# Limitations to consider when picking a cut-off frequency low-pass filter for PID control?

Considering a first-order low-pass filter transfer function: $$\frac{\omega_c}{s + \omega_c}$$

Where $$\omega_c$$ is the cut-off frequency. Are there any limitations on where to place this pole? For my PID response, it would be nice to have it at 100-200 rad/s, but I'm not sure if this is practical given my other poles are at much smaller frequencies. I'm still new to tuning PID, so any insight would be extremely helpful. Thanks!

• Are you talking about adding the LPF into the loop to cut noise? For small-signal loop stability, it doesn't matter, but the effect on the closed loop vs disturbance rejection will be different if it goes into the "forward path" (like before the plant) vs "reverse path" (like right after the sensor reading) in the loop. If the noise being filtered causes something to saturate, that is also a consideration in position. Finally, the pole will of course impact the controller's performance if it's low enough. Nov 25, 2021 at 16:22
• No, I was talking about the LPF that you add before the derivative term to prevent amplifying derivative noise. Nov 26, 2021 at 9:18
• In that case, the analysis is pretty much the same as if you added that pole to the plant. If you have the loop designed without the additional pole, compare the frequency of the additional pole vs the loop's bandwidth (i.e. BW of the noise gain). If the pole has comfortably higher frequency (e.g. 10x) compared to the bandwidth, I think you can not worry about it much unless fine tuning. Otherwise, repeat all analysis including the new pole. Can include e.g. bode plots of gain going around the loop, input and disturbance responses, and step or impulse responses for input/disturbance. Nov 27, 2021 at 17:21