Semi-Active Suspension Suboptimal Control Using Dynamic Programming of a Quarter Car Suspension System

Many modern vehicle control systems utilize automatic braking and torque control to enhance driver inputs for improved stability and deceleration performance of passenger cars. A semi-active suspension approach may allow changes to the suspension characteristics under various conditions or driver inputs during vehicle operation. Suspensions are increasingly using semi active components to enhance handling characteristics by electronically adjusting vehicle dynamics. The active style of adjustment includes modifying suspension parameters directly such as electronic damping rates. The type of controller is important to react or adjust dynamically to the nonlinear nature of suspension systems. An optimal controller is introduced in attempt to improve ride comfort or road handling capability by manipulating the damping coefficient for a given trajectory. A suboptimal approach is given by utilizing a type of receding horizon control. The cost function, as used by Savaresi, contains a bias parameter to shift focus between road holding and passenger comfort. A dynamic quarter car suspension model is presented for simulation of nonlinear vehicle dynamics. During simulation at a given time step, various control inputs are simulated for finite steps into the future. The control input that minimizes the cost function is selected and the simulation time is allowed to advance with that input. The model is simulated using parameters for a typical passenger car and a 100 millisecond update rate from the suboptimal controller. A road profile with a bump is simulated and its transients are analyzed. The suboptimal controller is compared to its purely mechanical realization with a fixed damping coefficient. It is shown when manipulating the cost function ride comfort is desired chassis accelerations are minimized and when maximum road holding is desired tire deflection is minimized.