Nonlinearity Of Piezoelectric Actuator Research Articles

Modelling of a shear-type piezoelectric actuator for AFM-based vibration-assisted nanomachining

Recent research investigations have reported the benefit of enhancing conventional AFM-based nanoscale machining operations by the introduction of high frequency vibrations between the AFM tip and the processed material. The technique relies on piezoelectric actuation and is relatively straight forward to implement in practice. However, the non-linearity of piezoelectric actuators when operated under high electric field and frequency conditions can affect the dimensional accuracy of the fabricated nanostructures. To address these issues, the paper reports a method based on coupled mechanical-electrical Finite Element (FE) modelling to predict the relative motion between an AFM tip and a workpiece for vibration-assisted AFM-based nanomachining applications. In particular, the novelty of the proposed method is that it combines two classical approaches for modelling the nonlinear behaviour of piezoelectric materials. More specifically, two sources of non-linearity are considered simultaneously by combining the field-dependant model from Muller and Zhang with the frequency-dependant model from Damjanovic. The resulting combined model is employed to establish the piezoelectric constitutive equations implemented in the developed coupled field FE model. A further distinguishing characteristic of the work is that the proposed approach was subsequently validated by comparing the predicted widths of nanoscale grooves against those machined with a custom AFM-based vibration-assisted nanomachining configuration.

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.

Polynomial-based Stability Analysis of Modified IMC-PID Controller for Piezoelectric Actuator System in Time Delay Environment

Piezoelectric actuators are widely used in several industrial applications requiring precision positioning. However, the positioning accuracy of this nonlinear actuator is severely limited by physical phenomenon such as hysteresis, uncertainties. Accordingly, to improve the performance of piezo micro–nano positioning system, appropriate control laws are designed to linearize the hysteresis through closed-loop approaches. A modified internal model controller (MIMC) is useful with regard to efficient computational hardware resource utilization when compared with the conventional approach provided the resulting controller is stable. This paper focuses on one such widely used and computationally inexpensive control framework in the form of PID-based MIMC to mitigate hysteretic nonlinearity in piezoelectric actuators with the aim to investigate the time delay uncertainty handling range of the controller. The system stability pertaining to time delay has been analyzed numerically and the maximum delay that the system can withstand without losing its stability, i.e. the delay margin has been determined using polynomial-based approach. It has been found that upon increasing the delay beyond a specific critical value, the controller performance is limited and the system turns unstable. Simulations carried out in time delay environment validate the theoretically achieved results.

Modeling and Compensation Algorithms of Asymmetric Nonlinearity for Piezoelectric Actuators Based on Madelung's Rules

This article presents a hysteresis modeling algorithm to describe the asymmetric nonlinearity in piezoelectric actuators (PEAs). The proposed algorithm primarily consists of two parts: 1) the wiping-out mechanism, and 2) the description method for the current hysteresis curve (CHC). The first part is associated with the realization of the wiping-out mechanism. It is used to determine the hysteresis curve where the hysteresis trajectory moves along, and this curve represents the CHC. In the second part, the information of the major ascending or descending curve is used to describe the CHC, and meanwhile, the trajectory is also described. The proposed algorithm works in real-time, which provides an intuitive mechanism to understand and investigate the asymmetric hysteresis nonlinearity in PEAs. Furthermore, the analytical inverse modeling algorithm is proposed to reduce the hysteresis effect. Experiments are conducted to validate the effectiveness of the proposed algorithms.

Elman neural network–based identification of rate-dependent hysteresis in piezoelectric actuators

Rate-dependent hysteresis nonlinearity in piezoelectric actuators severely limits micro- and nanoscale system performance. It is necessary to establish a dynamic model to describe the full behavior of rate-dependent hysteresis. In this article, the Elman neural network–based hysteresis model is developed for piezoelectric actuators. An improved dynamic hysteretic operator is proposed to transform the multi-valued mapping of hysteresis into one-to-one mapping on a newly constructed expanded input space. Then, Elman neural network incorporated with the improved dynamic hysteretic operator is utilized to approximate the behavior of rate-dependent hysteresis. The combination of Elman neural network and the improved dynamic hysteretic operator can dually embody the dynamic property and is capable of fully extracting the characteristics of rate-dependent hysteresis. The experimental results are presented to illustrate the potential of the proposed modeling technique.

Asymmetrically Dynamic Coupling Hysteresis in Piezoelectric Actuators: Modeling Identification and Experimental Assessments

An asymmetrically dynamic coupling hysteresis (ADCH) model is proposed as an extension of the Prandtl–Ishlinskii (PI) model to characterize the hysteretic nonlinearities in piezoelectric actuators (PEAs). When subject to two-input: dynamic excitation and external loads. In this model, the developed asymmetrically one-side play operator helps to represent the saturation, nonlinearity, and centrally asymmetric properties of PEAs employed inverse hyperbolic envelope functions. The dynamic threshold functions are put in place to characterize the width of rate-dependent hysteresis property. Introductions of continuously coupled density functions are beneficial to the cross-coupled hysteresis behaviors of external load/excitation voltage-to-expansion. Besides, the proposed ADCH model is verified to satisfy indeed the wiping-out property and equal vertical chords property, which means that it can be regarded as well-suited in modeling the complicated hysteresis nonlinearity of PEAs. Furthermore, this paper also tackles the identification issue of the proposed ADCH model by using a global research method, which possesses satisfactory accuracy without strict requirements for the initially iterative value.

Measurement of Radial Elasticity and Original Height of DNA Duplex Using Tapping-Mode Atomic Force Microscopy.

Atomic force microscopy (AFM) can characterize nanomaterial elasticity. However, some one-dimensional nanomaterials, such as DNA, are too small to locate with an AFM tip because of thermal drift and the nonlinearity of piezoelectric actuators. In this study, we propose a novel approach to address the shortcomings of AFM and obtain the radial Young’s modulus of a DNA duplex. The elastic properties are evaluated by combining physical calculations and measured experimental results. The initial elasticity of the DNA is first assumed; based on tapping-mode scanning images and tip–sample interaction force simulations, the calculated elastic modulus is extracted. By minimizing the error between the assumed and experimental values, the extracted elasticity is assigned as the actual modulus for the material. Furthermore, tapping-mode image scanning avoids the necessity of locating the probe exactly on the target sample. In addition to elasticity measurements, the deformation caused by the tapping force from the AFM tip is compensated and the original height of the DNA is calculated. The results show that the radial compressive Young’s modulus of DNA is 125–150 MPa under a tapping force of 0.5–1.3 nN; its original height is 1.9 nm. This approach can be applied to the measurement of other nanomaterials.

Modeling rate-dependent hysteresis in piezoelectric actuators using T-S fuzzy system based on expanded input space method

Piezoelectric actuators (PEAs) are favorable choices in the nanopositioning applications due to their high stiffness, fast response and ultrahigh precision. However, the undesired hysteresis nonlinearity in PEAs can dramatically degrade the positioning/tracking performance. In this paper, a Takagi-Sugeno (T-S) fuzzy system-based approach of identification for rate-dependent hysteresis is proposed. First, a novel hysteretic operator is proposed to describe the change tendency and extract the dynamic property of rate-dependent hysteresis. Then, the proposed hysteretic operator is added into the inputs to construct the expanded input space. Thus, it may transform the multi-valued mapping of hysteresis into one-to-one mapping, which enables the T-S fuzzy system to model the hysteresis. Finally, the experimental results are presented to illustrate the potential of the proposed modeling technique.

Non-Linear Piezoelectric Actuator with a Preloaded Cantilever Beam

Piezoelectric actuation is widely used for the active vibration control of smart structural systems, and corresponding research has largely focused on linear electromechanical devices. This paper investigates the design and analysis of a novel piezoelectric actuator that uses a piezoelectric cantilever beam with a loading spring to produce displacement outputs. This device has a special nonlinear property relating to converting between kinetic energy and potential energy, and it can be used to increase the output displacement at a lower voltage. The system is analytically modeled with Lagrangian functional and Euler–Lagrange equations, numerically simulated with MATLAB, and experimentally realized to demonstrate its enhanced capabilities. The model is validated using an experimental device with several pretensions of the loading spring, therein representing three interesting cases: a linear system, a low natural frequency system with a pre-buckled beam, and a system with a buckled beam. The motivating hypothesis for the current work is that nonlinear phenomena could be exploited to improve the effectiveness of the piezoelectric actuator’s displacement output. The most practical configuration seems to be the pre-buckled case, in which the proposed system has a low natural frequency, a high tip displacement, and a stable balanced position.

A rate-dependent Prandtl-Ishlinskii model for piezoelectric actuators using the dynamic envelope function based play operator

In this paper, a novel rate-dependent Prandtl-Ishlinskii (P-I) model is proposed to characterize the rate-dependent hysteresis nonlinearity of piezoelectric actuators. The new model is based on a modified rate-dependent play operator, in which a dynamic envelope function is introduced to replace the input function of the classical play operator. Moreover, a dynamic density function is utilized in the proposed P-I model. The parameters of the proposed model are identified by a modified particle swarm optimization algorithm. Finally, experiments are conducted on a piezo-actuated nanopositioning stage to validate the proposed P-I model under the sinusoidal inputs. The experimental results show that the developed rate-dependent P-I model precisely characterize the rate-dependent hysteresis loops up to 1000 Hz.

Corrigendum #2 to “On Synergistic Integration of Adaptive Dithering Based Internal Model Control for Hysteresis Compensation in Piezoactuated Nanopositioner”

Piezoelectric-stack actuated platforms are very popular in the parlance of nanopositioning with myriad applications like micro/nanofactory, atomic force microscopy, scanning probe microscopy, wafer design, biological cell manipulation, and so forth. Motivated by the necessity to improve trajectory tracking in such applications, this paper addresses the problem of rate dependent hysteretic nonlinearity in piezoelectric actuators (PEA). The classical second order Dahl model for hysteresis encapsulation is introduced first, followed by the identification of parameters through particle swarm optimization. A novel inversion based feedforward mechanism in combination with a feedback compensator is proposed to achieve high-precision tracking wherein the paradoxical concept of noise as a performance enhancer is introduced in the realm of PZAs. Having observed that dither induced stochastic resonance in the presence of periodic forcing reduces tracking error, dither capability is further explored in conjunction with a novel output harmonics based adaptive control scheme. The proposed adaptive controller is then augmented with an internal model control based approach to impart robustness against parametric variations and external disturbances. The proposed control law has been employed to track multifrequency signals with consistent compensation of rate dependent hysteresis of the PEA. The results indicate a greatly improved positioning accuracy along with considerable robustness achieved with the proposed integrated approach even for dual axis tracking applications.

On Synergistic Integration of Adaptive Dithering Based Internal Model Control for Hysteresis Compensation in Piezoactuated Nanopositioner

Piezoelectric-stack actuated platforms are very popular in the parlance of nanopositioning with myriad applications like micro/nanofactory, atomic force microscopy, scanning probe microscopy, wafer design, biological cell manipulation, and so forth. Motivated by the necessity to improve trajectory tracking in such applications, this paper addresses the problem of rate dependent hysteretic nonlinearity in piezoelectric actuators (PEA). The classical second order Dahl model for hysteresis encapsulation is introduced first, followed by the identification of parameters through particle swarm optimization. A novel inversion based feedforward mechanism in combination with a feedback compensator is proposed to achieve high-precision tracking wherein the paradoxical concept of noise as a performance enhancer is introduced in the realm of PZAs. Having observed that dither induced stochastic resonance in the presence of periodic forcing reduces tracking error, dither capability is further explored in conjunction with a novel output harmonics based adaptive control scheme. The proposed adaptive controller is then augmented with an internal model control based approach to impart robustness against parametric variations and external disturbances. The proposed control law has been employed to track multifrequency signals with consistent compensation of rate dependent hysteresis of the PEA. The results indicate a greatly improved positioning accuracy along with considerable robustness achieved with the proposed integrated approach even for dual axis tracking applications.

Adaptive Kalman filter and dynamic recurrent neural networks-based control design of macro-micro manipulator

In this paper, a composite control scheme for macro-micro dual-drive positioning stage with high acceleration and high precision is proposed. The objective of control is to improve the precision by reducing the influence of system vibration and external noise. The positioning stage is composed of voice coil motor (VCM) as macro driver and piezoelectric actuator (PEA) as micro driver. The precision of the macro drive positioning stage is improved by the combined PID control with adaptive Kalman filter (AKF). AKF is used to compensate VCM vibration (as the virtual noise) and the external noise. The control scheme of the micro drive positioning stage is presented as the integrated one with PID and intelligent adaptive inverse control approach to compensate the positioning error caused by macro drive positioning stage. A dynamic recurrent neural networks (DRNN) based inverse control approach is proposed to offset the hysteresis nonlinearity of PEA. Simulations show the positioning precision of macro-micro dual-drive stage is clearly improved via the proposed control scheme.

Precision Positioning of Piezo-Actuated Stages Based on Feedback Control with GA Modeling

The piezo-actuated stages are composed of the piezo-electric actuator and the positioning mechanism. The positioning accuracy of the piezo-actuated stage is limited due to hysteretic nonlinearity of the PEA and friction behavior of the positioning mechanism. To compensate this nonlinearity of piezoelectric actuator, a PI feedback control associated with feedforward compensating based on the hysteresis observer is proposed in this paper. Identifying its parameters is very important; so the genetic algorithm is studied to find the optimal parameters. To verify the feasibility of the proposed method, it is implemented on the precision positioning task of the piezo-actuated stage in the real-time control architecture.

Energy Optimization in Local Shape Control of Structures with Nonlinear Peizoelectric Actuators

Shape control of a local part of a structure rather than the entire structure is often encountered in engineering practice using as less control energy as possible. Energy optimization for local shape control of structures integrated with nonlinear piezoelectric actuators is investigated. The local shape is maintained by assigning the generalized displacements to the desired ones at some given points. The distortion of the residual shape is also limited to a given range. This optimal control voltage distribution is solved by using elimination and the Lagrange multiplier method. A unique solution scheme based on Cholesky decomposition and eigenvalue problem is given to reduce the computational load for finding the Lagrange multipliers from an algebraic equation. The final optimal control voltage distribution for the nonlinear system is obtained by an iteration procedure. Finally, an example is given to illustrate the present method, and the results show that proper relaxation of the error tolerance of the residual shape can significantly reduce the control energy requested for the local shape control of the designated area.

Optimal Voltage Design for Static Shape Control of Smart Structures with Nonlinear Piezoelectric Actuators

In this paper, static shape control of structures with nonlinear piezoelectric actuators is investigated. Firstly, an adhesive element is developed to model smart plates with nonlinear piezoelectric actuator patches. The adhesive element combines a pair of collocated four-node quadrilateral elements for the upper and lower adherents and a pseudo-adhesive layer element with constant shear and peel strains along its thickness. Secondly, after establishing the equilibrium equations with nonlinear actuating forces, an explicit iterative algorithm for finding the optimal control voltage distribution on the nonlinear piezoelectric actuators is formulated, and the converging speed of this iterative algorithm is also estimated. Finally, a simulation example is given to illustrate that the present algorithm is effective in finding the optimal control voltage distribution for shape control of nonlinearly actuated structures. Significant effect of the nonlinear piezoelectric constitutive relationship on the optimal control voltage is also observed.

Static shape control of structures using nonlinear piezoelectric actuators with energyconstraints

Static shape control of composite plates with nonlinear piezoelectric actuators subject toenergy constraint is investigated in this paper. The optimal control voltages are determinedby using Lagrange multipliers so as to minimize a weighted generalized errorfunction at a given energy level. An eigenspace based algebraic equation of theunknown Lagrange multiplier is derived in order to reduce the computation load offinding the multipliers. Two methods, an iteration algorithm and a shape updatingalgorithm, are presented for iteratively finding the optimal control voltages forthe nonlinearly actuated composite plates. In the iteration algorithm, a controlvoltage vector is calculated after the Lagrange multipliers are solved for in eachiteration, and the iteration continues until an assigned precision is satisfied. Inthe shape updating algorithm, the actuated shape is calculated in each iterationand then the difference between the actuated and the desired shape is used asthe new desired shape in the next iteration. The control voltage vector will beupdated using new desired shapes repeatedly until convergence is reached. Finally, asimulation example is given to demonstrate the effectiveness of the present methods.

An incremental algorithm for static shape control of smart structures with nonlinear piezoelectric actuators

Optimum control voltage design for static shape control of structures with nonlinear piezoelectric actuators is studied in this paper. In order to perform static shape control, the finite element equations of plates with nonlinear piezoelectric actuator patches is formulated using an eight-node adhesive element which combines a pair of collocated four-node quadrilateral elements for the upper and lower plates and a pseudo-adhesive layer element. An iteratively calibrated incremental method is presented to find the optimal control voltages that can actuate a shape best matching the desired shape. In this method, the desired shape is expressed by the sum of a number of small incremental desired shapes, and the control voltages to achieve each incremental desired shape are calculated step by step. The control voltages in each step are then calibrated by using the accumulated intermediate desired shape iteratively. Finally, a simulation example is given to illustrate that the present algorithm is effective in finding the optimal control voltage distribution for shape control of nonlinearly actuated structures. The results show that the present method can give satisfactory control voltages with a reasonable number of incremental steps.

Active control of vibration using a fuzzy control method

Active control of vibration has been the subject of a lot of research in recent years. Adaptive linear filtering techniques have been extensively used for the active control of vibration. A popular adaptive filtering algorithm is the filtered-X LMS algorithm because of its simplicity and its relatively low computational load. However, the filtered-X LMS algorithm is limited to linear control problems using feedforward control techniques. A fuzzy logic system based control structure and adaptive algorithm suitable for driving non-linear feedforward active vibration control systems is presented in this paper. This kind of non-linear fuzzy control method is used in two kinds of active vibration control problems, as follows: (1) A fuzzy logic system is used to approximate a non-linear sensor path function and to suppress the primary disturbance that is a non-linear function of the reference signal. (2) A fuzzy logic system is used in active control of vibration with non-linear piezoelectric actuators. The numerical simulation results show the effectiveness of this adaptive fuzzy control method.

Linear Drive of Non-Linear Piezoelectric Actuators.

Piezoelectric ceramics are ferroelectric, and are fundamentally nonlinear in their response to the applied voltage signal, showing a significant hysteretic loop. This paper deals with the linear drive of nonlinear piezoelectric ceramic actuators. It is shown that the expansion of a ceramic actuator can be approximated by a third-order polynomial in the applied voltage. A linear drive method is proposed for the ceramic actuators that compensates for the hysteretic loop, and then a simple nonlinear preamplifier is developed based on the drive method proposed. An experiment is conducted to verify the effectiveness of the amplifier. It is shown that the hysteretic loop disappears when the nonlinear preamplifier is installed between the d. c. amplifier and the input voltage generator.