Modeling of Piezoelectric Actuators Based on Bayesian Regularization Back Propagation Neural Network

Chapter 2 - Generalized Scalar Preisach Models of Hysteresis

A piezoelectric stack with its large output force and small displacement cannot satisfy the requirement of the opening of the cone valve core of the actual situation. Piezoelectric hydraulic actuator AMESIM model was established, and the influence on the output displacement and the driving force factors related to simulation and analysis was determined. The results show that the area of the piezoelectric stack has no effect on the output displacement of piezoelectric hydraulic actuator, but with the increase of the area of the maximum output of the piezoelectric hydraulic actuator drive led to nonlinear growth. In the simulation range of 0~60 Hz, the former has better vibration suppression effect than the latter. At some frequencies, the body vibration suppression ability can reach 6.4 times that of the latter.

Due to the artificial muscle advantage properties of light weight, low energy consumption and high power to weight ratio, an underactuated humanoid hand was designed with ionic polymer metal composite (IPMC) actuating distal joint unit and shape memory alloy (SMA) actuating unit. The SMA actuating unit could complete compliant enveloping grasping task for daily life goods. The IPMC actuating distal joint unit could complete grasping task for fragile and light weight goods. The SMA actuating unit was fabricated by multi-piece SMA wires in series to increase output displacement and this series part in parallel to increase output force. This SMA actuator possessed both large output displacement and large output force, solving the mutual restrain problem between output displacement and output force of SMA actuator. Finally, the humanoid hand had completed the bottle, the card and other daily life goods grasping task in experiment, which gave a potent demonstration to the grasping effectiveness.

Piezoelectric functional materials have been extensively studied and employed in numerous devices. With the rapid development of modern industries, such as power plants, aerospace, automotive, renewable energy and material processing industries, the high temperature piezoelectric materials that can work in extreme environments are in great demand. Piezoelectric materials including piezoelectric single crystals, ceramics and films, are at the heart of electromechanical actuation and sensing devices. A variety of applications where piezoelectric actuators and sensors operate at elevated temperatures (T 200℃) would be extremely desired. The actuators need to work efficiently with high strokes, torques, and forces while operating under relatively harsh conditions. These include high-temperature fans and turbines, motors for valves or natural gas industries, kiln automation, and actuators for automotive engines such as fuel injectors and cooling system elements. Yet, the majority of industrial actuator applications are at or below the 250℃ temperature limit. In addition to the increase in operational temperatures of piezoelectric motors and actuators, a future area of interest is high-temperature MEMS research, which can be used for high-temperature valving. On the other hand, the piezoelectric sensors have been widely used for structural health monitoring applications. This is due to their wide bandwidth, versatility, simplicity, high rigidity, high stability, high reproducibility, fast response time, wide operating temperature range, insensitivity to electric and magnetic fields, the capacity for miniaturization and minimal dependence on moving parts and low power consumption, and wide piezoelectric materials and mechanisms selections, which will greatly benefit the sensing applications. In addition to the temperature usage range, the piezoelectric sensors must withstand the harsh environments encountered in space, engine, power plants, and also need to possess high sensitivity, resistivity, reliability, stability and robustness. In order to use the piezoelectric materials for a specific high temperature application, many aspects need to be considered together with piezoelectric properties, such as phase transition, thermal aging, thermal expansion, chemical stability, electrical resistivity, and the stability of properties at elevated temperature. In this paper, ferroelectric materials with high Curie point, including perovskite-type ferroelectrics, bismuth layer structured ferroelectrics, tungsten-bronze structured ferroelectrics, together with non-ferroelectric piezoelectric single crystals, are surveyed. The crystal structure characteristics, high temperature piezoelectric properties, and recent research progress are discussed. A series of high temperature piezoelectric devices and their applications are reviewed, including high temperature piezoelectric detectors, sensors, transducers, actuators, etc. Finally, recent important research topics, the future development of high temperature piezoelectric materials and the potential new applications are summarized.

Compensation of hysteresis nonlinearities in smart material based actuators presents a challenging task for their applications. Many approaches have been proposed in the literature, including the inverse multiplicative scheme. The advantage for such a scheme is to avoid direct model inversions. However, the approach is mainly developed for the Bouc-Wen model. Focusing on the Preisach model which is utilized to describe magnetostrictive actuators, in this paper an inverse compensation approach for Preisach model using the inverse multiplicative structure is developed. Since the input signal is implicitly involved in the Preisach model, it imposes a great challenge to construct the inverse function of the model. To obtain an explicit expression of the input signal from its implicit form so that the inverse multiplicative technique can be applied, the Preisach model is decomposed into a non-memory part and memory part. Using this separation, it only requires to solve the inverse of the non-memory part to obtain an explicit expression of the input signal, thus avoiding constructing the inverse for entire complex dual integral formulation of the Preisach model. Experimental results for a magnetostrictive actuator demonstrate the effectiveness of the proposed approach.

Piezoelectric actuators have been applied in many research and industrial fields. However, how to improve the working performance of piezoelectric actuators is still a hot issue. Up to now, many new motion principles have been developed for new piezoelectric actuators. The bionic type piezoelectric actuator is a kind of the novel piezoelectric actuators, and it imitates the motion style of different creatures in nature to overcome the limitation of traditional piezoelectric actuators. Bionic type piezoelectric actuators are able to achieve large working stroke or large output force, which is of great significance for the development of piezoelectric actuators. The principle, design, and future of some bionic type piezoelectric actuators are discussed in this chapter.

Consideration of piezoceramic actuator nonlinearity in the active isolation of deterministic vibration

The main purpose of this study is to design a tracking controller for a dual-axes piezoelectric actuated platform. First, a Preisach model is used to numerically describe the hysteresis behavior of piezoelectric actuators. Next, on the basis of the Preisach model, a feed-forward controller is developed to compensate for the hysteresis nonlinearity. Then, a PID controller is introduced to further suppress the tracking error due to the modeling inaccuracy and hence to get precision tracking control. We utilize evolution algorithm to choose three optimality control gain for PID controller. The dual-axes motion control problem for the piezoelectric actuated platform is also investigated. A neural-net based decoupling control scheme is proposed to eliminate the contour error which is typical in dual-axes tracking control problem. The developed approaches are numerically and experimentally verified which demonstrate performance and applicability of the proposed designs under a variety of operating conditions.

Nanorobotics have been successfully applied to investigate the physical and biomedical properties in the nano scale. As the center piece of nanorobotcis Scanning probe microscope (SPM) has been widely used to measure the topography information of sample surface as well as serving as a manipulation and sensing tool to modify and measure the mechanical and physical properties of sample. However, the manipulation accuracy of the SPM based nanorobot has been considered as a serious issue because of the hysteresis, creep and thermal drift of its piezoelectric actuator. Generally, creep is linear, which is easy to model; thermal drift is unpredictable, however, it is slow and has an ultimate balance state, thus easy to reduce. Unlike creep characteristic, hysteresis is nonlinear and exists ubiquitously in smart material actuators and seriously affects behaviors of them. Thus cancelation of it will significantly improve motion precision using actuator such as piezoelectric actuators. In this research, we proposed a novel hysteresis modeling and compensation strategy: Polynomial Prandtl-Ishlinskii (PPI) operator superposition model, and its inverse compensator. The property of PPI model is that, it possesses a similar modeling capacity as Preisach model, more important, it can be represented as compressive as the classical PI model. The PPI inverse compensator is then combined with a PID controller, named PPI Inverse Aided PID (PIA-PID) controller, to reduce the output error caused by hysteresis, creep and some unknown drift of our atomic force microscope (AFM) based nanorobot.

Position control of shape memory alloy actuator based on the generalized Prandtl–Ishlinskii inverse model

This brief investigates a possible application of the inverse Preisach model in combination with the feedforward and feedback control strategies to control shape memory alloy actuators. In the feedforward control design, a fuzzy-based inverse Preisach model is used to compensate for the hysteresis nonlinearity effect. An extrema input history and a fuzzy inference is utilized to replace the inverse classical Preisach model. This work allows for a reduction in the number of experimental parameters and computation time for the inversion of the classical Preisach model. A proportional-integral-derivative (PID) controller is used as a feedback controller to regulate the error between the desired output and the system output. To demonstrate the effectiveness of the proposed controller, real-time control experiment results are presented.

Preisach model has enjoyed extensive applications in describing the hysteresis phenomena. However an important open question in the analysis of hysteresis using Preisach models is the determination of the model parameters. This is to determine the parameter of Preisach function and is referred as the identification problem. However, no general mathematical methods appear to be available for the identification of nonlinear hysteresis system. As a result customized identification algorithms must be developed for each specific area of applications. In order to more closely describe physical systems, it becomes increasingly difficult to compute the Preisach function and its associated parameters from experimental results as the complexity of hysteresis models increases. This paper presents a new approach -- a Wavelet identification of Preisach model. A wavelet can generate a special basis for all functions with finite energy and has some important properties such as orthogonality, symmetry, short support and accuracy. In this application the output of system and the Preisach functions are represented by a series of wavelets. The experiment data is used to determine the coefficients of the base functions. Then the Preisach function and the output of the hysteresis system can be directly calculated by using wavelet methods.

Tactile sensors are basically arrays of force sensors. Most of these force sensors are made of polymers or conductive rubbers to lower the cost, especially in the case of large area low-medium resolution tactile sensors. The price to pay for such decrease in the cost and complexity is a worse performance. Hysteresis and drift are the two main sources of error. This paper presents a method to reduce the error caused by hysteresis. This method is based on the generalized Prandtl- Ishlinskii model that has been applied to characterize hysteresis and saturation nonlinearities in smart actuators. The classical Prandtl-Ishlinskii model is not suitable because the lack of symmetry the output curves from the sensor show. Other alternatives like the Preisach model are too complex to implement, especially taking into account that a tactile sensor provides many data to process. The approximation error depends on several parameters as well as on the envelope functions that are chosen. Different alternatives are explored in the paper. Moreover, the model can also be inverted. This inverted model allows obtaining the force values from the tactile sensor output while reducing the errors caused by hysteresis. Since implementations of tactile sensors usually have the electronics close to the raw sensor, and this hardware is also commonly based on a microcontroller or even on a FPGA, it is possible to add the algorithms presented in this paper to the set of compensation and calibration procedures to run in the smart sensor.

The piezoelectric actuators have high resolution, wide operating frequency and low power consumption, but they suffer hysteresis which affects their linearity. In this paper are presented comparatively the analog and digital techniques for improvement (reducing) of nonlinear behavior of this type of actuators using charge amplifiers. First an analog charge amplifier and its performance analysis are presented. Then a model of digital charge amplifier with linearity performance considerably improved (91% reduced), but which shows a pronounced drift is presented. In the last section several methods for drift reducing are presented and analyzed, one of them having a reduction with 87%. A number of functional diagrams and response graphs for the developed techniques and methods are presented. Introduction The application area of the piezoelectric actuators has been spectacular developed, especially due to their remarkable qualities. Compared to other nano-positioning actuators, these have high resolution, high force, wide operating frequency and low power consumption. It is enough to mention some of their applications [1, 2, 3]: in micro and nano-devices for mechanical positioning with below micrometrics accuracy (optical and electronics microscopy, high precision cutting devices (error correction), robotics and positioning of magnetic heads and optical recordingplayback); in deformable mirrors (adaptive optics systems); in ultrasonic motors; in the impact controlled on/off devices; in fuel injectors of diesel engines etc. But, the piezoelectric materials have important non-linear characteristics determi-ned by the existence of hysteresis and creep, which can reduce the positioning accuracy of a piezoelectric actuator. When it is applied to a piezoelectric actuator a sudden voltage, the length will quickly respond then it will change slowly due to the creep effect. Creep is the polarization result of the piezoelectric actuator which continues to change after the applied voltage reaches its final value. Commonly, this effect is an issue at low frequencies and it is not important for higher frequencies [4]. Hysteresis is another undesired effect: when the input voltage is gradually increased, the actuator displacement is different from when the voltage is decreased for the same voltage value applied. For hysteresis reducing, many techniques have been implemented: the model-based control [5]; the displacement feedback control [6]; the charge control [7]. Without going into details, it is worth mentioning that, none of these techniques do not provide an acceptably hysteresis dimi-nution to allow the piezoelectric actuators to do the very high precisions displacement. In this paper, a model of digital charge amplifier is presented. By this model, a significant reduction of the piezoelectric actuators nonlinear behaviour is obtained. 94 | T h e 3 9 t h A R A P r o c e e d i n g s In the following sections we present this digital model. The analog charge amplifier To make the transition to digital charge amplifier, we present a simple analog charge amplifier in this section. In Figure 1(a) the circuit diagram of this analog charge amplifier is shown. It contains a comparator (Ʃ) and amplifier (K), a stack piezoelectric (SP) with capacity, Cpa, a sensing capacitor with capacitance, CS. R1 is used to model the operational amplifier (OA) input terminal leakage, and R2 is due to the leakage of the sensing capacitor. The circuit feedback loop is used to equalize the reference voltage, Vr, with the actual voltage across the sensing capacitor. If the OA, SP and sensing capacitor would be ideal, R1 and R2 can be removed and ideal Laplace transfer function would be:

Flexure-guided fast tool servo (FTS) driven by piezoelectric actuator (PEA) has the advantages of high accuracy and high speed, which makes it has been widely applied in the microstructure surface processing. Unfortunately, PEA has complicated hysteresis nonlinearity, which will greatly reduce the processing accuracy. The common PID and other traditional control methods are hard to handle complex hysteresis nonlinearity issue. As a classic method of intelligent hysteresis modeling, the traditional artificial neural network (TANN) algorithm can model the hysteresis nonlinearity accurately, however, the high-frequency dynamic hysteresis modeling based on TANN is difficult to be achieved on-line. Therefore, a novel on-line sequential extreme learning machine (OS-ELM) modeling method is proposed in this work. A compound control strategy consists of the OS-ELM model and PID feedback (OSEP) controller is proposed. A series of validation experiments are successfully carried out. The parameter identification results show that the training speed of the OS-ELM model is 836 times faster than that of the TANN model, and the identification accuracy is improved by 475 times. The closed-loop control results show that the positioning accuracy with OS-ELM hysteresis compensation is 13 times higher than with TANN model. It proves that the FTS system can achieve a satisfactory performance (stroke: $\pmb{120}\mu \mathbf{m}$ , average linearity: 0.54%) under high closed-loop bandwidth 200Hz.