This paper deals with the synthesis of an optimal yet practical finite preview controller for a semi-active dissipative suspension system based on a two-degree-of-freedom (2-DOF) vehicle model. The proposed controller utilizes knowledge about approaching road disturbances obtained from preview sensors to minimize the effect of these disturbances. A truly optimal control law, which minimizes a quadratic performance index under passivity constraints, is derived using a variational approach. The optimal closed loop system becomes piecewise linear varying between two passive systems and a fully active one. It is shown that the steady state system response to a periodic input is also periodic and its amplitude is proportional to the amplitude of the input. Therefore, frequency domain characteristics in a classical sense can be generated. The problem formulation and the analytical solution are given in a general form and hence they apply to any bilinear system with system disturbances that are a priori unknown but some preview information is possible. The results of this analysis are applied to a quarter car model with semi-active suspension whose frequency domain and time domain performances are evaluated and compared to those of fully active and passive models. The effect of preview time on the system performance is also examined.

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