In P Controller what is the difference between Proportional Gain (Kp or Gp) and Proportional band (PB)?


1.What is Gain and Band in P Control Mode ?
2. Where Gain used and where Band used ?
3. Why gain used and why band used ?
4. What is the significant to go for such variations ?


P- Mode is a basic Proportional Control Mode, where the gain is a multiplier of change in out put in relation to the size of Error. Proportional Band or Band is a % value suggesting the gain but it is an inverse of Gain. Both can be used by any Technician with basic PID control knowledge.

The On -OFF control has two parameters to adjust:

  • Proportional band (Bp): is the zone or strip where the control acts.
  • Gain: is the slope or constant that acts in conjunction with the BP at the output of the controller.

The two parameters coexist together, in the ON-OFF control when setting the Bp is set the Gain and vice versa. It is used in very simple processes where an error is not too small.

In proportional controller, the proportional gain decides the sensitivity of the controller to its error input (Set point-Process Value ), higher the gain higher will be the output of the proportional controller even to small deviations from the setpoint. Whereas the proportional band is the operating range within which the system being controlled can react, Ex. many actuators operate on 4-20 mA range, this range is the proportional band provided the actuator is controller by proportional controller

A better way to look at PB & Gain is to use percentage % values for both. So a 4 - 20mADC input & output or, a 3 - 15 PSIG input and output would be viewed as 0 - 100%.
For a gain = 1 (100% PB ) a 1% change in Measured Variable (input) would generate a 1% change in Control Variable (output) within a PID controller. The change being from the Setpoint. Being a PID controller the change can be + or - based upon whether the controller is set for Direct Action (+) or, Reverse Action (-). Rest Action (Integral Action ) is required to bring the Measured Variable back to the Setpoint.