Relation between filters and controllers

Hello All,

I am having a tough time figuring out the relationship between a filter and a controller.
Here is my understanding of the two terms (irrespective of implementation: analog or digital)

1. Filter : A block of hardware or software that when fed with a given signal generates an output with signals of only those frequencies for which it is designed for. Accordingly , we have different types of filters such as LPF, HPF etc.

2. Controller: This block of hardware or software basically has two inputs : A reference signal and the fed back output signal. The controller, in a typical negative feedback topology), calculates the instantaneous difference between the reference and fed back output to generate a 'control' output such that the error signal should reduce to zero.

With this background, I fail to understand how are a filter and a controller related? For example, how is it that a 2 pole 2 zero filter is also used as a 2 pole 2 zero controller (like in digital power control applications). I am just not able to figure out the intuitive link between the two, that should allow me to view one as the dual of the other.

Any suggestions? What am I missing?

Thanks a lot!

Filter :- We use it for allowing only desired part of signal.
Controller :- We use it for reducing error and making system stable.
So filter can be used at controller if it fulfilling the requirements.
Example :- A noisy signal..if you use a noise removal filter,one can get the less noisy output.But if sometimes we use a controller,it can add/remove noise .
Read 1st para of this doc :- https://www.controlguru.com/wp/p84.html