Assuming no filter is used to measure error (or rate of change in error) with respect to a desired state, would a PI controller more/less/about equally robust to signal input noise compared to a PD controller? And why?
My intuition tells me that they would be about equally bad/good because wild changes in the measured state would generate equally bad spikes in either the I or D terms. I have, however, read some (probably not reliable) sources alluding to the possibility that PI controllers are generally more robust to noisy measurements than PD controllers. Is this true? And if it is true, why would a PI controller be more robust to noise than a PD?