I'm working on implementing a filter with a very slow step response. This filter is implemented as a cascaded second-order-section filter (transposed direct form 2). I'm using the output of this filter as the input to a controller. Thus I'm trying to slow down how quickly the controller set point is able to change.
I'm running into an issue where I would like to initialize the set point of this controller. In order to do this, I need to provide initial conditions to the filter.
Let's assume I have a 7th order filter implemented in SOS stages as described above. Is it is a trivial task to find initial conditions such that I can specify the output but also have it such that the there is no "momentum" in the filter for it to drive from its initial output?
If this were an analog filter, I am essentially trying to specify that y(0) = constant, while y'(0), y"(0), ... etc. all equal zero.
I've never attempted to do something similar with a digital filter. Is this trivial? Is this non-trivial? Are there any references on the subject?
Thanks for the help!
Edit: So I've changed up my system design such my filter output isn't the setpoint, but rather a deviation from a setpoint. This allows me to simply zero the filter to achieve what I was originally trying to do. However, my question still stands for a matter of interest.