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An active suspension system with preview under stochastic optimal control of a vehicle travelling on an irregular surface is discussed. The vehicle is modelled as a mass-damper-spring system with two degrees of freedom and the dynamic behaviour of the irregular surface is described by a first-order system subject to a gaussian white random input. The acceleration of the vehicle and the irregular quantity of the surface ahead of the vehicle are in a noisy environment measured using sensors mounted on the vehicle. The state variables of the vehicle dynamics and the dynamic behaviour of the irregular surface are estimated using the Kalman filter. The stochastic optimal control is determined by minimizing the given performance index, and is composed of the weighted linear combination of the estimated state variables of the vehicle dynamics and the dynamic behaviour of the irregular surface. A numerical example shows the effectiveness of the proposed active suspension system with preview.
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Yoshimura et al. (1991) studied this question.
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