Comparison of speed control techniques in field oriented control of permanent magnet synchronous motor: Lyapunov approach

Abstract

The main focus of this study is the minimization of Permanent Magnet Synchronous Motors (PMSM) steady-state speed error. In order to do this, a Lyapunov candidate function that contained the speed error is defined and a Based Lyapunov Theory (BLT) speed controller is designed. The novelty of this paper is the smoother pre-filter applied to the reference speed guarantees the stable operation of the nonlinear controller at step change in reference signal. The pre-filter design is carried out in a way that does not have a negative effect on the settling time, which is one of the step response characteristics. A proportional-integral (PI) speed controller is designed for comparison. FOC technique is used for inverter control. As the speed controller of the system, PI and BLT controllers are designed separately. Simulation studies are run in MATLAB/Simulink. PI speed controller coefficients are determined using the pole assignment method. For this purpose, PI coefficients for operating the controller at the selected frequency and the desired damping ratio are calculated. Stability analyses are carried out for PI and BLT speed controllers. A low pass filter that allows the system to apply a smoothed reference speed is designed in order to eliminate the range in which the derivative of the reference speed used in the BLT speed controller is undefined. Three different simulations are modeled. In the first one, the reference speed is changed in both directions by step function, under constant load torque. The speed and torque performances of both speed controllers are compared with the performance criteria including settling time, overshoot, peak value, peak time, root mean squared error (RMSE), and integral of time weighed absolute error (ITAE), and the results of the comparison are shown in figures and tables. In addition, a second simulation including reference load changes is made to model load torque disturbance as a robustness test, and a third simulation containing resistance changes is made to model parameter uncertainty are carried out. Both transient response and steady state response of controllers against parameter changes are examined in simulation 2 and 3. With the proposed BLT controller, the transient and steady-state response of the speed is improved both at the time of torque change and at the time of winding resistance change. The results are given in figures and tables.

Keywords

• PMSM
• Speed Control
• Signal Smoothing
• Nonlinear Control
• FOC
• Vector Control
• SVPWM
• Lyapunov Function
• PI
• Barbalat’s Lemma
• Stability Analysis
• RMSE
• ITAE

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