Improved frequency‐domain design method for the fractional order proportional–integral–derivative controller optimal design: a case study of permanent magnet synchronous motor speed control

An improved frequency‐domain method for the fractional order controller design is proposed in this study. A proportional relation between the integral gain and derivative gain of the controller is built, while the derivative order is set to be equal to the integral order. Applying the improved method, the controller parameters can be calculated analytically according to different design requirements. The proportional coefficient between the integral and derivative gains is studied and then the model of the optimal proportional coefficient for the commonly used permanent magnet synchronous motor speed control system is built. Based on the established model, the optimal controllers are obtained analytically applying the proposed method. Motor speed control simulations and experiments are performed, comparing the performance of the controllers obtained using the proposed method and those obtained using the current frequency‐domain method and other design methods. Simulation and experimental results show that the control system obtained using the proposed method achieves the specified stability, robustness to gain variations and the optimal dynamic performance.