Design of Fractional Order PID Controller for DC Motor using Genetic Algorithm

Design of fractional order PID (FOPID) controller for DC motor is proposed in this paper. A FOPID (PID) is a PID controller whose derivative and integral orders are fractional numbers rather than integers. Design stage of such controller consists of determining six parameters – proportional constant (Kp), integral constant (Ki), derivative constant (Kd), filter time constant (τd), integral order (λ) and derivative order (μ). The proposed approach poses the problem as designing a DC motor speed controller on the concept of fixed structure robust controller and mixed sensitivity H∞ method. The uncertainty caused by the parameter changes of motor resistance, motor inductance and load are formulated as multiplicative uncertainty weight, which are used in the objective function in the design. Genetic Algorithm (GA) and Simulated Annealing (SA) are employed to carry out the aforementioned design procedure. Comparisons are made with a PID with derivative first order filter controller and it is shown that the proposed FOPID controller can highly improve the system robustness with respect to model uncertainties. The comparison of PID and FOPID controllers is also been done on the basis of Time Domain Performance index i.e. ISE (Integral of Square Error).