Energy-efficient control of electric vehicles based on linear quadratic regulator and phase plane analysis

Highlights: • A phase plane-based energy-efficient controller is proposed for electric vehicles. • A self-stable boundary is developed for vehicle stability identification. • The gain scheduling on two LQR modes is designed for better vehicle performance. • The vehicle stability and power consumption are integrated in torque allocation. • The proposed controller saves up to 9.68% and 3% energy at two typical maneuvers. Electric vehicles (EVs) have advantages in the aspect of energy, environment, and vehicle motion control. However, it is still not competitive enough to conventional vehicles because of the limited driving range and the high cost of the battery. Therefore, the energy efficiency is of the most importance for the control of EVs. Existing range extension control systems on EVs mostly focus on longitudinal front and rear axle torque distribution or lower-level yaw moment allocation. It is a challenge to maintain the vehicle's stability at the cost of the minimum energy when the vehicle is cornering, this paper proposes a phase plane-based controller for EVs, focusing on the energy-efficient upper-level yaw stability control. The phase plane-based controller is automatically adaptive to driving situations through the optimization of weights on the performance of the vehicle handling and stability. Firstly, a friction constrained desired model is presented for the model-following control. Secondly, $\beta -\dot{\beta }$ phase plane analysis is conducted based on a nonlinear vehicle model to graphically identify the vehicle lateral stability in real time. The self-stable region can be determined by the vehicle velocity, the road friction coefficient, and the wheel steering angle. Then, energy optimizing (i.e. gain scheduling of LQR controllers) rules are designed based on the vehicle lateral stability identification. Finally, the proposed phase plane-based controller is evaluated and the yaw moment costs are compared to other controllers' in a realistic 7-DOF vehicle model. The results demonstrate that the proposed controller presents an excellent yaw stability control capability, and compared to the widely used Shino's controller, the proposed controller reduces the energy consumption by 9.68% and 3% at the 'light' and 'severe' maneuver, respectively.