Abstract
The operation of the electrorheological clutch is simulated by anonlinear parabolic equation which describes the motion ofelectrorheological fluid in the gap between the driving and drivenrotors. In this case, the velocity of the driving rotor isprescribed on one part of the boundary. Nonlocal nonlinear boundarycondition is given on a part of the boundary, which corresponds tothe driven rotorA problem on optimal control ofacceleration or braking of the driven rotor is formulated andstudied. Functions of time of the angular velocity of the drivingrotor 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 minimizedunder the restriction that at some instant, the angular velocity andthe acceleration of the driven rotor are localized within givenregions. In the case of braking, the energy production is maximized.The existence of a solution of optimal control problem is proved andnecessary optimality conditions are established.
Highlights
Electrorheological fluids are smart materials that are composed of small polarizable particles dispersed in nonconducting dielectric liquids
With an applied electric field, the dielectric mismatch creates polarization forces that cause the particles to form chains aligned with the electric field
The direct problem for the clutch reduces to finding the velocity function of the electrorheological fluid, which is the solution of the nonlinear parabolic equation that satisfies nonlocal nonlinear boundary condition on the surface of the driven rotor and the Dirichlet condition on the other part of the boundary
Summary
Electrorheological fluids are smart materials that are composed of small polarizable particles dispersed in nonconducting dielectric liquids. The direct problem for the clutch reduces to finding the velocity function of the electrorheological fluid, which is the solution of the nonlinear parabolic equation that satisfies nonlocal nonlinear boundary condition on the surface of the driven rotor and the Dirichlet condition on the other part of the boundary. The functions of time of the voltages applied to electrodes and of the angular velocity of the driving rotor are considered to be controls. In this case, the coefficients of the parabolic equation and the nonlocal operator of boundary condition depend on the control. An electrorheological fluids is sandwiched between the driving and the driven rotors
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