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Control of hysteresis: Theory and experimental results
 IN SMART STRUCTURES AND MATERIALS 2001: MODELING, SIGNAL PROCESSING, AND CONTROL IN SMART STRUCTURES
, 2001
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Approximate inversion of hysteresis: Theory and numerical results
 in Proc. 39th IEEE Conf. Decision and Control
"... In previous work, we had proposed a low (6) dimensional model for a thin magnetostrictive actuator that was suitable for realtime control. One of the main results of this modeling effort was the separation of the rateindependent hysteretic effects from the ratedependent linear effects. The hystere ..."
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Cited by 16 (4 self)
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In previous work, we had proposed a low (6) dimensional model for a thin magnetostrictive actuator that was suitable for realtime control. One of the main results of this modeling effort was the separation of the rateindependent hysteretic effects from the ratedependent linear effects. The hysteresis phenomenon may also be captured by a (modified) Preisach operator with the average magnetic field as the input. If one can find an inverse for the Preisach operator, then the composite system can be approximately linearized. In this paper, we propose a new algorithm for computation of the inverse for the classical Preisach model. Prior approaches depended on the linearization of the operator at the operating point. As numerical differentiation is involved, this approach can cause divergence. Our algorithm does not linearize the Preisach operator, but makes use of its strictly incrementally increasing property. Convergence of the algorithm is proved using the contraction mapping principle. 1
Adaptive Identification and Control of Hysteresis in Smart Materials
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL,VOL
, 2005
"... Abstract—Hysteresis hinders the effective use of smart materials in sensors and actuators. This paper addresses recursive identification and adaptive inverse control of hysteresis in smart material actuators, where hysteresis is modeled by a Preisach operator with a piecewise uniform density functio ..."
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Cited by 14 (1 self)
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Abstract—Hysteresis hinders the effective use of smart materials in sensors and actuators. This paper addresses recursive identification and adaptive inverse control of hysteresis in smart material actuators, where hysteresis is modeled by a Preisach operator with a piecewise uniform density function. Two classes of identification schemes are proposed and compared, one based on the hysteresis output, the other based on the timedifference of the output. Conditions for parameter convergence are presented in terms of the input to the Preisach operator. An adaptive inverse control scheme is developed by updating the Preisach operator (and thus its inverse) with the outputbased identification method. The asymptotic tracking property of this scheme is established, and for periodic reference trajectories, the parameter convergence behavior is characterized. Practical issues in the implementation of the adaptive identification and inverse control methods are also investigated. Simulation and experimental results based on a magnetostrictive actuator are provided to illustrate the proposed approach. Index Terms—Adaptive control, hysteresis, identification, inversion, Preisach operator, smart materials.
Approximate Inversion of the Preisach Hysteresis Operator With Application to Control of Smart
"... Abstract—Hysteresis poses a challenge for control of smart actuators. A fundamental approach to hysteresis control is inverse compensation. For practical implementation, it is desirable for the input function generated via inversion to have regularity properties stronger than continuity. In this pap ..."
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Cited by 12 (0 self)
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Abstract—Hysteresis poses a challenge for control of smart actuators. A fundamental approach to hysteresis control is inverse compensation. For practical implementation, it is desirable for the input function generated via inversion to have regularity properties stronger than continuity. In this paper, we consider the problem of constructing right inverses for the Preisach model for hysteresis. Under mild conditions on the density function, we show the existence and weakstar continuity of the rightinverse, when the Preisach operator is considered to act on Hölder continuous functions. Next, we introduce the concept of regularization to study the properties of approximate inverse schemes for the Preisach operator. Then, we present the fixed point and closestmatch algorithms for approximately inverting the Preisach operator. The convergence and continuity properties of these two numerical schemes are studied. Finally, we present the results of an openloop trajectory tracking experiment for a magnetostrictive actuator. Index Terms—Approximate inversion, closestmatch algorithm, electroactive polymers, fixed point iteration algorithm, hysteresis, magnetostriction, piezoelectricity, Preisach operator, regularization, shape memory alloys, smart actuators.
Control of Smart Actuators
, 2002
"... Hysteresis in smart materials hinders wider applicability of such materials in actuators and sensors. In this dissertation we study modeling, identification and control of hysteresis in smart actuators. While the approaches are applicable to control of a wide class of smart actuators, we illustrate ..."
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Cited by 12 (7 self)
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Hysteresis in smart materials hinders wider applicability of such materials in actuators and sensors. In this dissertation we study modeling, identification and control of hysteresis in smart actuators. While the approaches are applicable to control of a wide class of smart actuators, we illustrate the ideas through the example of controlling a magnetostrictive actuator. Hysteresis exhibited by magnetostrictive actuators is rateindependent when the input frequency is low and we can model it by a Preisach operator. It becomes ratedependent when the input frequency gets high due to the eddy current effect and the magnetoelastic dynamics. In this case, we propose a new dynamic hysteresis model, consisting of a Preisach operator coupled to an ordinary differential equation in an unusual way. We establish its wellposedness and study its various systemtheoretic properties. Existence of periodic solutions under periodic forcing is proved. Algorithms for simulation of the model are also studied. Parameter identification methods for both the Preisach operator and the dynamic model are investigated.
Control of hysteresis in smart actuators with application to micropositioning
, 2005
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Modeling and Control of a Magnetostrictive Actuator
, 2002
"... The ratedependent hysteresis existing in magnetostrictive actuators presents a challenge in control of these actuators. In this paper we propose a novel dynamical model for the hysteresis based on the work of Venkataraman and Krishnaprasad. The model features the coupling of the Preisach operator w ..."
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Cited by 3 (1 self)
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The ratedependent hysteresis existing in magnetostrictive actuators presents a challenge in control of these actuators. In this paper we propose a novel dynamical model for the hysteresis based on the work of Venkataraman and Krishnaprasad. The model features the coupling of the Preisach operator with an ordinary differential equation. We prove the wellposedness of the model and study identification methods for the model. An inverse control scheme is developed based on the dynamical model. The effectiveness of the identification and inverse control schemes is demonstrated through experimental results.
Control of hysteresis in smart actuators, Part I: Modeling, parameter identification, and inverse control
, 2002
"... Hysteresis in smart actuators presents a challenge in control of these actuators. A fundamental idea to cope with hysteresis is inverse compensation. In this paper we study modeling, identification and inverse control of hysteresis in smart actuators through the example of controlling a commercially ..."
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Cited by 2 (1 self)
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Hysteresis in smart actuators presents a challenge in control of these actuators. A fundamental idea to cope with hysteresis is inverse compensation. In this paper we study modeling, identification and inverse control of hysteresis in smart actuators through the example of controlling a commercially available magnetostrictive actuator. The (rateindependent) Preisach operator has been used extensively to model the hysteresis in smart actuators. We present efficient inversion algorithms for the Preisach operator that are implementable in realtime. The magnetostrictive hysteresis is ratedependent at high frequencies. For this we propose a novel dynamic hysteresis model by coupling a Preisach operator to an ordinary differential equation. This model can capture the dynamic and hysteretic behavior of the magnetostrictive actuator, and it provides insight into modeling of ratedependent hysteresis in other smart materials. The effectiveness of the identification and inverse control schemes is demonstrated through extensive experimental results.
MODELING AND CONTROL OF MAGNETOSTRICTIVE ACTUATORS
"... Most smart actuators exhibit ratedependant hysteresis when the working frequency is higher than 5Hz. Although the Preisach model has been a very powerful tool to model the static hysteresis, it cannot be directly used to model the dynamic hysteresis. Some researchers have proposed various generaliz ..."
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Cited by 1 (0 self)
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Most smart actuators exhibit ratedependant hysteresis when the working frequency is higher than 5Hz. Although the Preisach model has been a very powerful tool to model the static hysteresis, it cannot be directly used to model the dynamic hysteresis. Some researchers have proposed various generalizations of the Preisach operator to model the ratedependant hysteresis, however, most of them are applicationdependant and only valid for low frequency range. In this thesis, a firstorder dynamic relay operator is proposed. It is then used to build a novel dynamic Preisach model. It can be used to model general dynamic hysteresis and is valid for a large frequency range. Real experiment data of magnetostrictive actuator is used to test the proposed model. Experiments have shown that the proposed model can predict all the static major and minor loops very well and at the same time give an accurate prediction for the dynamic hysteresis loops. The controller design using the proposed model is also studied. An inversion algorithm is developed and a PID controller with inverse hysteresis compensation is proposed and tested through simulations. The results show that the PID controller with