Design of Nonlinear PID and FOPID Controllers for Electronic Throttle Valve Plate’s Position

The electronic throttle valve (ETV) system is one of the essential parts of the automobile because it controls the amount of airflow into the engine’s combustion system. In fact, there are challenges in ETV control due to several nonsmooth nonlinearities, such as backlash, stick‐slip friction, and a discontinuous nonlinear spring. This paper proposes eight control schemes; the first two are the conventional proportional‐integral‐derivative (PID) controller and the fractional‐order PID (FOPID) controller, while the second two schemes are modified versions of conventional PID and FOPID using the integral of the arc tan function of the error rather than the error in the integral action. However, all these control schemes above have been studied with and without considering the technique of manipulating the windup problem or antiwindup. A metaheuristic optimization technique, namely, the grey wolf optimization (GWO) algorithm, is introduced for optimizing the controllers’ parameters while minimizing the integral of the cube time square error (IT^3SE) cost function. A comparison study between these control schemes and other controllers has been conducted based on numerical simulation. The computer simulation demonstrates that the performance of the arc tan FOPID (AT‐FOPID) controller is superior to that of the other optimal control schemes and other controllers, as follows: best value of performance criterion IT^3SE, best exponential transmission of transient response, least overshoot, least rise time, least settling time, low control effort, least oscillations of the control signal, and smooth phase trajectory from the initial state to the target state without circling about the target. Finally, the most important feature of this scheme is its superior robustness compared to others.