Tuning fractional order proportional differential controllers based on vector in the complex plane for second order systems

In this paper, the vector method design schemes of fractional order proportional differential controllers have been proposed. This method is to map the controller to get a set of vectors in the complex plane. According to the method of vector and geometric in the complex plane, the complicated derivation and calculation can be simplified in the process of the controller design. In addition, the established geometric relationship equations not only can still be used when the plant is different, but also can be programmed in MATLAB. Therefore, the repetitive process of formula derivation can be omitted. From the simulation results presented, the obtained parameters based on MATLAB program is unique and the designed fractional order proportional differential controllers work effective.