H. Salimi - Department of Electrical Engineering, Arak University of Technology (AUT), Arak, Iran.
A. Zakipour - Department of Electrical Engineering, Arak University of Technology (AUT), Arak, Iran.
M. Asadi - Department of Electrical Engineering, Arak University of Technology (AUT), Arak, Iran.

kground and Objectives: Permanent magnet synchronous motors (PMSM) have received much attention due to their high torque as well as low noise values. However, several PI blocks are needed for field, torque, and speed control of the PMSM which complicates controller design in the vector control approach. To cope with these issues, a novel analytical approach for time-response shaping of the Pi controller in the filed oriented control (FOC) of the PMSM is presented in this manuscript. In the proposed method, it is possible to design the controlling loops based on the pre-defined dynamic responses of the motor speed and currents in dq axis. It should be noted that as decoupled model of the motor is employed in the controller development, a closed loop system has a linear model and hence, designed PI controllers are able to stabilize the PMSM in a wide range of operation.Methods: To design the controllers and choose PI gains, characteristic of the closed loop response is formulated analytically. According to pre-defined dynamic responses of the motor speed and currents in dq-axis e.g., desired maximum overshoot and rise-time values, gains of the controllers are calculated analytically. As extracted equation set of the controller tuning includes a nonlinear term, the Newton-Raphson numerical approach is employed for calculation of the nonlinear equation set. In addition, designed system is evaluated under different tests, such as step changes of the references. Finally, it should be noted that as the decoupled models are employed for the PMSM system, hence exact closed loop behavior of the closed loop system can be expressed via a linear model. As a result, stability of the proposed approach can be guaranteed in the whole operational range of the system.Results: Controlling loops of the closed loop system are designed for speed control of the PMSM. To evaluate accuracy and effectiveness of the controllers, it has been simulated using MATLAB/Simulink software. Moreover, the TMS۳۲۰F۲۸۳۳۵ digital signal processor (DSP) from Texas Instruments is used for experimental investigation of the controllers.Conclusion: Considering the simulation and practical results, it is shown that the proposed analytical approach is able to select the controlling gains with negligible error. It has shown that the proposed approach for rise time and overshoot calculations has at most ۰.۰۱% for step response of the motor speed at ۵۰۰ rpm.

Electrical Motor Drive, Filed Oriented Control (FOC), Permanent Magnet Synchronous Motors (PMSM), Controller Tuning, Dynamic Responses