Mathematical Modeling and Comparative Evaluation of PI and PID Speed Controllers for Electric Vehicle Traction Systems

Although PI and PID controllers are mature control laws, their effect on energy-related variables is rarely isolated in a complete electric vehicle traction model when the plant, controller tuning basis and driving conditions are kept unchanged. A full-system MATLAB/Simulink model was developed, comprising a DC motor with PWM H-bridge, reduction gear, vehicle dynamics and a lithium-ion battery with SOC monitoring. Fixed-gain PI and PID configurations were compared under FTP75, with US06 added as a dynamic-cycle assessment. Speed tracking was evaluated using RMSE, MAE, IAE and ITAE, while energy behavior was assessed through SOC depletion, battery voltage, current and braking-command signals. Under FTP75, both controllers achieved nearly identical tracking accuracy, with an overall RMSE of 0.1525 km/h across the active intervals. Despite this kinematic equivalence, PID reduced SOC depletion by 0.980 percentage points over 4.963 km and produced a less intense but more distributed braking command. The additional 600 s US06 simulation did not confirm a general PID advantage: both controllers reached the same maximum speed and showed practically identical tracking accuracy, while PID did not reduce SOC depletion. The results show that the derivative channel changes the control-command pattern, but it does not automatically improve kinematic or energy performance under fixed-gain tuning.