Constraint-Based Adaptive Robust Control for Active Suspension Systems Under the Sky-Hook Model

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The control problem of active suspension systems (ASSs) with uncertainties is considered in this article by formulating control goals as a series of equality constraint (i.e., soft constraint) and inequality constraint (i.e., hard constraint). Uncertainties are (possibly fast) time varying, bounded, and include large mismatched portions. However, bounds are unknown. The objective is to design an adaptive robust control driving the system to converge to soft constraints provided by the sky-hook model, and simultaneously, ensuring the system to meet hard constraints at every instant. The adaptive robust control design is implemented in four steps. First, we investigate a transformation technique for incorporating hard constraints into soft constraints and the model. Second, a nominal control is presented without considering uncertainty. Third, an orthogonal decomposition technique is proposed for dividing uncertainty into matched and mismatched portions, which creatively allocates the mismatched portion for later control design. Fourth, a continuous adaptive law is constructed to emulate a constant design parameter vector associated with uncertainty bounds. It is proved that the proposed control guarantees uniform boundedness and uniform ultimate boundedness of ASSs in the presence of uncertainties and hard constrains. Furthermore, experimental and simulation results on the 2-DOF ASS are presented to validate the effectiveness of the proposed control.