Classical Control Theory
Control Theory 3
See these articles on classical control theory.
An important concept in control theory is the convolution integral. It allows one to determine the output of a system given an arbitrary input. After obtaining the system's impulse response (the derivative of the step response, by the way, which may be easier to measure), it can be convolved with a desired input to get the expected output (See this for an intuitive explanation of what a convolution is.)
Once you have the impulse response, you know everything about how that system will behave; you don't have to try a bunch of different inputs and measure the output of each one. You can then analyze the system offline, which is what FRC teams like 971 do. They start with mathematical models of their systems (a model for a DC brushed motor exists, which we'll cover in Classical and Modern Control Theory), measure the step response of each, then tweak their models to match them (measuring the step response is easier than the impulse response).