If you are new. Start with temp sensor and master how Derivative is used to anticipate rate changes with latency on air to sensor and Integral is used to amplify DC error on closure and Proportional gain keeps the loop tight. Phase margin with BODE PLOT is the measure of stability, where 60 deg is good and 90deg is nearly impossible.
So,latency, delay, inertial loads and other applications which cause Plant Control, feedback delays must be factored to control derivative gain. (Ad) and Ap, Ai are variable in this circuit.
I like to show Bob Pease's designs and his initials R.A.P. are similar R.I.P. which also indicates, he is retired from earth, but his ideas live forever.
**broken link removed**
After you master this then you can consider a design of a PLD industrial controller for automated servo controlled loops.
When you master that, then you can consider Smart PID, controllers which excite the servo to measure the inertial load and friction losses and compensate the PID gains for any installation. commercial solutions like this exist>$5k...$50k+with drivers but are essential for high power wide dynamic load servo speed controllers.
Now isn't that exciting?