What happens when your disturbances have similar frequencies to the reference you would like to track? (Is there still a way to reject disturbances?)

Tim Chung, 14 Oct 02

This is a great question, and the remedy to the problem described is nontrivial. The important thing to note is that tracking of a reference signal and disturbance rejection require "similar" actions: When tracking a reference, a feedback system tries to minimize the error, and the rejection of disturbance signals requires the system to "minimize" the effect of the disturbance.

One way you could do this is to increase the gains of the controller. Unfortunately, the trade-off is the performance of the system, defined by design specifications such as rise time, settling time, etc. Thus, it is up to the control designer to examine all factors, the disturbance type as one of them, and balance them according to the desired performance.

A more rigorous understanding of this issue is beyond the scope of this class, but is examined in advanced texts and courses like CDS 212.