an artificial bee colony algorithm (DeC-ABC) that are used to alter the system’s parameters. The study’s findings reveal that a system with high resilience can follow the signals from both composite and single input sources. Compared with the fractional order sliding mode control approach on the basis of extended state observer, the fractional order sliding mode control method based on single parameter adaptive law and the proportional integral sliding mode control method on the basis of feedforward compensation, this method has a quicker response time and lower tracking error.

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 analysis of a thrust anti-torque sensing actuator

In the field of intelligent drive and sense, the traditional actuator can realize linear actuation and lacks sensing function. Therefore, a new sensing actuator is designed, which can not only output force and displacement, but also have thrust anti-torque sensing function. Firstly, the model of piezoelectric actuator is designed, and the geometric and mechanical models are established. Furthermore, the geometric relationship of mechanical and electrical parameters is analyzed. Secondly, the optimal included angles are determined after finite element analysis and optimization. Finally, the maximum output displacement is obtained through finite element analysis, and the maximum strain position is pointed out. Besides, the rotational stiffness is obtained. The results show that the modeling method and simulation results are accurate.

A Novel Feedforward Model of Piezoelectric Actuator for Precision Rapid Cutting.

The piezoelectric actuator has been widely used in modern precision cutting technology due to its fast response speed and high positioning accuracy. In recent years, with the development of precision technology, modern cutting requires higher and higher cutting accuracy and efficiency. Therefore, this paper proposes a feedforward control method based on the modified Bouc-Wen (MBW) model. Firstly, a novel asymmetrical modified Bouc-Wen model with an innovative form of shape control function is developed to model the hysteresis nonlinearity property of piezoelectric actuators. Then, a self-adaptive cooperative particle swarm optimization (PSO) algorithm is developed to identify the parameters of MBW model. The comparative evaluation reveals that the MBW model outperforms the classical Bouc-Wen (CBW) model by 66.4% in modeling accuracy. Compared with traditional PSO algorithm, the self-adaptive cooperative PSO algorithm can obtain minimum fitness in parameter identification. Furthermore, the feedforward control strategy is realized to improve the position tracking accuracy. A position tracking experiment verifies that the feedforward control strategy improves the tracking accuracy of piezoelectric actuators significantly compared with the open-loop control strategy.

Robust Tracking Control of Piezo-Actuated Nanopositioning Stage Using Improved Inverse LSSVM Hysteresis Model and RST Controller

Nanopositioning technology is widely used in high-resolution applications. It often uses piezoelectric actuators due to their superior characteristics. However, piezoelectric actuators exhibit a hysteresis phenomenon that limits their positioning accuracy. To compensate for the hysteresis effect, developing an accurate hysteresis model of piezoelectric actuators is very important. This task is challenging, requiring some considerations of the multivalued mapping of hysteresis loops and the generalization capabilities of the model. This challenge can be dealt with by developing a machine learning-based model, whose inverse model can be used to efficiently design an accurate feedforward controller for hysteresis compensation. However, this approach depends on model accuracy and the type of data used to train the model. Thus, accurate prediction of the hysteresis behavior may not be guaranteed in the presence of disturbances. In this paper, a machine learning-based model is used to design a hysteresis compensator and then combined with a robust feedback controller to enhance the robustness of a nanopositioning control system. The proposed model is based on hysteresis operators, the least square support vector machine (LSSVM) method, and particle swarm optimization (PSO) algorithm. The inverse model is used to design the feedforward controller, and the RST controller is employed to develop feedback control. Our main contribution is the introduction of a hybrid controller capable of compensating for the hysteresis effect, and at the same time, eliminating remaining modeling errors and rejecting disturbances. The performance of the proposed approach is evaluated through MATLAB simulation, as well as through real-time experiments. The experimental results of our approach demonstrate superior tracking performance compared with the PID-LSSVM controller.

Parameter estimation of linear fractional-order system from laplace domain data

A novel parameter estimation method based on the Laplace transform and the response sensitivity method has been presented to recognize the parameters of linear fractional-order systems (FOS) rapidly. The proposed method consumes two orders of magnitude computational resources lower than the traditional time-domain method. Fractional-order operators are increasingly widely used in control and synchronization, epidemiology, viscoelastic material modelling and other emerging disciplines. It is difficult to measure the fractional-order α and system parameters directly in real engineering applications. This paper’s main work include: Firstly, a general linear fractional differential equation is transformed into an algebraic equation by the Laplace transform, and the parameter sensitivity analysis concerning the unknown parameters is also deduced. Then, the parameter estimation problem of the linear FOS is established as a nonlinear least-squares optimization in the Laplace domain, and the enhanced response sensitivity method is adopted to resolve this nonlinear minimum optimization equation iteratively. In addition, the Tikhonov regularization is employed to cope with the potential ill-posed situations, and the trust-region restriction is also introduced to improve the convergence. Finally, taking a differential system with two types of fractional-order operators, a multi-degree-of-freedom FOS with external excitation and an actual piezoelectric actuator model as examples, the specific implementation process is demonstrated in detail to test the robustness and validity of the proposed approach.

Design and research on tuning fork piezoelectric actuator based on stick-slip effect.

Aiming at the problems of low output speed, large size, and difficult miniaturization of stacked and sandwich piezoelectric actuators, a patch-type tuning fork piezoelectric actuator model based on the stick-slip effect was designed, in which the dynamic theoretical analysis, the simulation optimization to determine the stator structure parameters, and the experimental research were carried out to obtain the stator structure parameters. The externally applied conditions (the influence model of excitation voltage, excitation frequency, and pre-pressure) on the performance output of piezoelectric actuators will promote the miniaturization and industrialization of tuning fork piezoelectric actuators in the next step. The simulation results show that the integrated output performance of the piezoelectric actuator is best when the angle of the tuning fork is 15°. After optimizing the stator chamfer to 2.5 and 4.5mm, the tangential amplitude difference of the 15° tuning fork angle actuator is the smallest. The experimental results show that the output speed of the actuator is positively linearly related to the excitation voltage, the maximum output thrust is 8 N when the excitation voltage is 100V, the excitation frequency is 20.1kHz, the pre-pressure is 7.5 N, the phase difference of the excitation signal is π/2, and the output speed of the actuator can reach 116 mm/s.

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.

Design, Analysis and Experiment of the Fiber Push-Out Device Based on Piezoelectric Actuator.

In this study, a fiber push-out device based on a piezoelectric actuator was designed, analyzed and tested, and its experimental environment was designed. The piezoelectric actuator includes a flexible beam. By using response surface analysis (RSM), taking the large displacement as the objective function and on the premise of meeting the strength requirements, the structural parameters of the flexible beam were analyzed. In the process of fiber push-out, the interfacial shear stress was estimated by establishing the system integrating the fiber-matrix-composite three-phase model and the piezoelectric actuator model using the analytic method, and the theoretical analysis results of the fiber interface mechanical properties were given. A prototype of the system was made, and the performance tests of the piezoelectric actuator and the fiber push-out device were carried out. The test results showed that the designed piezoelectric actuator can achieve a stepping resolution of 6.67 μm and a maximum displacement of about 100 μm at the input voltage of 150 V, which is consistent with the design results. The extrusion test of a single fiber was carried out using a piezoelectric actuator. The mechanical properties of the interfacial layer during the push-out process were measured and the interfacial shear strength was calculated, which is consistent with the theoretical analysis results. Finally, based on the mechanical properties obtained from the test, the loading failure process of the fiber was simulated by finite element analysis, which well explained the failure process of the fiber, thus verifying the feasibility of the designed fiber push-out device.

Precision open-loop control of piezoelectric actuator

Due to space constraints, some micro-assemblies and micro-operating systems cannot install sensors, so it is challenging to achieve closed-loop control. For this reason, a precision open-loop control strategy for piezoelectric actuators is proposed. Firstly, based on the PI model and the proposed threshold partition method, the hysteresis model of the piezoelectric actuator with rate-dependent and few operators is established. Then the hysteresis error of the piezoelectric actuator is compensated by the inverse model obtained. Secondly, the creep model of the logarithmic piezoelectric actuator with simple expression and few parameters is established. Then, a creep controller without demand inverse is designed to compensate for the creep error of the piezoelectric actuator. Finally, a ZVD (Zero Vibration Derivative) input shaping method with good robustness is given to eliminate the oscillation generated by the piezoelectric actuator under the action of the step signal. The experimental results show that the displacement error of piezoelectric actuator is reduced from −9.07 to 9.46 μm to −1.22 to 1.78 μm when the maximum displacement is 120 μm after hysteresis compensation; after creeping compensation, within the action time of the 1200 s, the displacement creep of the piezoelectric actuator was reduced from 5.5 μm before compensation to 0.3 μm; after the oscillation control, the displacement overshoot of the piezoelectric actuator is reduced to 0.6% of that before control.

A comparative analysis of electromechanical model of piezoelectric actuator through Caputo–Fabrizio and Atangana–Baleanu fractional derivatives

The dynamical characteristics of the electrical and mechanical domains are usually detected by means of electromechanical model of piezoelectric actuator; this is because it manages extremely small displacements in the range from 10 pm (1 pm = 10−12 m) to 100 μm. This manuscript is dedicatedly written on the fractional modeling of electromechanical model of piezoelectric actuator through modern fractional definitions, namely, Atangan–Baleanu and Caputo–Fabrizio fractional operators, which are based on capturing the full memory effects with and without Markovian and non‐Markovian properties. The modeled governing partial differential equation of displacement is solved by means of Laplace transform method. The investigated solutions of displacement have been expressed in terms of Fox‐H function and series format for avoiding the involvement of gamma functions. A comparative analysis is performed graphically between solutions obtained from Atangan–Baleanu fractional operator and Caputo–Fabrizio fractional operator. Our results suggest that displacement via Atangan–Baleanu fractional operator dominates than displacement via Caputo–Fabrizio fractional operator for controller design even to bypass the hysteresis effect. Additionally, comparison of both fractional techniques on displacement suggests that the utilization of the frequency domain is much more effective than the displacement via classical approaches.

Model and Analysis of Piezoelectric Actuator in Practical Three-Stage Mechanism

Piezoelectric elements (PEMs) are used in a variety of applications. In this paper we developed a full analytical model of a piezoelectric actuator which includes piezostack elements and a three-stage amplification mechanism. The model was derived separately for each unit of the system. Next, the units were combined, while taking into account their coupling. The hysteresis phenomenon, which is significant in piezoelectric materials, was extensively described. A number of hysteresis calculating algorithms were investigated and a new simple method of examining piezoelectric hysteresis was demonstrated. The theoretical model was verified in a laboratory setup. This setup includes a piezoelectric actuator, measuring devices and an acquisition system. The measured results were compared to the theoretical results, while taking into account the nonlinear phenomena of the piezoelectric materials and the three-stage amplification mechanism, and were found to be very similar. Due to its simplicity, this model can easily be modified in order to be applied to other PEMs or other amplification mechanism methods. The main novelty of this work lies in its system-level approach for piezoelectric actuators. All of the system elements include non-linear phenomena, which mutually influence each other. First, each part of the system will be described separately and then, the combined subsystems and the coupling between their parts will be represented. Finally we treat this system as one whole unit.

Analytical analysis of a circular unimorph piezoelectric actuator in the range of low voltages and pressures

In this study, the static displacement behaviour of a three-layer axisymmetric circular piezoelectric unimorph actuator subjected to voltage and uniform pressure loads for different mechanical and geometric properties of layers was investigated. The closed-analytical model of piezoelectric actuator based on the classical laminated thin plate theory was performed. Kirchhoff’s thin plate theory for the mathematical model in closed form of the actuator was utilized. The superposition of transverse and lateral deflections expressions was used to obtain the displacement equation of the piezoelectric actuator. Then, the analytical model solutions were compared by finite element model solutions. It was observed that the results obtained from analytical model and finite element analysis were sufficiently compatible with each other. The effects of nondimensional physical and mechanical properties on the static deflection performance of the piezoelectric actuator were discussed using the analytical model. According to the results obtained, the physical and mechanical properties of the actuator had significant effects on the actuator displacement. Therefore, the results obtained in this study can be used to optimize the performance of the circular piezoelectric actuator.

Intelligent Rate-Dependent Hysteresis Control Compensator Design With Bouc-Wen Model Based on RMSO for Piezoelectric Actuator

Piezoelectric actuators (PAs) require high precision positioning for the applications of micro electrical mechanical systems, but it exhibits hysteresis nonlinearity which deteriorates positioning accuracy if no proper compensation is given. Hysteresis nonlinear modeling of PAs is a prime choice for hysteresis compensation. This paper proposes a novel intelligent positioning control algorithm based on Bouc-Wen (BW) model for the compensation of a bi-morph type piezoelectric actuator (PA) suffering rate-dependent hysteresis. A region based mixed-species swarm optimization (RMSO) algorithm is proposed for BW modeling to capture the dynamic nonlinearity of a piezoelectric actuator which exhibits rate-dependent hysteresis. Results of numerical simulations have been disclosed to illustrate the performance enhancement of RMSO over classical algorithm while they are applied to the parameter fitting problem of BW model for experimentally acquired datasets. An model based adaptive Fuzzy neural network (Fuzzy-NN) controller of PA is utilized to compensate the hysteresis for the positioning tracking control. Experimental results also illustrate the good performance of the proposed RMSO-BW based control scheme for the hysteresis compensation control of the PA.

Hysteresis modeling of piezoelectric actuators with the frequency-dependent behavior using a hybrid model

In order to overcome the problem of positioning inaccuracy caused by nonlinear hysteresis of piezoelectric actuators, a hybrid model based on least-squares support vector machine and Bouc–Wen model is proposed to model the rate-dependent hysteresis of piezoelectric actuators. A rate-independent Bouc–Wen model and its parameters identification method is established as the basis of least-squares Bouc–Wen model. Least-squares support vector machine, which is optimized by particle swarm optimization, is introduced to improve the Bouc–Wen model into a rate-dependent model by adjusting parameters of Bouc–Wen dynamically. Experiment is carried out to validate both Bouc–Wen model and the proposed least-squares Bouc–Wen model. The results show that the proposed least-squares Bouc–Wen method is a valid and a more precise method compared to the rate-independent Bouc–Wen model.