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Journal ArticleDOI

Modeling and Control for Giant Magnetostrictive Actuators with Rate-Dependent Hysteresis

16 Sep 2013-Journal of Applied Mathematics (Hindawi)-Vol. 2013, Iss: 2013, pp 1-8

TL;DR: A relevance vector machine (RVM) model is proposed for describing the hysteresis nonlinearity under varying input current and a proportional integral derivative (PID) control scheme combined with a feedforward compensation is implemented on a giant magnetostrictive actuator for real-time precise trajectory tracking.

AbstractThe rate-dependent hysteresis in giant magnetostrictive materials is a major impediment to the application of such material in actuators. In this paper, a relevance vector machine (RVM) model is proposed for describing the hysteresis nonlinearity under varying input current. It is possible to construct a unique dynamic model in a given rate range for a rate-dependent hysteresis system using the sinusoidal scanning signals as the training set input signal. Subsequently, a proportional integral derivative (PID) control scheme combined with a feedforward compensation is implemented on a giant magnetostrictive actuator (GMA) for real-time precise trajectory tracking. Simulations and experiments both verify the effectiveness and the practicality of the proposed modeling and control methods.

Topics: Feed forward (54%), PID controller (52%), Hysteresis (51%)

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Citations
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Journal ArticleDOI
Abstract: The various mathematical models for hysteresis such as Preisach, Krasnosel’skii–Pokrovskii (KP), Prandtl–Ishlinskii (PI), Maxwell-Slip, Bouc–Wen and Duhem are surveyed in terms of their applications in modeling, control and identification of dynamical systems. In the first step, the classical formalisms of the models are presented to the reader, and more broadly, the utilization of the classical models is considered for development of more comprehensive models and appropriate controllers for corresponding systems. In addition, the authors attempt to encourage the reader to follow the existing mathematical models of hysteresis to resolve the open problems.

291 citations


Cites methods from "Modeling and Control for Giant Magn..."

  • ...In [130,131], an inverse model was proposed for magneto-rheological dampers to enhance force tracking control under the effect of nonlinear hysteresis....

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Journal ArticleDOI
TL;DR: A comprehensive model, which thoroughly considers the electric, magnetic, and mechanical domain, as well as the interactions among them, is developed and demonstrates that the comprehensive model presents an excellent agreement with dynamic behaviors of the magnetostrictive actuator.
Abstract: Magnetostrictive actuators featuring high energy densities, large strokes, and fast responses are playing an increasingly important role in micro/nano-positioning applications. However, such actuators with different input frequencies and mechanical loads exhibit complex dynamics and hysteretic behaviors, posing a great challenge on applications of the actuators. Therefore, it is important to develop a dynamic model that can characterize dynamic behaviors of the actuators, including current-magnetic flux nonlinear hysteresis, frequency responses, and loading effects, simultaneously. To this end, a comprehensive model, which thoroughly considers the electric, magnetic, and mechanical domain, as well as the interactions among them, is developed in this paper. To validate the developed model, the parameters of the model are identified where the hysteresis of the magnetostrictive actuator is described, as an illustration, by the asymmetric shifted Prandtl–Ishlinskii model. The experimental results demonstrate that the comprehensive model presents an excellent agreement with dynamic behaviors of the magnetostrictive actuator.

24 citations


Cites background from "Modeling and Control for Giant Magn..."

  • ...Digital Object Identifier 10.1109/TII.2016.2543027 I. INTRODUCTION M AGNETOSTRICTIVE materials are a class of materi-als that change their shape when exposed to an external magnetic field....

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Journal ArticleDOI
Abstract: In controlling nonlinear uncertain systems, compensating for rate-dependent hysteresis nonlinearity is an important, yet challenging problem in adaptive control. In fact, it can be illustrated through simulation examples that instability is observed when existing control methods in canceling hysteresis nonlinearities are applied to the networked control systems (NCSs). One control difficulty that obstructs these methods is the design conflict between the quantized networked control signal and the rate-dependent hysteresis characteristics. So far, there is still no solution to this problem. In this paper, we consider the event-triggered control for NCSs subject to actuator rate-dependent hysteresis and failures. A new second-order filter is proposed to overcome the design conflict and used for control design. With the incorporation of the filter, a novel adaptive control strategy is developed from a neural network technique and a modified backstepping recursive design. It is proved that all the control signals are semiglobally uniformly ultimately bounded and the tracking error will converge to a tunable residual around zero.

17 citations


Journal ArticleDOI
Abstract: The cerebella model articulation controller is used as a feedforward controller to establish a nonlinear inverse model of giant magnetostrictive material (GMM). This controller can eliminate the effect of nonlinear hysteresis response of GMM and realize linear control. A PID feedback control is employed to improve the stability and accuracy of the system. The output of the system can map the target input of the system accurately using the compound controller. An experimental platform was built, and the availability of the compound controller was tested on it. Most of the errors of the controlled system were limited in 6 %.

11 citations


Journal ArticleDOI
Jiang Jinjun, Weijin Gao, Liang Wang1, Teng Zhaohua, Yongguang Liu1 
TL;DR: Active vibration control to suppress structural vibration of the flexible structure is investigated based on a new control strategy considering structure-actuator interaction, and the interaction model based on magnetomechanical coupling is incorporated into the control system.
Abstract: Active vibration control to suppress structural vibration of the flexible structure is investigated based on a new control strategy considering structure-actuator interaction. The experimental system consists of a clamped-free rectangular plate, a controller based on modal control switching, and a magnetostrictive actuator utilized for suppressing the vibrations induced by external excitation. For the flexible structure, its deformation caused by the external actuator will affect the active control effect. Thus interaction between structure and actuator is considered, and the interaction model based on magnetomechanical coupling is incorporated into the control system. Vibration reduction strategy has been performed resorting to the actuator in optimal position to suppress the specified modes using LQR (linear quadratic regulator) based on modal control switching. The experimental results demonstrate the effectiveness of the proposed methodology. Considering structure-actuator interaction (SAI) is a key procedure in controller design especially for flexible structures.

4 citations


References
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Journal ArticleDOI
Michael E. Tipping1
TL;DR: It is demonstrated that by exploiting a probabilistic Bayesian learning framework, the 'relevance vector machine' (RVM) can derive accurate prediction models which typically utilise dramatically fewer basis functions than a comparable SVM while offering a number of additional advantages.
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Proceedings Article
30 Jun 2000
TL;DR: This paper shows how the RVM can be formulated and solved within a completely Bayesian paradigm through the use of variational inference, thereby giving a posterior distribution over both parameters and hyperparameters.
Abstract: The Support Vector Machine (SVM) of Vapnik [9] has become widely established as one of the leading approaches to pattern recognition and machine learning. It expresses predictions in terms of a linear combination of kernel functions centred on a subset of the training data, known as support vectors. Despite its widespread success, the SVM suffers from some important limitations, one of the most significant being that it makes point predictions rather than generating predictive distributions. Recently Tipping [8] has formulated the Relevance Vector Machine (RVM), a probabilistic model whose functional form is equivalent to the SVM. It achieves comparable recognition accuracy to the SVM, yet provides a full predictive distribution, and also requires substantially fewer kernel functions. The original treatment of the RVM relied on the use of type II maximum likelihood (the 'evidence framework') to provide point estimates of the hyperparameters which govern model sparsity. In this paper we show how the RVM can be formulated and solved within a completely Bayesian paradigm through the use of variational inference, thereby giving a posterior distribution over both parameters and hyperparameters. We demonstrate the practicality and performance of the variational RVM using both synthetic and real world examples.

393 citations


"Modeling and Control for Giant Magn..." refers methods in this paper

  • ...The relevance vector machine (RVM) introduced by Tipping [17, 18] is a probabilistic model similar to the support vector machine (SVM), but where the training takes place in a Bayesian framework, and predictive distributions of the outputs instead of point estimates are obtained....

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Journal ArticleDOI
01 Sep 1991
Abstract: A novel technique, directly using artificial neural networks, is proposed for the adaptive control of nonlinear systems. The ability of neural networks to model arbitrary nonlinear functions and their inverses is exploited. The use of nonlinear function inverses raises questions of the existence of the inverse operators. These are investigated and results are given characterising the invertibility of a class of nonlinear dynamical systems. The control structure used is internal model control. It is used to directly incorporate networks modelling the plant and its inverse within the control strategy. The potential of the proposed method is demonstrated by an example.

369 citations


Journal ArticleDOI
TL;DR: This paper introduces SVM's within the context of recurrent neural networks and considers a least squares version of Vapnik's epsilon insensitive loss function related to a cost function with equality constraints for a recurrent network.
Abstract: The method of support vector machines (SVM's) has been developed for solving classification and static function approximation problems. In this paper we introduce SVM's within the context of recurrent neural networks. Instead of Vapnik's epsilon insensitive loss function, we consider a least squares version related to a cost function with equality constraints for a recurrent network. Essential features of SVM's remain, such as Mercer's condition and the fact that the output weights are a Lagrange multiplier weighted sum of the data points. The solution to recurrent least squares (LS-SVM's) is characterized by a set of nonlinear equations. Due to its high computational complexity, we focus on a limited case of assigning the squared error an infinitely large penalty factor with early stopping as a form of regularization. The effectiveness of the approach is demonstrated on trajectory learning of the double scroll attractor in Chua's circuit.

304 citations


Journal ArticleDOI
TL;DR: This paper considers rate-independent and rate-dependent semilinear Duhem models with provable properties with sufficient conditions for convergence to a limiting input-output map.
Abstract: The classical Duhem model provides a finite-dimensional differential model of hysteresis. In this paper, we consider rate-independent and rate-dependent semilinear Duhem models with provable properties. The vector field is given by the product of a function of the input rate and linear dynamics. If the input rate function is positively homogeneous, then the resulting input-output map of the model is rate independent, yielding persistent nontrivial input-output closed curve (that is, hysteresis) at arbitrarily low input frequency. If the input rate function is not positively homogeneous, the input-output map is rate dependent and can be approximated by a rate-independent model for low frequency inputs. Sufficient conditions for convergence to a limiting input-output map are developed for rate-independent and rate-dependent models. Finally, the reversal behavior and orientation of the rate-independent model are discussed.

237 citations