Loop Gain, Sensors, and Limits

Sensor Scale Changes the Loop Equation

The sensor gain is part of the feedback equation. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The sensor scale is part of the loop

A sensor gain of 1/2 makes a 6 volt output read as 3 volts.

m=12y=3 Vm={1\over 2}y=3\ \text{V}
Sensor scalingMeasured feedback is checked separately from output.outputmeasurederrorcommand

The command still closes the ideal loop

Target 6 volts minus measured 3 volts leaves error 3 volts; gain 2 gives command 6 volts.

6+−3=3,2⋅3=66+-3=3,\quad 2\cdot 3=6
Scaled sensor loopOutput, measurement, error, and command all agree.outputmeasurederrorcommand