Home
CS
Sites
ABdA
Help
abda@engineer.com
E-mail

WEEK 06: MODES OF CONTROL: PROPORTIONAL


Sections: On-Off | Proportional | P-Integral | P-Derivative | P-I-D

Proportional Mode of Control

Description. The final correcting device has a continuous range of possible positions which is proportional to the error signal, thus the output of the controller is proportional to the input.

ProportionalReferring to the graph on the right, the proportional band is the difference between the measured value when the valve is 100% open and when the valve is 0% open.

Universal Characteristic. Using a particular controller, variations in process control may require a setpoint of 65% Valve Opening [V.O.] at 180°F for under heavy load but a setpoint of 90% V.O. at 180°F for a very heavy load. If different loads exist, the slopes of the signal would not change, only the horizonal locations, or the abscissa.

Outside this proportional band, the response to any signal ceases. As in differential gap, the proportional band is also adjustable. Controllers of this mode, can exhibit direct or inverse proportionality, depending on the respective industrial application.

Proportional Band [P.B.]. Usually expressed as percentage of the full controller range, F.C.R., by which the measured value must change in order to cause the final correcting device to change by 100%.

Three types of proportional bands are: the Narrow, usually from 0% to 20%, the Medium, usually from 21% to 50%, and the Wide, usually from 50% to 100%. All these types, and owning to the characteristic of a proportional controller, the actual measured value does not return to the original level after a disturbance. Thus a good choice of proportional band is imperative.

 Example Calculations.
Given a controller with the following specifications, full range [F.R.]: 60°F to 300°F, and Proportional Band [P.B.]: 20%, operating at a setpoint of 180°F at 40% Valve Opening [%V.O.], determine the temperature at which the valve is 100% open or 0% open [closed]. Express these values, respectively, into percentages of full range.

Solution:
F.R. = 300°F - 60°F = 240°F
P.B.temp
= ( 20%)(240°F) = 48°F
 x
= (20%)(240) / (100) = 19.2°F
t"2
= 180 + x = 199.2°F
t"1
= 199.2 - 48 = 151.2°F
Therefore:
t1 = 199.2 - 60 = 139.2°F
t2
= 151.2 - 60 = 91.2°F
As percentages of Full Range:
t1 = 139.2 / 240 = 58%
t2
= 91.2 / 240 = 38%
tSP
= 180 - 60 / 300 = 40%.

Offset. The permanent difference between the setpoint and the control value. This phenomenon only exists on all proportional modes of control, including the proportional-integral, proportional-derivative, and the proportional-integral-derivative.

 In (A), when the setpoint is changed in the opposite direction of the first offset, the new setpoint causes a better, or smaller, offset than the first.
In (B) when the setpoint is changed in the same direction as the first offset, the new setpoint results in a worse offset.

On-Off Mode . Proportional-Integral Mode


Home | CS | Sites | ABdA | Help | E-mail