Vehicle longitudinal dynamics control based on LQ

Trend of autonomous vehicles and e-mobility is in favor of an advanced control system development and deployment. Vehicle dynamics level control systems providing safety limits and high performance response, especially during high dynamics maneuvers, are necessary. This work provides solution for vehicle longitudinal dynamics (vehicle acceleration) considering physical limits given by road, tire and vehicle dynamics respectively. The goal is to maximize vehicle longitudinal acceleration by controlling each wheel longitudinal slip ratio. Considered mathematical model is non-linear single track model incorporating non-linear Pacejka magic formula as a tire model. Design model for control system is derived as a linearized state-space model at constant acceleration operation point. Therefore, the common linearization approach, at system equilibrium, is not possible and the linearization along system trajectory is used. Such solution results in involvement of LPV techniques, as vehicle velocity is state variable. Finally, the LQ optimal control framework is employed to deliver control algorithms providing constant vehicle acceleration trajectory tracing. This is accomplished by longitudinal slip ratio control for each wheel.