Fractional Order Controller Design Using the Direct Synthesis Method

A method to design fractional order controllers for fractional order processes using the direct synthesis (DS) approach is proposed. The DS method is one of the most commonly used technique for tuning proportional-integral-derivative (PID) controllers. However, this approach has not been used for fractional order models. In this work, the DS method is adopted to take advantage of its simplicity; moreover, the procedure results in the structure of the controller as well as the controller parameters and the fractional orders of controller components. The resulting fractional order controllers are similar to the tilt-integral-derivative (TID) controller. Mathematical formulations are provided to obtain controllers for models with different degrees of the denominator polynomial; time-delay models are also considered. Simulation results are presented to demonstrate the efficacy of the designed controllers.