Fractional robust control of lightly damped systems

The article proposes a method to design a robust controller ensuring the damping ratio of a closed-loop control. The method uses a contour parameterized by the damping ratio in the Nichols plane and the complex non-integer (or fractional) differentiation to compute a transfer function whose open-loop Nichols locus tangents this contour, thus ensuring dynamic performance. The proposed method is applied to a flexible structure (a clamped-free beam with piezoelectric ceramics). The aims of the control loop are to decrease the vibrations and to ensure the damping ratio of the controlled system.