Nonlinear Dynamics of a Vehicle with a Semi-Active Suspension

This paper presents results of a study of dynamical properties of a vehicle with semi-active suspension. The especially designed control algorithm, based on so called skyhook, groundhook abstract models is considered. A vehicle is described by a quarter car model in two versions: the first variant, with linear passive suspension and the second, with a semi-active system which uses a magnetorheological (MR) damper. The semi-active suspension system approximates the performance of the abstract hybrid model with dampers located between sprung mass and sky (skyhook) and unsprung mass and ground (groundhook). The control algorithm is realized by MR damper, with properties described by Bouc-Wen model. Parameters of Bouc-Wen model have been identified on the basis of the experimental characteristic as a function of a damper's piston velocity. The relationship of selected parameters on the input current on a coil circuit dynamics is included in the model. Both variants of the suspension, passive and semi-active, are compared using objective criteria. A ride comfort is defined by a sprung mass vertical acceleration and a ride safety by a dynamic tyre force. In general, the criteria are in conflict, therefore by using multi-objective methodology a complex performance index which binds together all criteria by arbitrarily chosen coefficients is defined. The values of these coefficients have been adjusted on the basis of the linear model for which parameters are optimal (minimum value of the objective function). The dynamics of the semi-active vehicle suspension is tested for random excitation. A road profile is generated using the spectral representation method. The advantages of the designed semi-active suspension together with the proposed control strategy are presented in the paper.