This paper is concerned with multivariable coupled hysteretic systems. The traditional Bouc-Wen monovariable hysteresis model devoted to 1 degree of freedom (DoF) actuated systems is extended to model the hysteresis in systems with multiple DoF, which typify strong cross-couplings. The proposed approach is able to model and to compensate for known hysteresis nonlinearities that affect smart materials. First, after presenting the new multivariable hysteresis Bouc-Wen model, a procedure of identification of its parameters is proposed. Then, we propose a multivariable compensator for the hysteresis. The compensator is based on the combination of the inverse multiplicative structure with the model, which permits to avoid additional calculation of its parameters. Such advantage is essential when the number of DoF is high. All along this paper, the cases of underactuated, overactuated, and fully actuated hysteretic systems are discussed. Finally, the proposed method is used to model and to compensate for the hysteresis in a 3-DoF piezoelectric tube actuator. The experimental results demonstrate its efficiency to linearize the hysteresis in the direct transfers and to minimize the hysteresis of the cross-couplings.Index Terms-Classical Bouc-Wen approach, compensation, inverse multiplicative structure, monovariable and multivariable hysteresis, piezoelectric actuators, smart materials, static or rate-independent hysteresis. 1063-6536

The present work deals with the application of coevolutionary algorithms and artificial neural networks to perform input selection and related parameter estimation for nonlinear black-box models in system identification. In order to decouple the resolution of the input selection and parameter estimation, we propose a problem decomposition formulation and solve it by a coevolutionary algorithm strategy. The novel methodology is successfully applied to identify a magnetorheological damper, a continuous polymerization reactor and a piezoelectric robotic micromanipulator. The results show that the method provides valid models in terms of accuracy and statistical properties. The main advantage of the method is the joint input and parameter estimation, towards automating a tedious and error prone procedure with global optimization algorithms.

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In the literature, the generalized Bouc-Wen model can track precisely asymmetric hysteresis nonlinearity. In this paper, we propose to extend this generalized model to multivariable hysteresis model that can track the nonlinearities in multi-degrees of freedom (multi-DoF) hysteretic actuated systems. In particular, these systems are typified by strong hysteresis couplings. Then, a method of identification of the multivariable hysteresis model is proposed. Finally, based on the inverse multiplicative structure, we propose a multivariable feedforward compensator of the nonlinearity. The proposed approach has been applied to a multi-DoF piezoelectric tube (piezotube) used in scanning probe microscopy and the experimental verification demonstrated its validity in terms of model precision and compensation efficiency.

This paper presents the control of a two degrees of freedom (2-DOF) piezoelectric actuator that exhibits hysteresis nonlinearity, creep nonlinearity, badly damped vibration and cross-couplings without using feedback sensors. The principle consists in compensating first the hysteresis, then the creep and finally the vibration. The proposed compensation technique is multivariable and therefore is also able to reduce the crosscouplings which are unwanted phenomena. The experimental tests demonstrate that the hysteresis which initially exceeds 19% is reduced to about 0.01% while the creep is reduced from 5.5% to 0.04%. Regarding the vibration, the related overshoot which was initially 45% is completely removed.Note to Practitioners This paper describes an approach to control and to automate dexterous precise positioning systems based on multi-axes piezoelectric actuators. Two problems have motivated the approach investigated in the paper: i) the presence of nonlinearities (hysteresis and creep), of badly damped vibration and of cross-couplings in the multi-axes piezoelectric actuators, ii) and the lack of convenient sensors to feedback control them. Therefore, this paper proposes multivariable and complete feedforward control approach that does not require external sensors. This sensor-less control architecture permits a low cost and a high integration features additionally to the fact that it is of great interest in applications at small scales where implementation of real-time measurement system is often difficult.

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This paper deals with the characterization, the modeling and the closed-loop control of multivariable piezoelectric actuators, with an application to a 3-DOF piezoelectric tube scanner, widely used in precise positioning. These actuators are typified by hysteresis and creep nonlinearities, badly damped oscillation and strong couplings between their axis. First, during the modeling, we propose to decouple the system and to use a linear model where the couplings and the two nonlinearities are integrated through an external fictive disturbance. From the obtained monovariable systems, monovariable H ∞ controllers are calculated by using specifications based on model approximation. The experimental tests demonstrate the efficiency of the method to reject simultaneously the couplings, hysteresis, creep and badly damped oscillations. Furthermore, the bandwidth of the closed-loop and the open-loop systems are compared and the results show that the proposed control technique allows to achieve a convenient closed-loop bandwidth and precision for all the axis of the precise positioner.