Optimal design of linear and nonlinear PID controllers for speed control of an electric vehicle

Electric vehicles (EVs) as a sustainable safety system are being increasingly used and receiving attention from researchers for several reasons including optimal performance, affordability for consumers, and environmental safety. EV speed control is a crucial issue that requires reliable and intelligent controllers for maintaining this matter. The primary goal of this research is to design the linear and nonlinear Proportional, Integral, and Derivative (PID) controllers to control EV speed based on the minimum value of ITAE plus ISU (integral square of control signal) as well as satisfy the constrain on response overshoot. All the proposed PID controllers, conventional PID controller, arc tan PID controller, and nonlinear PID controller (NL-PID) are used in cascade with EV model. In all these PID controllers, a filter is used with the derivative term to avoid the effect of the noise. The tuning of the proposed controller gains is achieved using Aquila Optimization algorithm. The controllers’ parameter tuning is primarily determined by reducing the Integral Time Absolute Error (ITAE) and integral square control signal. Numerical simulation, system modelling, and controller design are done using MATLAB. By comparing the results, the proposed controllers’ efficacy is demonstrated. The proposed NL-PID controller provides promising EV speed regulation control and robustness to external disturbances. Where, the performance specifications of the proposed NL-PID controller when using unit step input with step disturbance of 0.2 and −0.2, and the model parameters increased by 25% from its nominal value are the rise time is 2.608, settling time is 2.608, overshoot is 0.073%, the maximum control signal is 6.230, number of slope sign change in the control signal is 231, and ITAE is 17.6064. The comparative results show the NL-PID controller’s superior performance for tracking the reference signal with the lowest peak for the control signal, rejection of disturbances, ability to overcome model uncertainties, and lowest ITAE value.