Control system gain

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I’m notoriously good at overcomplicating things; however, I want to explain a bit of technology that I’m passionate about to a co worker operating in a d9fferent disciple of engineering. This tech involves them to know about control system gain.
How do I explain the concept well without using examples involving resistors or overshooting?

In: Engineering
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‘Gain’ in a control system is simply the ratio between output and input.

In laymen’s terms, it’s the ‘amplification’ of the system.

Or you can look at it with basic physical models. If I have a lever that’s shorter on one side than the other, it forms a system where the distance moved by the shorter side has a ‘gain’ in distance on the longer side based on where the fulcrum is (the longer side moves further than the shorter side does).

If you’re driving and you make a lane change slowly, that’s going to take a few seconds but you will smoothly leave your current lane and smoothly arrive at your new lane. That’s low gain.

If you need to make a lane change quickly to avoid an accident, you’ll jerk your steering wheel. It won’t be smooth, and you’ll probably end up wobbling around on the new line as you overdo it and have to correct, and perhaps overcorrect, but you’ll change lanes faster. That’s high gain.

If you’re really in a panic and slam your wheel to one side, you’ll probably run off the road. That’s a gain so high the system is unstable.

Obviously there are simplifications here, “gain” can mean more than one thing (e.g. P, I, D gains in a PID controller), but you can use that kind of analogy to try to explain things.