Optimal control of electrorheological clutch described by nonlinear parabolic equation with nonlocal boundary conditions

  • The operation of the electrorheological clutch is simulated by a nonlinear parabolic equation which describes the motion of electrorheological fluid in the gap between the driving and driven rotors. In this case, the velocity of the driving rotor is prescribed on one part of the boundary. Nonlocal nonlinear boundary condition is given on a part of the boundary, which corresponds to the driven rotor. A problem on optimal control of acceleration or braking of the driven rotor is formulated and studied. Functions of time of the angular velocity of the driving rotor and of the voltages are considered to be controls. In the case that the clutch acts as an accelerator, the energy consumed in the acceleration of the driven rotor is minimized under the restriction that at some instant, the angular velocity and the acceleration of the driven rotor are localized within given regions. In the case of braking, the energy production is maximized. The existence of a solution of optimal controlThe operation of the electrorheological clutch is simulated by a nonlinear parabolic equation which describes the motion of electrorheological fluid in the gap between the driving and driven rotors. In this case, the velocity of the driving rotor is prescribed on one part of the boundary. Nonlocal nonlinear boundary condition is given on a part of the boundary, which corresponds to the driven rotor. A problem on optimal control of acceleration or braking of the driven rotor is formulated and studied. Functions of time of the angular velocity of the driving rotor and of the voltages are considered to be controls. In the case that the clutch acts as an accelerator, the energy consumed in the acceleration of the driven rotor is minimized under the restriction that at some instant, the angular velocity and the acceleration of the driven rotor are localized within given regions. In the case of braking, the energy production is maximized. The existence of a solution of optimal control problem is proved and necessary optimality conditions are established.show moreshow less

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Metadaten
Author:William G. LitvinovGND
URN:urn:nbn:de:bvb:384-opus4-10858
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/1285
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2009-20)
Type:Preprint
Language:English
Publishing Institution:Universität Augsburg
Release Date:2009/07/23
Tag:electrorheological fluid; parabolic equation; nonlocal boundary condition; existence; optimality condition
GND-Keyword:Elektrorheologie; Randwertproblem; Nichtlineare parabolische Differentialgleichung; Optimalwertregelung; Optimalitätsbedingung
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):Deutsches Urheberrecht mit Print on Demand