Several control laws for active and semi-active suspension based on a linear half car model are derived and investigated. The strategies proposed take full advantage of the fact that the road input to the rear wheels is a delayed version of that to the front wheels, which in turn can be obtained either from the measurements of the front wheels and body motions or by direct preview of road irregularities if preview sensors are available. The suspension systems are optimized with respect to ride comfort, road holding and suspension rattle space as expressed by the mean-square-values of body acceleration (including effects of heave and pitch), tire deflections and front and rear suspension travels. The optimal control laws that minimize the given performance index and include passivity constraints in the semi-active case are derived using calculus of variation. The optimal semi-active suspension becomes piecewise linear, varying between passive and fully active system and combinations of them. The performances of active and semi-active systems with and without preview were evaluated by numerical simulation in the time and frequency domains. The results show that incorporation of time delay between the front and rear axles in controller design improves the dynamic behavior of the rear axle and control of body pitch motion, while additional preview improves front wheel dynamics and body heave.

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