Tuning of FOPID Controller Using Taylor Series Expansion

In this paper, a direct synthesis approach to fractional order controller design Is investigated. The proposed algorithm makes use of Taylor series of both desired closed-loop and actual closed-loop transfer function which is truncated to the first five terms. FOPID Controller parameters are synthesized in order to match the closed-loop response of the plant to the desired closed-loop response. The standard and stable second-order model is considered for both plant and the desired closedloop transfer functions. Therefore for a given plant with damping ratio 1 and natural frequency 1 n . The tuned FOPID controller results in the desired closed-loop response with damping ratio 2 and natural frequency 2 n . An example is presented that indicates the designed FOPID results in actual closed-loop response very close to desired response rather than PID controller. It is shown that the proposed method performs better than Genetic Algorithm in obtaining the desired response.