Algorithm for designing fractional order PDμ controller via integer order controller

A fractional PD controller is denoted by PD^μ where μ is an additional parameter which increases the flexibility of tuning. In this work, we present an algorithm about how to tune a fractional PD controller which is applied to a fractional plant. Firstly we consider an integer approximation of the fractional plant in order to use the method of dominant roots, thus we can find the tuning parameters (K_p and T_d correspond to the proportional and differentiation constants, respectively) given the specifications of setting time and damping ratio. Once the parameters K_p and T_d are set, the unknown parameter μ of the fractional controller is found by computing the error between the response of the fractional plant and its corresponding integer approximation. The value of μ parameter is determined by the minimum error and this values is used to tune again the parameter T_d. Satisfactory results are shown using this algorithm applied to fractional controllers for fractional plants.