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In the proportional-only controller the output will change from 0% to 100% depending on the amount of gain and the amount of error. E.g., if you have a product such as soup that you'd like to heat in a kettle that has a steam jacket, the amount of steam that's allowed to flow into the steam jacket will determine how hot the soup will become. The figure below shows a graph that indicates the percentage the steam valve opens from 0% to 100% along the x-axis, and the temperature of the soup in the kettle along the y-axis of the graph. Notice that the soup will be at 70°F when the valve is closed (0% open) and the soup will be 170°F when the valve is 100% open. This represents a 100°F span (70° to 170°).
Proportional band is used in some controllers instead of gain. This tends to be somewhat confusing because gain-type control is referred to as proportional control. Proportional band is the amount of change in error that will cause the output to go from full on to full off. The amount of change in error is calculated Was a percentage of full-scale error. This can also be defined as PB = 100/KP
The figure below shows several examples of proportional band. From the first example one can notice that if the proportional band is 10%, a change of 10% of the full-scale error will cause the output to swing 100%. In the second example, notice that if the proportional band is 25%, a change of 25% will cause the output to swing 100%.
Proportional band is also the inverse of proportional control (gain) and in modern microprocessor controllers it refers to the number of units such as degrees (°F) that the controller is trying to hold around the SP. If the proportional band is 10 and the controller is a temperature controller, it's trying to hold the temperature of the system within 10°F of the SP. This normally means the controller will not change the output if the PV temperature isn't more than 5°F above or below the SP, which is a span (band) of 10°F.
Proportional band can be calculated by the formula:
PB = 1/Gain
This formula will provide the amount of proportional band
as a percent of fullscale error. If the gain is large, the proportional
band will be small, and vice versa. E.g., a gain of 10 will provide
a proportional band of 0.1, and a gain of 50 will mean a proportional
band of 0.02. Conversely, if the controller has a proportional band of
5, the gain would be 0.2.
Above: Graphs showing the effects of 10% proportional band and 25% proportional
band.
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