Hysteresis In Piezoelectric Actuators Research Articles

A modified Preisach model and its inversion for hysteresis compensation in piezoelectric actuators

Purpose– Piezoelectric actuators (PEAs) exhibit hysteresis nonlinearity in open-loop operation, which may lead to unwanted inaccuracy and limit system performance. Classical Preisach model is widely used for representing hysteresis but it requires a large number of first-order reversal curves to ensure the model accuracy. All the curves may not be obtained due to the limitations of experimental conditions, and the detachment between the major and minor loops is not taken into account. The purpose of this paper is to propose a modified Preisach model that requires relatively few measurements and that describes the detachment, and then to implement the inverse of the modified model for compensation in PEAs.Design/methodology/approach– The classical Preisach model is modified by adding a derivative term in parallel. The derivative gain is adjusted to an appropriate value so that the measured and predicted hysteresis loops are in good agreement. Subsequently, the new inverse model is similarly implemented by adding another derivative term in parallel with the inverse classical Preisach model, and is then inserted in open-loop operation to compensate the hysteresis. Tracking control experiments are conducted to validate the compensation.Findings– The hysteresis in PEAs can be accurately and conveniently described by using the modified Preisach model. The experimental results prove that the hysteresis effect can be nearly completely compensated.Originality/value– The proposed modified Preisach model is an effective and convenient mean to characterize accurately the hysteresis. The compensation method by inserting the inverse modified Preisach model in open-loop operation is feasible in practice.

Iterative Learning Control of Hysteresis in Piezoelectric Actuators

We develop convergence criteria of an iterative learning control on the whole desired trajectory to obtain the hysteresis-compensating feedforward input in hysteretic systems. In the analysis, the Prandtl-Ishlinskii model is utilized to capture the nonlinear behavior in piezoelectric actuators. Finally, we apply the control algorithm to an experimental piezoelectric actuator and conclude that the tracking error is reduced to 0.15% of the total displacement, which is approximately the noise level of the sensor measurement.

1D33 A Neural-Preisach Model for Hysteresis Control of Piezoelectric Actuators(The 12th International Conference on Motion and Vibration Control)

Piezoelectric actuators have been widely applied in micro-positioning devices. The hysteresis nonlinearity of piezoelectric materials degrades the control accuracy. To improve the system performance, modern controllers are designed with a mathematical model which can describe the hysteresis behavior. Preisach model is the most popular model in hysteresis modeling, and it can precisely describe the hysteresis of piezoelectric actuators. But classic Preisach model needs a large quantity of weight parameters to achieve more accuracy, which complicates the model identification and controller design. Neural network has a lot of successful applications in system identification, and its weight parameters are easy to be identified with available training algorithm, but it cannot describe multi-valued mapping of hysteresis. A neural-Preisach model is proposed for modeling and control of piezoelectric actuators. The neural-Preisach model inherits the advantages of Preisach model and neural network, which can describe the hysteresis and update parameters by training algorithm. An inverse controller was designed with the inverse neural-Preisach model, and then experiments of tracking control were performed to validate the effectiveness of the neural-Preisach model. The maximal error is reduced by 74.50%, compare in case without control. This indicates that control accuracy with hysteresis compensation is greatly improved compared to that without hysteresis compensation.

Inverse compensation for hysteresis in piezoelectric actuator using an asymmetric rate-dependent model

This paper presents a modified Bouc-Wen model for asymmetric rate-dependent hysteresis in piezoelectric actuator. On this basis, we develop a new digital inverse controller with a simple structure cascaded in the feedforward path for piezoelectric actuator. In order to eliminate modeling errors and parameter uncertainties, the developed inverse controller is combined with a feedback loop to establish a hybrid control scheme. In our experiments, the proposed model together with the developed hybrid control scheme has shown significantly reduced tracking errors caused by asymmetric rate-dependent hysteresis in piezoelectric actuator.

Modeling and Control with Hysteresis of Piezoelectric Smart Materials Actuators

Hysteresis hinders the effective use of piezoelectric smart materials in sensors and actuators. This paper proposes a hybrid model that can precisely portray hysteresis in piezoelectric actuators, which is constructed by a preisach operator with a piecewise uniform density function. Then, the corresponding inverse model for hysteresis is developed. It studies online recursive identification of hysteresis drift. Based on the obtained models, a method for simultaneous compensation of the hysteresis of piezoelectric actuator is applied to the control of system nonlinearities. Simulation and experimental results based on an IPMC actuator are provided to illustrate the proposed approach. The result verified the validity of the model and effectiveness of the controller.

Improved charge amplifier using hybrid hysteresis compensation

We present a novel charge amplifier, with a robust feedback circuit and a method for compensating piezoelectric actuator's hysteresis at low frequencies. The amplifier uses a modified feedback circuit which improves robustness to the addition of series load impedance such as in cabling. We also describe a hybrid hysteresis compensation method for enabling the charge amplifier to reduce hysteresis at low frequencies. Experimental results demonstrate the utility of the new amplifier design.

Simulation and experimental analysis for hysteresis behavior of a piezoelectric actuated micro stage using modified charge system search

The main goal of this study is to investigate the hysteresis behavior of a piezoelectric actuated micro stage. The hysteresis of piezoelectric actuators (PA) is formulated using the generalized Duhem model (GDM) and a modified charge system search (CSS) is proposed to identify the hysteresis model. Different from the present CSS method, the proposed method applies a construction factor to prevent converging to a local optimum. The modified CSS is used to evaluate the parameters of the GDM to compare with the particle swarm optimization (PSO). The use of MCSS-based optimization is superior to the CSS and the PSO for identification of the GDM. The experimental result also validated the modeling correctness using the proposed method.

Motion Control of a Redundant Flexure Based Mechanism Using Piezoelectric Actuators

A 3-PRR flexure based mechanism which is used as a redundant mechanism providing only x-y micro positioning is designed and controlled in this paper. The aim of this work is to eliminate the unpredictable motions due to manufacturing and assembling errors by implementing sliding mode control (SMC) with disturbance observer (DOB) using piezoelectric actuator models. The system is designed to be redundant to enhance the position control. In order to see the effects of the redundant system firstly the closed loop control is implemented for 2 piezoelectric actuators and the remainder piezoelectric actuator is treated as a fixture. Then the position control is implemented for 3 piezoelectric actuators. As a result, our redundant mechanism tracks the desired trajectory accurately and its workspace is bigger. Finally we have compared the proposed position control with the conventional PID control. It is seen that SMC with DOB gives better results. We have achieved to make the position control of our mechanism, which has unpredictable position errors due to rough manufacturing, assembly, piezoelectric actuator hysteresis etc. The designed 3-PRR flexure mechanism can be used as a micro positioner with the available measurement in the laboratory.

A simple fuzzy system for modelling of both rate-independent and rate-dependent hysteresis in piezoelectric actuators

In this paper, a novel fuzzy system based method for modelling both rate-independent and rate-dependent hysteresis in the piezoelectric actuator is proposed. First, the partial Takagi–Sugeno (T–S) fuzzy rule is designed. The antecedent structure of the fuzzy system is identified through uniform partition of its input variable. Then, the parameters of the consequent structure are optimized via the recursive least squares (RLS) algorithm. The modelling method is simple to implement and highly efficient to compute. Experimental results show that the proposed method is efficient to model both rate-independent and rate-dependent hysteresis. Based on the inverse of the developed model, feed-forward hysteresis compensation experiments at the frequencies of 50Hz and 100Hz are also conducted with the hysteresis effects being obviously reduced. The major contribution of this paper is that the inverse of the model can be analytically computed and the method can be applied to the case of real-time on-line modelling.

Modeling of hysteresis in piezoelectric actuator based on adaptive filter

A novel adaptive transversal filter modeling is presented for the hysteresis characteristic in PEA (piezoelectric actuator). First, the hysteresis modeling capability of delay operator based adaptive transversal filter is explored. On this basis, delay operators of adaptive transversal filter are replaced with Backlash operators to compose a new serial structure of adaptive transversal filter model, and LMS (least mean square) algorithm is used to adjust the weight values. And then, as LMS algorithm brings a serious confrontation of the convergence speed and steady-state offset, a new improved adaptive method focus on the convergence factor is brought in. The new filter with this improved algorithm makes the contradiction of convergence speed and steady-state offset could be unified to some extent. At last, the two adaptive transversal filters are applied to model for hysteresis characteristic of PEA, and the modeling effect is verified via a micro-positioning system experiment platform based on PEA. Experimental results show that the proposed Backlash operator based adaptive filter can achieve accurate hysteresis modeling, and the effectiveness of the improved adaptive algorithm is also demonstrated.

Ultra-precise tracking control of piezoelectric actuators via a fuzzy hysteresis model

In this paper, a novel Takagi-Sugeno (T-S) fuzzy system based model is proposed for hysteresis in piezoelectric actuators. The antecedent and consequent structures of the fuzzy hysteresis model (FHM) can be, respectively, identified on-line through uniform partition approach and recursive least squares (RLS) algorithm. With respect to controller design, the inverse of FHM is used to develop a feedforward controller to cancel out the hysteresis effect. Then a hybrid controller is designed for high-performance tracking. It combines the feedforward controller with a proportional integral differential (PID) controller favourable for stabilization and disturbance compensation. To achieve nanometer-scale tracking precision, the enhanced adaptive hybrid controller is further developed. It uses real-time input and output data to update FHM, thus changing the feedforward controller to suit the on-site hysteresis character of the piezoelectric actuator. Finally, as to 3 cases of 50 Hz sinusoidal, multiple frequency sinusoidal and 50 Hz triangular trajectories tracking, experimental results demonstrate the efficiency of the proposed controllers. Especially, being only 0.35% of the maximum desired displacement, the maximum error of 50 Hz sinusoidal tracking is greatly reduced to 5.8 nm, which clearly shows the ultra-precise nanometer-scale tracking performance of the developed adaptive hybrid controller.

Novel models for one-sided hysteresis of piezoelectric actuators

The hysteretic behavior of a plant with a non-negative input, referred to as one-sided hysteresis, is characterized by an initial ascending curve and hysteresis loops. It is observed that the widely-used classical Preisach hysteresis model and its modifications cannot represent such one-sided hysteresis due to the limitation of the Preisach hysteresis operator. To address this issue, a novel hysteresis operator modified from the Preisach hysteresis operator is proposed in this study and on this basis, a rate-independent hysteresis model and a rate-dependent hysteresis model are developed with methods to estimate their parameters. An algorithm to invert the rate-independent hysteresis model and its application to tracking control are also presented. The models and control schemes developed were verified experimentally on a commercially-available piezoelectric actuator. The results obtained show that the models developed are promising to represent the one-sided hysteresis of the piezoelectric actuator and that the inverting algorithm of the rate-independent hysteresis model is effective as applied to the tracking control of piezoelectric actuators.

MODELLING AND CONTROL OF A KIND OF PARALLEL MECHANISM DRIVEN BY PIEZOELECTRIC ACTUATORS

We describe a micro-operating mechanism for a human-scale teleoperating system. The Bouc-Wen model was used to describe the hysteresis in piezoelectric actuators and parameters were identified to characterize the hysteresis using a genetic algorithm. To improve the performance of the system, a model reference adaptive controller was designed based on the Lyapunov stability theory. Both numerical simulations and experimental results imply that the controller was effective in eliminating the hysteresis in the piezoelectric actuators.

Using output voltage of charge drivers to reduce hysteresis of piezoelectric actuators

Proposed is a new method to reduce the hysteresis of piezoelectric actuators. A reference piezoelectric actuator driven by a charge controller was used to obtain the driving voltage, which was applied to a target actuator via a suitable voltage amplifier. Experiments showed that a reduction of 84–90% at frequencies from 0.05 to 10 Hz was obtained compared with the direct voltage drive method. This method has the ability of affording very high voltage for bulk piezoelectric actuators to reach maximum elongation, and an easy common ground wiring which is feasible for practical piezoelectric element driving circuits, compared with the traditional charge drive for eliminating piezoelectric element's hysteresis.

Hysteresis in Piezoelectric Actuators: Modeling and Compensation

AbstractPiezoelectric stack actuators are characterized by their high resolution and precision in micro and nanometric displacements, being capable of very fast responses and reaching bandwidth ranges in the order of kHz. Consequently, these actuators are extensively used both for positioning and active vibration damping in demanding applications such as SPM (Scanning Probe Microscopy), AFM (Atomic Force Microscopy) or manufacturing systems for MEMS (Micro-Electro-Mechanical Systems). However, piezoelectric materials and actuators suffer from two important drawbacks, which have to be taken into account for effectively reaching the highest combination of precision and speed: hysteresis and rate dependence. In this paper, we describe a framework for modeling stack-based piezoelectric actuators using a Bond-Graph representation. The model considers the hysteresis nonlinearity and the rate-dependence, taking into account both direct and inverse piezoelectric effects. Based on this representation, and on the variation of the effective electrical capacitance of the actuator due to the hysteresis phenomenon, a compensation strategy is developed. Experimental results obtained with amplified piezoelectric actuators are introduced for validating the model, the identification strategy and the benefits of the proposed compensation algorithm in comparison with previously reported work in the literature.

Tracking control of piezoelectric actuator system using inverse hysteresis model

The intrinsic hysteresis behavior of piezoelectric materi al limits the tracking control accuracy of the actuators. Th is paper describes a tracking control method for piezoelectric actuators based on the combination of feedforward and feedback loops. The hysteresis of piezoelectric actuators is linear ized in feedforward loop with an inverse hysteresis model based on a neural network. The number of parameters in the neural network based inverse model is relatively small and the parameters are easy to identify. The feedback loop is used to reduce the accumulated error produced by the inverse hysteresis model. The experimental results show that the accuracy is significantl y improved in tracking control by using the combination of feedback and feedforward control.

Modeling of rate-dependent hysteresis in piezoelectric actuators using a family of ellipses

Abstract In this paper, a new ellipse-like mathematic model is proposed to describe the rate-dependent hysteresis in piezoelectric actuators. Since the expressions of the model are completely analytical and can be determined only by a set of parameters, this method simplifies the modeling of complicated hysteresis behaviors. To represent the hysteresis effects, experiments are performed with designed sinusoidal excitations under different frequencies in the range 0.5–300 Hz. The rate-dependent hysteresis is characterized as increasing maximum hysteresis error (MHE) and decreasing peak-to-peak output amplitude (PPOA) phenomenons with the increase of input frequencies. Then, the parameters of the developed model are extracted from the experimental data using the direct least square method through MATLAB offline. The simulation results well correspond to the measured data and demonstrate that the developed model can precisely predict the rate-dependent hysteresis. We also investigate the parameters’ properties with hysteresis characteristics. In the developed model, the length of the minor radius describes the MHE varying with the input frequencies and amplitudes, while the length of major radius and the orientation of the ellipses represent the decreasing PPOA phenomenon. Finally, a real-time feedforward controller with an inverse model is designed to compensate for the rate-dependent hysteresis under different input frequencies. The experimental results show that the hysteresis effects are obviously reduced at both the lower and higher frequencies.

Switched capacitor charge pump reduces hysteresis of piezoelectric actuators over a large frequency range

Piezoelectric actuators exhibit large hysteresis between the applied voltage and their displacement. A switched capacitor charge pump is proposed to reduce hysteresis and linearize the movement of piezoelectric actuators. By pumping the same amount of charges into the piezoelectric actuator quantitatively, the actuator will be forced to change its length with constant step. Compared with traditional voltage and charge driving, experimental results demonstrated that the piezoelectric stack driven by the charge pump had less hysteresis over a large frequency range, especially at ultralow frequencies. A hysteresis of less than 2.01% was achieved over a frequency range of 0.01-20 Hz using the charge pump driver.

High-speed tracking control of piezoelectric actuators using an ellipse-based hysteresis model

In this paper, an ellipse-based mathematic model is developed to characterize the rate-dependent hysteresis in piezoelectric actuators. Based on the proposed model, an expanded input space is constructed to describe the multivalued hysteresis function H[u](t) by a multiple input single output (MISO) mapping Gamma:R(2)-->R. Subsequently, the inverse MISO mapping Gamma(-1)(H[u](t),H[u](t);u(t)) is proposed for real-time hysteresis compensation. In controller design, a hybrid control strategy combining a model-based feedforward controller and a proportional integral differential (PID) feedback loop is used for high-accuracy and high-speed tracking control of piezoelectric actuators. The real-time feedforward controller is developed to cancel the rate-dependent hysteresis based on the inverse hysteresis model, while the PID controller is used to compensate for the creep, modeling errors, and parameter uncertainties. Finally, experiments with and without hysteresis compensation are conducted and the experimental results are compared. The experimental results show that the hysteresis compensation in the feedforward path can reduce the hysteresis-caused error by up to 88% and the tracking performance of the hybrid controller is greatly improved in high-speed tracking control applications, e.g., the root-mean-square tracking error is reduced to only 0.34% of the displacement range under the input frequency of 100 Hz.

A modified prandtl-ishlinskii model for modeling asymmetric hysteresis of piezoelectric actuators

Piezoelectric actuators can offer high resolution of displacement and this makes them suitable for precise driving tasks. However, most piezoelectric actuators are made of piezoceramics which have a major drawback related to their natural hysteresis nonlinearity. To compensate the hysteresis nonlinearity of piezoelectric actuators, many hysteresis models have been proposed such as the Preisach model, the classical Prandtl-Ishlinskii model, and so on. This paper provides a new approach to model the asymmetric hysteresis nonlinearity of piezoelectric actuators. Unlike the classical Prandtl-Ishlinskii model, the proposed model is based on a combination of two asymmetric operators which can independently simulate the ascending branch and descending branch of hysteresis. Moreover, the proposed model can be calculated using the recursive least-squares method and this makes the model easy and convenient to be calculated. The validity of the proposed model is demonstrated by comparing its simulation results with experimental measurements. The results show that the proposed model is capable of modeling asymmetric hysteresis of piezoelectric actuators with very high accuracy.