Abstract
In this paper, a fractional-order PI plus D (PIλ-D) structure is proposed for second-order integrating plants. A feedback controller is designed to locate the integrating pole(s) to improve the stability region of the controlling system. Then, the explicit formulae are derived to construct the complex root boundary (CRB) for a given plant model with fractional integrator. By stabilizing approach, it is feasible to put the constraint to calculate the optimal controller parameters. Its effectiveness is presented through numerical examples and a hardware experiment on physical integrating system, namely the altitude control of a quadrotor. The results reveal the improved performances with robustness by the new approach.