Source-Factor Depth Scans

Target Size Three-Row Scan

With sensor gain and forward gain fixed, changing the target size scales the closed-loop output and remaining error in the same simple pattern. The 4, 8, and 12 V targets close at 3, 6, and 9 V with errors 1, 2, and 3 V exactly for the ideal proportional loop; real loops add sensor calibration error, actuator limits, noise, delay, bandwidth limits, stability margin, drift, and voltage measurement uncertainty.

Holding sensor and gain fixed shows target size scaling every checked loop value. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Four volt target leaves one volt of error

With sensor gain 1 and forward gain 3, target 4 volts closes at output 3 volts and error 1 volt.

y=124=3 V,e=1 Vy={12\over 4}=3\ \text{V},\quad e=1\ \text{V}
Target size scan rowThe whole closed-loop ledger scales with the target.outputmeasurederrorcommand

Eight volt target doubles the output and error

The same loop with target 8 volts 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}
Target size scan rowOnly the target source value changes.outputmeasurederrorcommand

Twelve volt target leaves three volts of error

Target 12 volts gives output 9 volts and error 3 volts.

y=364=9 V,e=3 Vy={36\over 4}=9\ \text{V},\quad e=3\ \text{V}
Target size scan rowThree rows make target scaling visible.outputmeasurederrorcommand