A New Method to Tune a Fractional-Order PID Controller for a Twin Rotor Aerodynamic System

Abstract

This paper proposes a new method to tune a fractional-order Proportional–Integral–Derivative controller (also called $\mathrm {P}\mathrm {I}^{\uplambda }\mathrm {D}^{\upmu }$ ) for a Twin Rotor Aerodynamic System, which is a nonlinear highly coupled Multi-Input–Multi-Output system. The five parameters of the controller are tuned using optimization to minimize a performance index which is a weighted sum of absolute values of four frequency domain specifications: gain crossover frequency, phase margin, ISO damping property (to be robust against process gain variation), and magnitude peak value at the resonant frequency, where the latter is the new control design specification that is suggested by this paper. The performance of the proposed controller is compared with that of an integer-order Proportional–Integral–Derivative (PID) controller. Simulation results shows that the fractional-order controller outperforms its integer-order counterpart in minimizing the performance index, which results in satisfying the required design specification more accurately. This is demonstrated by first testing the performance of the of the closed-loop system where the fractional-order controller gives better performance than the integer-order controller and second by testing the robustness of the system by changing one of the process parameters, where the fractional-order controller is much more robust, unlike the integer-order controller where the closed-loop system becomes unstable.