On the LMI optimization of active and semi active vehicle suspensions

In this study, a seven degrees of freedom full car model with linear parameters is derived, and three type of suspension systems, namely, passively, actively and semi actively suspended systems are reviewed to study car's vibration under random road excitation. The performance of suspension systems are determined by measuring the body accelerations, suspension travels and tire deflections to assess ride comfort and drive safety of the vehicle. The active suspension system is controlled by single and multi objectives controllers and for each controller the vehicle behavior is observed. An LQG control is presented and a trade off in cost function between the output indices is made. A different scenarios for mixed H_2/H_infinity syntheses with regional pole placement constraints are generated and a dynamic output feedback solutions are solved using LMIs. For the semi active suspension system, a classical approaches Skyhook, Groundhook and Hybrid are used to control the system since these approaches feature simplicity and lower cost compared to their active counterparts. A mixed H_2/H_infinity static output feedback controller realized by MR damper which utilizes the measurements of the velocity at each corner of sprung mass and the suspension travel speeds as feedback signals is designed for two types of Skyhook control law and solved via LMI to obtain the damping characteristics of MR dampers. For the proposed controllers, the effectiveness is validated by simulation results and the achieved RMS responses are compared. Keywords: Full car model, Active suspension, Semi active suspension, Road model, Multi-objective control, LMI optimization, H∞ performance, H2 performance, Static output feedback, Dynamic output feedback, State feedback, LQG control, Skyhook control, Groundhook control, Hybrid control