Keywords: vehicle dynamics, quarter car model, skyhook, groundhook, random excitation, magnetorheological damper.

The paper presents results of a study of dynamical properties of a vehicle with semi-active suspension. The especially designed control algorithm, based on the 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 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) [1,2]. The control algorithm is realized using a MR damper, with properties described using the Bouc-Wen model [3]. The parameters of Bouc-Wen model have been identified on the basis of the experimental characteristics as a function of a damper's piston velocity. The relationship of selected parameters on the input current on coil circuit dynamics [4] 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 [1]. The advantages of the designed semi-active suspension together with the proposed control strategy are presented in the paper.

Models presented in the literature with skyhook and groundhook dampers do not take into account the properties of real actuators. This paper presents the possible realization of the control strategy by a magnetorheological damper. The first analysis attempt is presented in the work [5]. In this paper coil circuit dynamics is included into the MR damper model and the system is tested for random signal excitation, which describes the profile of a real road.

1

M. Valasek, M. Novak, Z. Sika, O. Vaculin, "Extended ground-hook - New concept of semi-active control of truck's suspension", Vehicle System Dynamics, 27, 289-303, 1997. doi:10.1080/00423119708969333

2

G. Verros, S. Natsiavas, C. Papadimitriou, "Design optimization of qarter-car models with passive and semi-active suspensions under random road excitation", Journal of Vibration and Control, 11, 581-606, 2005. doi:10.1177/1077546305052315

3

B.F. Spencer, S.J. Dyke, M.K. Sain, J.D. Carlson, "Phenomenological model of magnetorheological damper", ASCE Journal of Engineering Mechanics, 123(3), 230-238, 1997. doi:10.1061/(ASCE)0733-9399(1997)123:3(230)

4

L.M. Jansen, S.J. Dyke, "Semi-active control strategies for MR dampers: a comparative study", ASCE Journal of Engineering Mechanics, 126(8), 795-803, 2000. doi:10.1061/(ASCE)0733-9399(2000)126:8(795)

5

A. Mitura, J. Warminski, "Analysis of oscillations of vehicle suspension with magnetorheological dampers", Machine Dynamics Problems, 32(1), 64-72, 2008.

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