Dynamic Characteristics of Non-smooth Suspension System Under Fractional-order Displacement Feedback

Vehicle suspension systems generally have non-smooth factors, such as clearances, collision, and constraint. The bad dynamic behaviors caused by these non-smooth factors have not been controlled effectively, thus influencing the driving performance and riding comfort of vehicles. To explore the dynamic characteristics of non-smooth suspension systems for controlling the bad dynamic behaviors, an approximate analytical solution to the response of a two-degree of freedom nonlinear suspension system, which has a fractional-order displacement feedback under harmonic excitation, was deduced by the Krylov–Bogoliubov (KB) method. This analytical solution was verified by the numerical solution of the suspension system. Moreover, the response of the suspension system with fractional-order displacement feedback control was compared with those of the systems without feedback control and traditional integer-order control. The influences of the main parameters of the system on the dynamic suspension characteristics were analyzed thoroughly. Finally, the stability of the suspension system was analyzed by plotting the maximum Lyapunov index diagram. Results show that compared with the systems without feedback control and with traditional integer-order control, the nonlinear suspension system with fractional-order displacement feedback control can significantly improve vehicle acceleration, the dynamic deflection of the suspension, and the displacement of the vehicle body. Controlling the nonlinear stiffness coefficient of the suspension system within 103–106 is conducive to decreasing the dynamic deflection of the suspension system of vehicles, while increasing the fractional-order control coefficient and the fractional order is beneficial to controlling the dynamic deflection of the suspension system and the displacement of the vehicle body. Conclusions obtained in the study can provide unique references for the optimal design and control of nonlinear suspension systems with fractional-order displacement feedback control. Keywords: suspension; non-smooth; fractional order; dynamics; analytical solution; nonlinear.