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22 June 2000 Smart fluid damping: shaping the force/velocity response through feedback control
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It is now well known that smart fluids [electrorheological (ER) and magnetorheological (MR)] can form the basis of controllable vibration damping devices. With both types of fluid, however, the force/velocity characteristic of the resulting damper is significantly non-linear, possessing the general form associated with a Bingham plastic. In a previous paper the authors showed that by using a linear feedback control strategy is it possible to produce the equivalent of a viscous damper with a continuously variable damping coefficient. In the present paper the authors illustrate an extension of the technique, by showing how the shape of the force/velocity characteristic can be controlled through feedback control. This is achieved by using a polynomial function to generate a set point based upon the damper velocity. The response is investigated for polynomial functions of zero, 1st and 2nd order. It is shown how the damper can accurately track higher order polynomial shaping functions, while the zero order function is particularly useful in illustrating the dynamics of the closed-loop system.
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Neil D. Sims, Roger Stanway, Andrew R. Johnson, David J. Peel, and William A. Bullough "Smart fluid damping: shaping the force/velocity response through feedback control", Proc. SPIE 3985, Smart Structures and Materials 2000: Smart Structures and Integrated Systems, (22 June 2000);

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