A Human-optimized Model Predictive Control Scheme and Extremum Seeking Parameter Estimator for Slip Control of Electric Race Cars

Abstract

This paper presents a longitudinal slip control system for a rear-wheel-driven electric endurance race car. The control system integrates Model Predictive Control (MPC) with Extremum Seeking Control (ESC) to optimize the traction and regenerative braking performance of the powertrain. The MPC contains an analytical solution which results in a negligible computation time, whilst providing an optimal solution to a multi-objective optimization problem. The ESC algorithm allows continuous estimation of the optimal slip reference without assuming any prior knowledge of the tire dynamics. Finally, the control parameters are determined using a human-driven preference-based optimization algorithm in order to obtain the desired response. Simulation results and comparisons with other methods demonstrate the system's capability to automatically determine and track the optimal slip values, showing stability and performance under varying conditions.

Figures (7)

• Figure 1: InMotion's fully electric endurance race car.
• Figure 2: Simplified architecture of the implemented slip control strategy. The ESC Algorithm estimates the optimum slip through gradient estimation, which is subsequently scaled to account for lateral dynamics. The MPC uses information of the wheel speeds to control the slip of the rear tires by modulating the motor torque.
• Figure 3: Quarter vehicle model of a vehicle traveling at the speed of $v_{\mathrm{x}}$, which exerts a vertical force $F_\mathrm{z}$ on the wheel. The wheel has a radius $r_\mathrm{w}$, and speed $\omega$, which is dependent on the brake torque $T_\mathrm{b}$, drive torque $T_\mathrm{d}$ and longitudinal force $F_\mathrm{x}$
• Figure 4: An example of the relation between the longitudinal slip and the longitudinal force produced by the tire.
• Figure 5: Simulation maneuver which was used to compare the parameter sets for c-GLISp with respect to tracking error, disturbance rejection, overshoot and damping. The simulation included a range of disturbances, such as changes in friction coefficient (at 5 seconds and 7 seconds), steering input (between 8 and 10 seconds) and braking input (between 10 and 12 seconds).