Identification of Preisach-Type Hysteresis Operators

Koutný, Jan; Kružík, Martin; Kurdila, Andrew J.; Roubíček, Tomáš

doi:10.1080/01630560701872730

Cited by 6 publications

(7 citation statements)

References 15 publications

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“…General considerations regarding this class of integral operators can be found in [31] or [32]. The particular form of the integral operator used in this formulation is based on [33], a generalized play operator.…”

Section: History Dependent Aerodynamic Modelmentioning

confidence: 99%

Adaptive control for flapping wing robots with history dependent, unsteady aerodynamics

Dadashi

Feaster

Bledt

et al. 2015

2015 American Control Conference (ACC)

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This paper derives a history dependent formulation of the equations of motion of a flapping wing, groundbased robotic system and constructs an associated adaptive control strategy to track observed flapping motions in insect flight. A general methodology is introduced in which lift and drag forces are represented in terms of history dependent integral operators to model and identify the unknown and unmeasurable aerodynamic loading on the flapping wing robot. The resulting closed loop system constitutes an abstract Volterra integral equation whose state consists of the finite-dimensional vector of generalized coordinates for the robotic system and an infinite dimensional unknown function characterizing the kernel of the history dependent integral operator. Finite dimensional approximations of the state equations are derived via quadrature formula and finite element methods. These approximations yield history dependent equations that evolve in euclidean space. An adaptive control scheme based on passivity principles is derived for the approximate history dependent system. Lyapunov analysis guarantees stability of the closed loop system and that the tracking error and its derivative converge to zero. The novel control strategy introduced in this paper is noteworthy in that by introducing a history dependent adjoint operator in the state estimate equation, the analysis for convergence of the closed loop history dependent equations closely resembles the analysis used for conventional ODE systems.

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Section: History Dependent Aerodynamic Modelmentioning

confidence: 99%

Adaptive control for flapping wing robots with history dependent, unsteady aerodynamics

Dadashi

Feaster

Bledt

et al. 2015

2015 American Control Conference (ACC)

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“…It should be mentioned that whenever the rate of input u(t) change sign, the value of memory variable ξ p (t), depending on the kernel k p , is updated. As mentioned formerly, time continuity of an operator is very important for physical considerations, while the parametric continuity is just useful for designing well-posed identification methodologies [19]. It was proved in [20] that for a fixed input ] , 0 [ ) (…”

Section: Krasnosel'ski-pokrovkii (Kp) Hysteresis Modelmentioning

confidence: 99%

“…3). It is reasonable to consider μ(p 1 ,p 2 )≥0 which will automatically ensure monotone output on monotone input, provided r(x) is nondecreasing [19]. It should be mentioned here that since every KP kernels can be expressed an integration of infinite weighted Preisach relays, the KP kernel provides more information of the nonlinearity than the Preisach operator.…”

Section: Krasnosel'ski-pokrovkii (Kp) Hysteresis Modelmentioning

confidence: 99%

“…Along with the set of Preisach operators is an arbitrary weight function, called the Preisach Density Function (PDF), which works as a local influence of each operator in overall hysteresis model. The time continuity of an operator is important for physical considerations, while the parametric continuity is important for designing well-posed identification methodologies [19]. However, the kernel of the Preisach operator has no continuity in time space or in parameter space.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Characterizing Hysteresis Nonlinearity Behavior of SMA Actuators by Krasnosel’skii-Pokrovskii Model

Zakerzadeh¹,

Salarieh²,

Zanjani³

2012

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Krasnosel'skii-Pokrovskii (KP) model is one of the great operator-based phenomenological models which is used in modeling hysteretic nonlinear behavior in smart actuators. The time continuity and the parametric continuity of this operator are important and valuable factors for physical considerations as well as designing well-posed identification methodologies. In most of the researches conducted about the modeling of smart actuators by KP model, especially SMA actuators, only the ability of the KP model in characterizing the hysteretic behavior of the actuators is demonstrated with respect to some specified experimental data and the accuracy of the developed model with respect to other data is not validated. Therefore, it is not clear whether the developed model is capable of predicting hysteresis minor loops of those actuators or not and how accurate it is in this prediction task. In this paper the accuracy of the KP model in predicting SMA hysteresis minor loops as well as first order ascending curves attached to the major hysteresis loop are experimentally validated, while the parameters of the KP model has been identified only with some first order descending reversal curves attached to the major loop. The results show that, in the worst case, the maximum of prediction error is less than 18.2% of the maximum output and this demonstrates the powerful capability of the KP model in characterizing the hysteresis nonlinearity of SMA actuators.

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“…Operator-based hysteresis models in the phenomenological hysteresis models describe the nonlinearity by weighted superposition of elementary hysteresis operators with simple mathematical forms. The typical operator-based hysteresis models are the relay operator of the Preisach model [10,[19][20][21][22], the KP kernel of the Krasnoselskii-Pokrovskii model [7,23], and the play/stop operator of the Prandtl-Ishlinskii model [24][25][26][27][28]. The disadvantages of the operator-based hysteresis models are the characteristics of the model, including symmetry and saturation, depend on the elementary hysteresis operator.…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Hysteresis Modeling Approach Featuring “Inertial System + Shape Function” for Magnetostrictive Actuators

Bai

Qian

2020

Materials

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Hysteresis of the actuators based on magnetostrictive materials influences the control performance of the application systems. It is of importance and significance to establish an effective hysteresis model for the magnetostrictive actuators for precision engineering. In this paper, based on the analysis of the Duhem model, a first-order inertial system with hysteresis characteristic under harmonic input is used to describe the hysteresis caused by the inertia of the magnetic domains of magnetostrictive materials. Shape function is employed to describe the pinning of domain walls, the interactions of different magnetic domains of magnetostrictive materials, and the saturation properties of the hysteresis. Specifically, under an architecture of “inertial system + shape function” (ISSF-Duhem model), firstly a new hysteresis model is proposed for magnetostrictive actuators. The formulation of the inertial system is constructed based on its general expression, which is capable of describing the hysteresis characteristics of magnetostrictive actuators. Then, the developed models with a Grompertz function-based shape function, a modified hyperbolic tangent function-based shape function employing an exponential function as an offset function, a one-sided dead-zone operator-based shape function are compared with each other, and further compared with the classic modified Prandtl–Ishlinskii model with a one-sided dead-zone operator. Sequentially, feasibility and capability of the proposed hysteresis model are verified and evaluated by describing and predicting the hysteresis characteristics of a commercial magnetostrictive actuator.

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Identification of Preisach-Type Hysteresis Operators

Cited by 6 publications

References 15 publications

Adaptive control for flapping wing robots with history dependent, unsteady aerodynamics

Adaptive control for flapping wing robots with history dependent, unsteady aerodynamics

Characterizing Hysteresis Nonlinearity Behavior of SMA Actuators by Krasnosel’skii-Pokrovskii Model

Asymmetric Hysteresis Modeling Approach Featuring “Inertial System + Shape Function” for Magnetostrictive Actuators

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