Abstract-In this paper, a nonlinear optimal control law based on a quadratic cost function is developed, and applied on a half-car model for the control of active suspension systems. Nonlinear model of half-car is constructed using the nonlinear dynamics of the electro hydraulic actuator and dynamic characteristics of the dampings and springs. The states of half car model are first estimated by Extended Kalman Filter (EKF) and then the estimated states predicted by Taylor series expansion and finally a control law is introduced by minimizing the local differences between the predicted and desired states. The derived control law has an analytical form which is easy to apply and also it is not required online numerical computations in optimization. Performance of the nonlinear optimal controller is compared to the existing passive suspension system and the proportional integral sliding mode controller. The obtained results demonstrate that use of the proposed nonlinear optimal control technique improves the tradeoff between ride quality and suspension travel compared to the passive suspension system and the proportional integral sliding mode method.Index Terms-nonlinear optimal control, active suspension, nonlinear model, Extended Kalman Filter, proportional integral sliding mode.
I. INTRODUCTIONThe important functionality of the vehicle suspension system is to support the vehicle body as well as to provide the riding comfort to the passengers by rejecting the unpleasant vibratory motion induced from the irregular road inputs. Also, the suspension should maintain adequate vertical load to provide the vehicle stability when the car turns, brakes or accelerates [1]. The vehicle stability and riding comfort has mutually adverse effects, therefore, simply the passive damper, which is widely used in the usual vehicle, could not satisfy the riding comfort as well as driving stability simultaneously. To overcome this problem many researchers have proposed to use active suspensions [2]. Unlike passive systems which can only store or dissipate energy, active suspensions can continuously change the energy flow to or from the system when required. Furthermore, characteristics of active suspensions can adapt to instantaneous changes in driving conditions detected by sensors. As a result active suspensions can improve both riding comfort and handling performance to satisfactory levels. (Phone: +98-411-339 3728; fax: +98-411-3300819; e-mail: izadeh@ tabrizu.ac.ir, izadeh@ieee.com).However, as the recent trends of the vehicle industry is to be luxurious and driver comfort is more required, the electrical controlled suspension system is now installed and widely utilized [3]. Especially, the active damper is widely adopted for the luxurious vehicle because it can overcome the shortage of the passive damper by providing the ride comfort and vehicle stability at the same time. In the active suspension system, the sprung mass can vary according to the variation of passenger numbers and cargo as well as fuel loading condition. Also th...