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Originally Posted by Andrew Blair
I believe what Ken was referring to ...
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you are right about the step response. You hit the system with a fixed command value and see what it does, when there is no feedback path
for example, if you are trying to control wheel speed, you hit the motors with a step from 0 to 6V, and you record the speed of the wheel. It will speed up, kinda like your graph is showing, and at some point it will level off at some constant speed.
That response is due to several factors: the torque the motor can produce, the static and dynamic friction present in the drivetrain, the inertia of the components (motor, gears, chains, wheels) and how much load is present (is the wheel free spinning, on a tile floor, on a carpet, going up hill....)
the graph shown is in the time domain, the x axis is time in seconds. If you perform a Fourier transform on the response of the system you get the frequency domain response. Its much easier to work with control systems and feedback in the frequency domain (I know I am losing most readers here).
So going back to an intuitive perspective, once you have measured the inertia and torque output and friction and load.... of the system, you have characterized it. You can also do this with the spec sheet for the motor, the gears, the chain, the wheels, calculate the friction of the bearings.... and characterize the system that way.
Then you can do some real magic with the math and S (frequency) domain equations. This is how you do PID control design on most systems. If you are designing the flight control system for a 777, you dont fly the plane around, then turn up the I gain 3% then fly it around some more to see how it responds, you analysis the systems first, and design the control system to make the aircraft fly the way you want it to.