### The Nature of Control

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#### What to Do

In this tracking task, try to keep the lower line (the cursor) directly under the upper line (the target) by moving the mouse to compensate for the disturbances to the cursor. When you are able to do this you are able to control the distance between cursor and target. A graph of the results appears after several seconds of tracking. Press the "Run" button at any time to restart the tracking task.

This tracking task illustrates the basic variables and relationships involved in the process of control. In order to keep the cursor under the target (control the distance between cursor and target) you must move the mouse appropriately to compensate for the constantly changing disturbance to the cursor's position. The distance between cursor and target is called the controlled variable. When the controlled variable is kept near one value (such as zero, which corresponds to the cursor being under the target) it is under control. The value at which the controlled variable is maintained is called the reference value. When you control, you determine the reference value of the controlled variable.

#### What To Notice

The relationships between variables in this tracking task can be seen in the graph of the results. The numbers immediately below the data plot are measures of how well you controlled the cursor. RMS Error measures the average deviation (in pixels) of the controlled variable from a reference value of zero; the closer RMS Error is to 0.0, the better is your control of the cursor. Stability measures the ratio of expected to observed variation of the controlled variable. Expected variation is the amount the controlled variable would have varied if you had done nothing to control it; observed variation is the actual amount of variation of the controlled variable. If expected and observed variation are the same, there is no control and Stability is 1.0. If expected is much larger than observed variation of the controlled variable then this variable is under control and Stability is >> 1.0. The greater the Stability measure, the better your control of the controlled variable.

RMS Error can be used to measure control when the reference value of the controlled variable is known. The Stability measure makes it possible to measure control when the reference value of the controlled variable is not known. To see why this is important, try keeping the cursor about an inch to the right of target. Now the reference value of the controlled variable is about 100 pixels. The RMS Error will be large (suggesting poor control) but the Stability will also be large, indicating that control is actually quite good

At the bottom of the graphic display are measures of the correlation between the variables in this control task. The number on the left is the correlation between cursor and mouse movements (C-M). The number in the center is the correlation between mouse and disturbance (M-D) movements. And the number on the right is the correlation between cursor and disturbance (C-D).

When you are able to control the distance between cursor and target, keeping that controlled variable equal to zero, you will see that the cursor-mouse correlation is rather low (usually between -.2 and .2). This is surprising if you think of cursor movements as the stimulus for the mouse movements (the response). You will also see that the disturbance-mouse correlation is very high (usually greater than .99). This is also very surprising since the disturbance in this task is invisible. All you can see in this task is cursor movement, which is at all times a combined result of disturbance and mouse movements. Nevertheless, mouse movements are strongly (negatively) correlated with the invisible disturbance rather than with the visible cursor movements. Finally, you will see that the cursor-disturbance correlation is very low, indicating that the disturbance has little or no effect on the cursor. This result shows that the position of the cursor is under control -- protected from the effects of disturbance.

The data plot above the correlation numbers shows the temporal changes in the values of the variables in this control task; cursor position (C), mouse position (M) and disturbance value (D). Note that the trace of cursor position (C) is nearly a straight line when the cursor is under control. The traces of mouse (M) and disturbance (D) mirror one another, as they must if the cursor is to stay nearly constant (under control).

#### What Works Best

It may take a while to develop the ability to control the cursor skillfully. But the basic relationships between variables should show up even if you cannot keep the cursor exactly under the target. You should practice this task until you are able to obtain an RMS Error measure of control that is less than about 4.0 .