Calculation of Stabilizing PDμ Controllers for a Class of Fractional Order Systems with Time Delay

In this paper, a simple and effective stabilization method for a class of systems with time delay controlled by PD
^μ
controllers is presented. Based on D-decomposition method, the explicit formulae corresponding to Real Root Boundary(RRB) and Complex Root Boundary(CRB) are derived in terms of the PD
^μ
controller parameters. The stability region of the control system is determined by the implicit function theorem. The set of stability regions in (kd, kp)-plane when 11 equals to different values in (0, 2) can be obtained. To verify the accuracy of the proposed method, two examples are given. The simulations verify that the fractional order PD
^μ
controllers can provide larger stability regions, which is beneficial for designing the controller.