Control of active suspension system in the presence of nonlinear spring and damper

The present study developed two simple and easy methods in terms of compu-tation and application using State Dependent Riccati Equation (SDRE) and Approximating Sequence of Riccati Equation (ASRE) techniques to control active suspension system in the presence of nonlinear spring and damper. In addition, this study made a comparison regarding the effectiveness of both control methods developed by the mentioned techniques. To this end, rst, the methodologies of both approaches were discussed. Second, the nonlinear dynamics of the vehicle suspension system was described in terms of conveniently selected state variables for better control performance. Third, a cost function was proposed considering the suspension and tire de ections, sprung mass velocity and acceleration, and unsprung mass velocity variables to improve the ride quality, suspension de ection, and tire de ection. In addition, a convenient representation of this cost function in terms of state variables was obtained to realize better control. Two forms of road disturbance were also taken into account called the bump, expressed as a sinusoidal function, and road roughness, expressed as a white noise. Finally, a quarter-car suspension system, which was the equivalent model of Ford Fiesta Mk2, was used as an example to perform simulations using the developed control methods the results of which were compared with the performance requirements and corresponding passive suspension system.