Symbols count in article: 1.9kReading time ≈2 mins.
1. Introduction to Proportional-Resonant Controller
First, let's see the transfer function of PR controller and its bode diagram:
where the is the resonant frequency.
As can be seen in the bode diagram, the gain at 50Hz (314 rad/s) is infinite, so PR controller can be used to track reference of specific frequency. However, the reference frequency is not always a constant, e.g. the frequency of electricity grid. In practice, Quasi-Proportional-Resonant(QPR) can be used to solve this problem.
The transfer function of QPR and its bode diagram:
where the addition of reduces the gain at resonant frequency but increase the band width around resonant frequency.
You can change the parameter and run the demo code below to see how it changes the shape of bode diagram.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
s = tf([1, 0], 1) ;
Kp = 15 ; Kr = 2000 ; wr = 50 * 2 * pi ; wi = pi ;