about control system

greetings...

i am after examples of control system running with overdamped, underdamped, critically damped and underdamped designs.

i was hoping that you could help to find great sites where I could get good discussions on how they were designed.

designs with control theory includes elevator, cars, airplanes, trains...... etc...
but i don't know how to classify as to whether they are overdamped ......

please help.... thanks to everyone who would make a reply..
links are highly appreciated.

I think they are designed for a specific response, settling time, and overshoot rather than the 3 terms you used in that case. If those 3 terms are being used, I would think they are aiming for critically damped.

are there any sites you could refer for me to look why they should be critically damped or not??? I was after examples of system with all those sort of damping...
thanks..
i was particularly interested with elevator and train designs......
thanks...

Maybe you are looking for something about PID control loops?
https://newton.ex.ac.uk/teaching/CDHW/Feedback/ControlTypes.html