Robust Control of a Class of Fractional Order Plants in the Presence of Pole Uncertainty

In recent years some approaches for robust control of plants with uncertainty in their poles have been suggested. Recently a new approach for tuning controllers has been introduced that can preserve phase margin in desirable value despite large variations in location of one of the poles and also it is able to provide required gain crossover frequency in the nominal case. In this paper by benefiting from this approach, a fractional order proportional derivative controller is introduced to control the plants with fractional order transfer function with uncertainty in their poles with order in the range (1, 2). Also, sufficient conditions on design specifications and plant parameters for ensuring applicability of the controller are derived. In addition, achievable region for the proposed FO[PD] controller is determined both analytically and graphically. Utilizing this proposed robust controller, not only gives desirable phase margin and gain crossover frequency in the nominal value of the pole but also it preserves phase margin despite large variations in location of the uncertain pole. Numerical examples will show the effectiveness of the proposed controller.