Differential Models of Hysteresis

Visintin, Augusto

doi:10.1007/978-3-662-11557-2

Cited by 896 publications

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“…For more details on this subject we refer to Visintin [20]. Let us consider a continuous input u : [0, +∞[→ R, a discontinuous output w : [0, +∞[→ {−1, 1}, and two different thresholds for the values of u, let us say ρ 1 and ρ 2 , with ρ 1 < ρ 2 , for which w respectively switches "down" from +1 to −1, and "up" from −1 to +1.…”

Section: On the Thermostat And Thermostatic Dynamicsmentioning

confidence: 99%

“…We then consider a discount factor λ > 0; two delayed relays defined as described in Section 2: 20) where ρ := (ρ 1 , ρ 2 ) and η := (η 1 , η 2 ); and the following controlled thermostatic dynamic system:…”

Section: The Optimal Bi-thermostatic Problemmentioning

confidence: 99%

“…In particular, if u(t) > ρ 2 (respectively u(t) < ρ 1 ) then w(t) = 1 (respectively w(t) = −1), otherwise, i. e. if ρ 1 ≤ u(t) ≤ ρ 2 , the value of w depends on the past evolution of u (see Figure 1). We refer the reader to the next section for more details on the delayed thermostat and to the book by Visintin [20] (and to the references therein), for the general theory of the mathematical models for hysteresis phenomena.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Infinite horizon optimal control problems with multiple thermostatic hybrid dynamics

Bagagiolo

Danieli

2012

Nonlinear Analysis: Hybrid Systems

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We study an optimal control problem for a hybrid system exhibiting several internal switching variables whose discrete evolutions are governed by some delayed thermostatic laws. By the dynamic programming technique we prove that the value function is the unique viscosity solution of a system of several Hamilton-Jacobi equations, suitably coupled. The method involves a contraction principle and some suitably adapted results for exit-time problems with discontinuous exit cost.

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Section: On the Thermostat And Thermostatic Dynamicsmentioning

confidence: 99%

Section: The Optimal Bi-thermostatic Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Infinite horizon optimal control problems with multiple thermostatic hybrid dynamics

Bagagiolo

Danieli

2012

Nonlinear Analysis: Hybrid Systems

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“…P 0 is called the Preisach plane, and each (β, α) ∈ P 0 is identified with the hysteronγ β,α . output of the Preisach operator Γ is defined as [11]:…”

Section: The Preisach Modelmentioning

confidence: 99%

“…The Preisach operator provides a means of developing phenomenological models that are capable of producing behaviors similar to those of physical systems. For a detailed treatment of the Preisach operator, we refer to [10,11,12].…”

mentioning

confidence: 99%

A robust control framework for smart actuators

Tan

Baras

Proceedings of the 2003 American Control Conference, 2003.

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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. But due to the open loop nature of inverse compensation, its performance is susceptible to model uncertainties and to errors introduced by inverse schemes. In this paper we develop a robust control framework for smart actuators by combining inverse control with the l 1 robust control theory, where the inversion error is modeled as an exogenous disturbance with a magnitude bound quantifiable in terms of parameter uncertainties and inversion schemes. Through the example of controlling a magnetostrictive actuator, we present a systematic controller design method which guarantees robust stability and robust trajectory tracking while taking actuator saturation into account. Simulation and experimental results are provided.

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Automatic control of the temperature in thermoviscoelasticity

Grasselli

1999

Math. Meth. Appl. Sci.

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A viscoelastic body which undergoes a thermomechanical process is considered. The evolution of the state variables, i.e., the displacement and temperature fields, is described by a coupled hyperbolic–parabolic integrodifferential system. The heat flux through a portion of the boundary is controlled automatically by a thermostat device acting on the external temperature according to suitable measurements of the boundary strain and/or the boundary temperature. Two types of control are analysed: relay switch and Preisach hysteresis operator. In both cases, the resulting model is an initial and boundary value problem for the evolution system with non‐linear and non‐local boundary conditions for the temperature. Existence and uniqueness results are proved. Copyright © 1999 John Wiley & Sons, Ltd.

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Differential Models of Hysteresis

Cited by 896 publications

References 0 publications

Infinite horizon optimal control problems with multiple thermostatic hybrid dynamics

Infinite horizon optimal control problems with multiple thermostatic hybrid dynamics

A robust control framework for smart actuators

Automatic control of the temperature in thermoviscoelasticity

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