Feedback Control Cross Scans

Loop Gain Error Three-Row Scan

gain shrinks steady error

Holding target and sensor fixed while gain changes shows the feedback equation as a three-point scan. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Forward gain one leaves four volts of error

Target 8 volts with sensor gain 1 and forward gain 1 closes at output 4 volts, so the error is 4 volts.

y=82=4 V,e=4 Vy={8\over 2}=4\ \text{V},\quad e=4\ \text{V}
Loop gain scan rowOutput, measured value, error, and command are checked.outputmeasurederrorcommand

Forward gain three cuts the error to two volts

Keeping target and sensor fixed, gain 3 gives output 6 volts and error 2 volts.

y=244=6 V,e=2 Vy={24\over 4}=6\ \text{V},\quad e=2\ \text{V}
Loop gain scan rowOnly forward gain changes between scan rows.outputmeasurederrorcommand

Forward gain seven leaves one volt of error

Gain 7 gives output 7 volts and error 1 volt. Three rows make the shrinking steady-state error visible.

y=568=7 V,e=1 Vy={56\over 8}=7\ \text{V},\quad e=1\ \text{V}
Loop gain scan rowThe checked command equals the ideal output.outputmeasurederrorcommand