Peter, your second link is a duplicate, you have another?
Washout filter. These are essentially high pass filters that are used on simulators.
https://en.wikipedia.org/wiki/Washout_filter
As for learning. I am retired and I am still learning.
I always liked Laplace transforms as a simple way to do differential equations using algebra. A PID is
PID(s)=Ki/s+Kp+Kd*s
Dividing by s, integrates
Multiply by s differentiates.
Simple.
That is a lot simpler than the formula you normally see using integrator and derivative symbols.
If I substitute j⍵ for s, where ⍵ is the input frequency, I can plot the frequency response of a Laplace transform in a Bode plot. I use Laplace transforms a lot.
If you can get Mathematica then great. It costs $2.5K the last time I checked. II
wxMaxima is pretty good for free.
Here is an example of how I use wxMaxima to compute the symbolic formula for the P and I gains for a simple velocity system.
https://deltamotion.com/peter/wxMaxima/AutoTuneEquations T0P1.html
I can see I need to update some of my wxMaxima examples that are 12 years old. wxMaxima has made big improvements since then.
Look for tutorials for anything you want to learn and go through the examples.
Learning is a marathon not a sprint. Only high school and college student think of learning as a sprint, AKA cramming for a test.