Control allocation for regenerative braking of electric vehicles with an electric motor at the front axle using the state-dependent Riccati equation control technique

In this paper the systematic development of an integrated braking controller for a vehicle driven by an electric motor on the front axle is presented. The objective is to engage the electric motor only during braking, up to the point at which the vehicle reaches its manoeuvrability and stability limit. The control challenges are to distribute the braking effort correctly between the hydraulic brakes at the four tyres and the electric motor, to handle the tyre saturation and motor constraints effectively and to adapt the control allocation based on the vehicle’s states. The controller is designed using the state-dependent Riccati equation control technique, the vehicle state estimation and the ‘magic formula’ tyre model. The state-dependent Riccati equation control technique is a suboptimal control design technique for non-linear systems. A novel method for constructing the state-dependent coefficient formulation of the system dynamics is proposed. Soft constraints in the state dynamics are described, while an augmented penalty approach is suggested for handling the system’s hard constraints. The performance of the controller was evaluated for different braking scenarios using simulations in a MATLAB/Simulink environment. An eight-degree-of-freedom non-linear vehicle model was utilized. The numerical results show that the controller suboptimizes the regenerative braking effort while considering the tyre force saturation, the motor torque limits, the vehicle yaw rate and the slip angle error. A comparison with a constrained linear quadratic regulator shows the advantages of the proposed controller.