Proportional Band:

Along with proportional control, the last control element has a definite position for every value of the measured variable.  Instead of, the outcome has a linear relationship along with the input. A Proportional band is the change in input required to generate a full range of change in the output due to the proportional control action.  Or easily, it is the percent change of the input signal needed to change the output signal from 0% to 100%.

The proportional band determines the range of output values from the controller which operate the last control element.  The last control element acts on the manipulated variable to determine the value of the controlled variable. The controlled variable is maintained inside a specified band of control points around a setpoint.

To elaborate, let's look at Figure.

Figure: Proportional System Controllers

In this instance of a proportional level control system, a flow of supply water into the tank is controlled to manage the tank water level inside prescribed limits. The demand which disturbances placed on the process system is such which the actual flow rates cannot be predicted.  Thus, the system is designed to control tank level inside a narrow band in order to minimize the chance of a large demand disturbance causing runout or overflow.  A fulcrum and lever assembly is used as the proportional controller. Float chamber is the level measuring element, and a 4-in stroke valve is the last control element.  The fulcrum point is set like in which a level change of 4-in causes a full 4-in stroke of the valve.  Thus, a 100% modification in the controller output equals 4-in.

The proportional band is the input band over that the controller gives a proportional output and is described as follows:

Proportional band = (% change in input/% change in output) x 100%

For this instance, the fulcrum point is such in which a full 4-in change in float height causes a full 4-in stroke of the valve.

P.B. = (100% change in input/100% change in output) x 100%

Thus:

P.B. = 100%

The controller has a proportional band of 100 percent that means the input must modification 100 percent to cause a 100 percent modify in the output of the controller.

The proportional band would become 50 percent if the fulcrum setting was changed so which a level change of 2 in, or 50 percent of the input, causes the full 3-in stroke, or 100 percent of the output. The proportional band of a proportional controller is important because it determines the range of outputs for generates inputs.