The Universal Error Curve

What to Do
What It's About
What To Notice
What Works Best

What to Do

Move the mouse back and forth slowly and notice that the two cursors seem to be pulled back toward the thick vertical line (the target). The cursors are being pulled toward the target by control systems that control the position of each cursor. Mouse movements are a disturbance to cursor position; the control systems act to protect the cursors from these disturbances, keeping the cursors near the target. Now try to force the cursors to the left or right of the thin vertical lines (the error limits).You will find that the control system controlling the upper cursor always brings the cursor back to the target position; however, the control system controlling the lower cursor "gives up" control of the cursor once the cursor is outside the error limits.

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What It's About

This demonstration shows one way a control system can be designed to avoid the problem of wasting its efforts when control is impossible. Control is impossible when disturbances are overwhelming and force a controlled variable well away from its reference value. When this happens, error is large and the system is generating as much output as it possibly can. But this output is not sufficient to counter the disturbance. So the output is not contributing to control; it is wasted effort. One way to avoid this waste is to design the control system's comparator function so that the error signal starts to decrease once the difference between reference signal (r) and controlled perceptual signal (p) reaches a certain threshold value. A graph of the comparator function relating the size of the error signal (e) to the size of the difference between reference and perceptual signal (r-p) would be an inverted U instead of a line always going up to the right. This inverted U relationship between e and (r-p) is called the Universal Error Curve.

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What To Notice

The control system controlling the top cursor is able to put out as much effort as necessary to compensate for any disturbance to cursor position. So no matter how you move the mouse the top cursor is always kept near the target position. The control system controlling the bottom cursor cannot generate the effort necessary to compensate for large disturbances to cursor position. This control system incorporates the Universal Error Curve in order to avoid wasting its efforts trying to compensate for disturbances it can't handle. Disturbances that move the bottom cursor outside the error limits lead produce a decrease rather than an increase in the error signal that drives the system's output. The system stops generating output (because error is small) even though the difference between reference and perceptual signal is large. The system appears to "give up" control of the bottom cursor; then this cursor is outside the error limit lines it is not being controlled; so you are able to move the bottom cursor around without resistance from the control system. If you move the bottom cursor back inside the error limit lines it will be "captured" by the control system; the error signal becomes large so the outputs of the control system drive the cursor to the reference (target) position.

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What Works Best

Make sure both cursors are between the error limit lines when you start moving the mouse. Also, make sure the cursor is over the gray panel when you move the mouse. Small movements of the mouse produce large disturbances so be sure to start by moving the mouse slowly or the bottom cursor will be immediately driven outside the error limits.

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Last Modified: January 2, 2003
MindReadings
Richard S. Marken