ISSN: 2250-3005 - ijcer

International Journal Of Computational Engineering Research (ijceronline.com) Vol. 2 Issue. 8II. Mathematical Model FormulationA two-degree-of-freedom “quarter-car” vehicle suspension system is shown in Figure 1. An advantage of this model isthat many published results are available, which makes it easy to verify and compare the results which those other researches. Itrepresents the vehicle system at each wheel i.e. the motion of the axle and of the vehicle body at any one of the four wheels ofthe vehicle. The suspension itself is shown to consist of a spring , a damper and an active force actuator . The activeforce can be set to zero in a passive suspension. The sprung mass represents the quarter car equivalent of the vehicle bodymass. The unsprung mass mu represents the equivalent mass due to the axle and tire. The vertical stiffness of the tire isrepresented by the spring . The variables , and represent the vertical displacements from static equilibrium of thesprung mass, unsprung mass and the road respectively[21]. In this paper it was assumed that only the suspension deflectioncould be measured and used by the controllers.Figure 1. Semi-active suspension system.(2)(1)Assume the followingWhere :is the suspension deflection (rattle space)is the absolute velocity of sprung massis the tire deflectionis the absolute velocity of unsprung massThe state equations of the sample power system can be written in the vector-matrix differential equation form as:The system matrix A, the control matrix , and the road input matrix are, respectively, denoted as, andThe suspension parameters are shown the Table 1.||Issn 2250-3005(online)|| ||December||2012 Page 173