Design of Fractional-Order PIα Controller with two modes

A kind of fractional-order PI^alpha controller is considered. Controller structure with two modes is presented, active status of two modes and mode switching are described. The Tustin operator is used for digital realization of the fractional-order PI^alpha controller. Different approximation order is discussed to get a tradeoff between approximation precision and complexity of discretization expression. Comparison of fractional-order PI^alpha controllers with two modes and without two modes is demonstrated by experimental examples of torsion vibration suppression in the two cases. Some conclusions are given