The Application Of Optimal Control Of Active Suspension Based On Precise Integral Method

Riding comfortably and handling safely of vehicles has been influenced directly by the dynamic performance of suspension system. As the parameter of conventional passive suspension system been fixed, the external energy has been absorbed and stored passively. With the surround traffic conditions and outside inputs changing, the passive suspension system can't take initiative to adapt it, greatly restricted the further improvement of vehicle performance. As the most advanced suspensions system, active suspension can be based on real-time conditions and adjust the damping or stiffness, so that the suspension system could be in the optimal damping states. In this paper, the quarter-vehicle of active suspension system with two degrees of freedom model has been set up by the vehicle dynamics theory. Furthermore, taking into account the road disturbance input of the suspension system of the important impact of dynamic performance, the integral form of white noise mathematical model of road roughness input, pulse and sinusoidal excitation model have been established and analyzed.As delays exist in the state and control input of optimal control of vehicle suspension systems, the state equation has been discussed respectively in Hamilton system, combing with the precision integral method (PIM) of Coats integral and linear interpolation. On the base of duality principle, which is applied to the optimal filter for linear systems with time delay in observations, the original delay problem is reduced into a non-delay problem and it's equation solved by PIM under the whole state. Considering the vehicle body's mass from the no-load to full-load and the changes of the stiffness of the tire since the aging, the internal pressure changes affect the performance of suspension system, finally, the quarter-vehicle model with time delay suspension has been considered and simulated individually in the MATLAB environment, compared with the traditional method. The results show that the proposed method has higher precision and stability and its precision can be controlled easily. That offers method for analysis of vehicle suspension systems and a new outlook for the PIM method applications.