Control of a quarter-car model with variable damping

摘要

Dynamics of a strongly nonlinear quarter-car model is investigated. The nonlinearity is due to a control strategy which selects the damping coefficient of the car suspension in a way that the resulting semi-active system approximates the performance of an active suspension system designed to produce sky-hook damping. According to this control strategy, the damping coefficient switches between two different positive values, leading to a piecewise linear dynamical model. For this model, the equation of motion is first presented in a general normalised form. Then, an appropriate methodology is applied for obtaining exact periodic motions for the case of forcing resulting from a road with harmonic profile. This methodology is based on employing the exact solution form within response intervals where the damping coefficients remain constant. TYhe unknowns of the problem are then determined by imposing a set of periodicity and matching conditions. The stability analysis of the located motions is also performed by applying a method which is suitable for piecewise linear systems. Next, this analysis is applied and representative numerical results are obtained. Namely, response diagrams are presented, showing the effect of the important system parameters on the existence, amplitude and stability properties of various branches of periodic solutions. The results are also compared to those of the conventional suspension system, including passive bilinear shock absorbers.