Influence of approximation methods on the design of the novel low-order fractionalized PID controller for aircraft system

In this paper, the effect of approximation approaches on a novel low-order fractionalized proportional–integral–derivative (LOA/FPID) optimal controller based on the Harris Hawks optimization algorithm (HHOA) for airplane pitch angle control is studied. The Carlson, Oustaloup and Matsuda methods are used separately to approximate the fractional integral order of the fractionalized PID controller. This technique consists in introducing fractional-order integrators into the classical feedback control loop without modifying the overall equivalent closed loop transfer function. To validate the effectiveness of the suggested approach, performance indices, as well as transient and frequency responses, were used. The comparative study was performed, and the results show that the proposed reduced fractionalized PID based on HHO algorithm with Carlson controller is better in terms of percentage overshoot, settling time and rise time than other controllers.