Design a robust and optimal fuzzy logic controller to stabilize the speed of an electric vehicle in the presence of uncertainties and external disturbances

In the nonlinear dynamic equations of the electric vehicle, parameters such as the coefficient of friction between the tires and the road, the coefficient of traction, the resistance of the anchor, and so on have ambiguities. Designing a controller that is robust to the existence of these parametric ambiguities and also to external disturbances, while still satisfying the optimality criteria, is a challenging task. In practical applications, in addition to the problems mentioned above, the computing load of the control input should also be taken into account and a sensible interaction between the performance desired by the controller and the computing volume should be offered. In the present work, a robust, optimally stable fuzzy controller based on parallel distributed compensation is designed using the Takagi-Sugeno fuzzy model of the electric vehicle. The fuzzy model stabilizer feedback gains, the upper bound of uncertainties, the upper bound of disturbance effect, and the upper bound of the cost function are obtained completely offline by solving a minimization problem based on the linear matrix inequality. Therefore, the calculation volume of the control input is extremely small. This allows the proposed control to be put into practice. The good performance of the proposed controller is demonstrated in five-stage simulations.