Applicability of Fractional-Order PID Controllers for Twin Rotor Aerodynamic System Objects

The availability of two additional tunable parameters compared with Proportional Integral Derivative (PID) controllers makes it possible to incorporate fractional-order (FO) integral/derivative actions. The selection of the optimization algorithm and objective function is important for tuning the fractional-order PID controller. This paper presents the formulation of the FOPID controller design as an optimization problem and its solution using four built-in algorithms in MATLAB. Each algorithm solves the optimization by minimizing two cost functions resulting eight sets of controller parameters. To overcome the sensitivity of algorithms to the initial and boundary values of the parameters, we considered nine different initial and boundary conditions. The proposed method considers the minimum of the optimal values obtained in each case. This provides globally-optimal FOPID controllers. To validate its efficiency, the proposed method uses a Twin Rotor Aerodynamic System (TRAS) as an example. Comparison with a nonlinear approach shows that the proposed approach ensures tracking with minimal and smooth control efforts.