A half-car vehicle model with variable dampers placed between the sprung mass and the unsprung masses was considered in the study. A suitable set of state variables were defined and state equations of the system were obtained. An integral performance index involving a weighted combination of the average squared heave accelerations of the sprung mass, and squares of suspension deflections was defined. The closed loop optimal control law which gives the optimal value of the damping coefficients of the variable dampers was obtained by using Pontryagin principle. The performance of a vehicle with an optimally controlled semi-active suspension was calculated for measured road profile inputs, and trade-off curves were obtained between the average sprung mass acceleration and suspension deflections. Performance of the vehicle with semi-active system was compared to the corresponding performance of a vehicle with a passive suspension system. Then, a time delay was introduced to the response of the damper and its effect on the performance of the semi-active system was investigated. The results of the study have shown that performance of the vehicle with variable damping semi-active suspension is much better than that of the vehicle with a passive suspension.
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