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What is meant by proportional band (Xp1, Xp2)?

In a purely proportional controller (P controller) the manipulating variable (controller output Y) is proportional to the control deviation within the proportional band (Xp). The gain of the controller can be matched to the process by altering the proportional band. If a narrow proportional band is chosen, a small deviation is sufficient to achieve a 100 % output, i.e. the gain increases as the proportional band (Xp) is reduced. The reaction of the controller to a narrow proportional band is faster and more pronounced. A proportional band that is too narrow will cause the control loop to oscillate. Any alteration of the proportional band will also affect the I and D action of a PID controller to the same extent.

If the proportional band is set to zero, the controller action is ineffective. This means that the controller operates solely as a limit contact. The selected hysteresis or switching differential is effective, the settings for the derivative time and the reset time, however, are not taken into account.
For all controller types, except for the 3-state (double-setpoint) controller, only the proportional band Xp1 is relevant. With 3-state controllers only, separate settings for the proportional band (for both operating senses) are necessary (e. g. Xp1 for heating and Xp2 for cooling).