Bouc-Wen modeling and inverse multiplicative structure to compensate hysteresis nonlinearity in piezoelectric actuators.

International audienceA new approach to compensate the strong hysteresis nonlinearity in piezoelectric materials is proposed. Based on the inverse multiplicative scheme, the approach avoids models inversion as employed in existing works. The compensator is therefore simple to implement and does not require additional computation as soon as the direct model is available. The proposed compensation technique is valuable for hysteresis that are modeled with the Bouc-Wen set of equations

Modeling, identification and feedforward control of multivariable hysteresis by combining Bouc-Wen equations and the inverse multiplicative structure.

International audienceThis paper deals with the modeling, identification and feedforward control of hysteresis found in multi-degrees of freedom (DOF) piezoelectric actuators. One main characteristic couplings. To express such multivariable hysteresis, we propose to extend the previous Bouc-Wen hysteresis monovariable model used for 1-DOF actuators. Then we propose to combine the resulting multivariable model with the inverse multiplicative structure in order to derive a multivariable compensator that suppresses the direct and the coupling hysteresis. Experimental tests on a piezotube scanner demonstrate the efficiency of the proposed approach

Hysteresis Modeling of Amplified Piezoelectric Stack Actuator for the Control of the Microgripper

This paper presents Bouc-Wen hysteresis modelling and tracking control of piezoelectric stack APA120S. The actuator is used to control a microgripper. A modified Bouc-Wen non-symmetric model is applied to study the behaviour of the system in static and dynamic state. The good agreement between predicted and measured curve showed that the Bouc-Wen model is an effective mean for modelling the hysteresis of piezoelectric actuator system. Subsequently, the inverse Bouc-Wen model is formulated and applied to cancel the non-linear hysteresis. In perspective of a control design, it is desirable to linearize the non-linear Bouc-Wen model to produce a static system. Finally, in order to increase damping of the actuator system and to improve the control accuracy, a cascaded PID controller is designed with consideration of the dynamics and static behaviour of the actuator. Experiment result shows that error is of only 5% if PID is cascaded with hysteresis compensation. Therefore, hysteresis compensation with PID controller greatly improves the micromanipulation accuracy of the microgripper actuated by piezoelectric stack

Modeling and Control of Magnetostrictive-actuated Dynamic Systems

Magnetostrictive actuators featuring high energy densities, large strokes and fast responses appear poised to play an increasingly important role in the field of nano/micro positioning applications. However, the performance of the actuator, in terms of precision, is mainly limited by 1) inherent hysteretic behaviors resulting from the irreversible rotation of magnetic domains within the magnetostrictive material; and 2) dynamic responses caused by the inertia and flexibility of the magnetostrictive actuator and the applied external mechanical loads. Due to the presence of the above limitations, it will prevent the magnetostrictive actuator from providing the desired performance and cause the system inaccuracy. This dissertation aims to develop a modeling and control methodology to improve the control performance of the magnetostrictive-actuated dynamic systems. Through thorough experimental investigations, a dynamic model based on the physical principle of the magnetostrictive actuator is proposed, in which the nonlinear hysteresis effect and the dynamic behaviors can both be represented. Furthermore, the hysteresis effect of the magnetostrictive actuator presents asymmetric characteristics. To capture these characteristics, an asymmetric shifted Prandtl-Ishlinskii (ASPI) model is proposed, being composed by three components: a Prandtl-Ishlinskii (PI) operator, a shift operator and an auxiliary function. The advantages of the proposed model are: 1) it is able to represent the asymmetric hysteresis behavior; 2) it facilitates the construction of the analytical inverse; 3) the analytical expression of the inverse compensation error can also be derived. The validity of the proposed ASPI model and the entire dynamic model was demonstrated through experimental tests on the magnetostrictive-actuated dynamic system. According to the proposed hysteresis model, the inverse compensation approach is applied for the purpose of mitigating the hysteresis effect. However, in real systems, there always exists a modeling error between the hysteresis model and the true hysteresis. The use of an estimated hysteresis model in deriving the inverse compensator will yield some degree of hysteresis compensation error. This error will cause tracking error in the closed-loop control system. To accommodate such a compensation error, an analytical expression of the inverse compensation error is derived first. Then, a prescribed adaptive control method is developed to suppress the compensation error and simultaneously guaranteeing global stability of the closed loop system with a prescribed transient and steady-state performance of the tracking error. The effectiveness of the proposed control scheme is validated on the magnetostrictive-actuated experimental platform. The experimental results illustrate an excellent tracking performance by using the developed control scheme

Hysteresis linearization control of a novel hybrid vibration isolator

The undesired hysteresis exists widely in smart-material actuators, which significantly reduces the accuracy and response speed of the actuators. In this paper, the static experiment of our previously developed hybrid vibration isolator (HVI) employing piezoelectric actuator is implemented to choose appropriate preload of the HVI. The preload-dependent hysteresis of the HVI is also proved in the static experiment. To achieve the hysteresis linearization control of the HVI, two linearization methods named the feedforward linearization and feedforward compensation and PI feedback hybrid linearization control are presented, respectively, which are based on the Bouc-Wen model and corresponding parameter identification model. To evaluate the effectiveness of the proposed linearization controllers for the HVI, the experiments are implemented. The experiment results demonstrate that both linearization controllers for the HVI can linearize the hysteresis characteristics and improve the HVI control accuracy. In addition, the feedforward compensation and PI feedback hybrid linear controller can achieve higher linearity than feedforward compensation controller

Modelling of Hysteresis in Vibration Control Systems by means of the Bouc-Wen Model

The review presents developments concerning the modelling of vibration control systems with hysteresis. In particular, the review focuses on applications of the Bouc-Wen model that describes accurate hysteretic behaviour in vibration control devices. The review consists of theoretical aspects of the Bouc-Wen model, identification procedures, and applications in vibration control

Sliding Mode-Based Robust Control for Piezoelectric Actuators with Inverse Dynamics Estimation

This paper presents an improved control approach to be used for piezoelectric actuators. The proposed approach is based on sliding mode control with estimation perturbation (SMCPE) techniques. Also, a proportional-integral-derivative (PID)-type sliding surface is proposed for position tracking. The proposed approach has been studied and implemented in a commercial actuator. A model for the system is introduced, which includes the Bouc-Wen (BW) model to represent the hysteresis, and it is identified by means of the System Identification Toolbox in Matlab/Simulink. Experimental data show that the proposed controller has a better performance when compared to a proportional-integral (PI) controller or a conventional SMCPE in motion tracking. Furthermore, a sub-micrometer accuracy tracking can be obtained while compensating for the hysteresis effect.This research was partially funded by the Basque Government through the project ETORTEK KK-2017/00033, and by the UPV/EHU through the projects PPGA18/04 and UFI 11/07

Design and control of a 6-degree-of-freedom precision positioning system

This paper presents the design and test of a6-degree-of-freedom (DOF) precision positioning system, which is assembledby two different 3-DOF precision positioning stages each driven by three piezoelectric actuators (PEAs). Based on the precision PEAs and flexure hinge mechanisms, high precision motion is obtained.The design methodology and kinematic characteristics of the6-DOF positioning system areinvestigated. According to an effective kinematic model, the transformation matrices are obtained, which is used to predict the relationship between the output displacement from the system arrangement and the amountof PEAsexpansion. In addition, the static and dynamic characteristics of the 6-DOF system have been evaluated by finite element method (FEM) simulation andexperiments. The design structure provides a high dynamic bandwidth withthe first naturalfrequency of 586.3 Hz.Decoupling control is proposed to solve the existing coupling motion of the 6-DOF system. Meanwhile, in order to compensate for the hysteresis of PEAs, the inverse Bouc-Wen model was applied as a feedforward hysteresis compensator in the feedforward/feedback hybrid control method. Finally, extensive experiments were performed to verify the tracking performance of the developed mechanism

Robust fractional-order fast terminal sliding mode control with fixed-time reaching law for high-performance nanopositioning

Open Access via the Wiley Agreement ACKNOWLEDGEMENTS This work is supported by the China Scholarship Council under Grant No. 201908410107 and by the National Natural Science Foundation of China under Grant No. 51505133. The authors also thank the anonymous reviewers for their insightful and constructive comments.Peer reviewedPublisher PD