Saturated Feedback Control to Improve Ride Comfort for Uncertain Nonlinear Macpherson Active Suspension System With Input Delay

A robust saturation control approach is developed for input-time delay Macpherson active suspensions, subject to dynamical uncertainties, exogenous disturbances, and road excitations. The proposed control method comprises of a linear combination of two smooth saturation functions of a filtered signal and a regulation error, hence the control law is smooth and bounded by a known and adjustable constant bound. An auxiliary signal involving a finite integral over the delayed time interval of past control values is exploited to convert the delayed system into a delay-free system, and Lyapunov-Krasovskii (LK) functionals are constructed to eliminate the residual delayed terms in a Lyapunov-based analysis. The vertical displacement and velocity of the sprung mass are proven to uniformly ultimately bounded regulating to improve the ride comfort, despite model uncertainties, additive disturbances and the input delay. Several simulations are performed to verify the improvement in the ride comfort under different road profiles, while the tire deflection and suspension deflection are within an admissible limitation in comparison with two other suspensions.