A Fractional Order (PID)<sup<<em<γ</em<</sup< Control Method for Integer-Order Systems

For first-order, second-order, and first-order-plus-integrals systems, a design method for fractional order controllers is proposed. Based on the principle of internal model control, a fractional order (PID)<sup<<em<γ</em<</sup< controller is created by using the fractional order filter. This controller only contains two adjustable parameters, so the difficulty of the fractional order controller tuning is reduced. The parameter tuning of the fractional order (PID)<sup<<em<γ</em<</sup< controller is realized according to the phase margin, <em<φ</em<<sub<m</sub<, and the cutoff frequency, <em<ω</em<<sub<c</sub<, of the system. Simulation results show that the proposed method is not only simple in design and convenient in its parameter tuning, but also that it provides better performance in both command value tracking and disturbance rejection, as well as an increased robustness against system perturbation parameters.