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Previous work by the authors on fully active control systems is extended to model semi-active systems which (a) can only dissipate energy and (b) involve some restrictions in their response characteristics. Various control laws are studied but the one which turns out to be of most interest includes the “wheelbase preview” effect, i.e. it takes advantage of the information that the rear input is a delayed version of that at the front wheel. For example, the semi-active system which includes this feedforward information is better overall than a fully active system which assumes uncorrelated inputs at the wheels.