How do I convert Ki, Kp, Kd to crossover frequencies or vice versa?
Ki, Kp, Kd and cross over frequency
Written by Paul Cracknell
Updated at October 27th, 2024
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The integrator or differentiator crossover frequencies are the frequencies where the integrator or differentiator gain is equal to the proportional gain (or 1 in cases when the proportional gain is not enabled). For the integrator, the gain is inversely proportional to frequency. For the differentiator, the gain is proportional to frequency. With 0 dB Ki and Kp, both the integrator and differentiator have 0 dB gain at 1 Hz.
Let's try an example. If we have 60 dB Ki, 20 dB Kp, and -80 dB Kd. For the integrator, it will have a 60 dB gain at 1 Hz, 40 dB gain at 10 Hz, and 20 dB gain at 100 Hz. As we have 20 dB Kp, the integrator crossover frequency is will be 100 Hz. For the differentiator, it will have -80 dB gain at 1 Hz, -60 dB gain at 10 Hz, -40 dB gain at 100 Hz..., and 20 dB gain at 100 kHz. So the integrator crossover frequency will be 100 kHz.
For more details, the transfer function of Moku PID Controller is:
Where: G_P is the proportional gain, S_I is the integrator gain, f_ic is the integrator crossover frequency, S_D is the differentiator gain, and f_dc is the differentiator crossover frequency.