Adaptive backstepping control with grey signal predictor for nonlinear active suspension system matching mechanical elastic wheel

•Propose a new mechanical elastic wheel to prevent tire explosion.•Adaptive backsteeping controller match the novel wheel with active suspension.•Ideal suspension motions generated according to an improved hybrid damping control.•Grey DGM (2,1) model is used for controlling in time. In order to stabilize the attitude and improve ride comfort of vehicles equipped with mechanical elastic wheel (MEW), an adaptive backstepping controller with grey signal predictor is presented for active suspension system, considering the uncertainty and nonlinearity of suspension and MEW. The MEW’s mathematical model is established through experiments firstly. Then the ideal suspension motions are generated according to a designed hybrid damping control. To track these ideal signals, Lyapunov theory and the thought of backstepping are used to estimate the nonlinearity of active suspension and obtain final control laws. Grey DGM (2,1) model is further applied to derive future motions of suspension, thus commands can be carried out in advance to realize control in time. The stability and convergence of whole scheme are also proved by Lyapunov-like lemma. Finally, simulations on two different road profiles (step and pulse) show that this strategy can effectively suppress the vertical motion of vehicle body by 19.7% and pitch motion by 9.5% respectively compared with that without control. And furthermore, the bounce of wheels is also decreased at the same time. The controller expands the application of MEW and establishes a good theoretical foundation for the novel wheels’ matching.