What do you mean by "gain" in the speed control example? What relation to sensing does it have?

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In this example, we let the engine force, , be proportional to . The "gain" is the proportionality constant . The use probably follows from that in electronic amplifiers.

We do not consider sensing problems in this example. Instead we assume perfect sensing/measurement of the output, which is the vehicle's velocity, . The gain is only related to the control law.