# proportional band

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Thread Starter

#### Anonymous

pl. can you briefly explain me the meaning of proptional band with an ex:for pb=25%, pb=250%.

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#### Anonymous

If PB is of span, 25% = 25% of span. Example: the process controller is 0-1000 units. 25% = 250 units wide. Below this 250 wide window, the process output is full ON. Above this window, the process is full OFF. Inside the 250 wide window, the process is ON or OFF a sliding analog percent.

The important requirement is to match the PB to the natural responsiveness of the application. Too wide = sluggish response. Too small = oscillations.

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#### Ian

Gain = 100/pb

Therefore

Gain = 4 for pb=25
Gain = 0.4 for pb=250

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#### Kent L. Gerhardt

In a PID controller, the PB (Proportional Band) is the inverse of the Gain. One can write:
PB = 100 / Gain or Gain = 100 / PB where PB is in percent.

Take, for example, a level controller on a tank where we measure the level from bottom to top as 0 to 100%. We have a control valve on the outlet of the tank whose job is to maintain the level in the tank. The PB is defined as the range of level over which the control valve will go from fully closed to fully open. Suppose we decide that if the tank level should fall to 20% we want the control valve fully closed (0% open). Additionally, if the tank level rises to 60% full, we want the control valve to be fully open (100% open). If the tank level is between 20% and 60% we want the control valve to be open "in proportion" the the level. So if the tank level were to rise to 40% (half way up the PB), the control valve should be set to 50% open). This controller would have a PB of 40% (60% - 20%).

A proportional band of 250% is a bit tougher to visualize. Since the process, the tank in our case, can only go 100%, then a PB of 250% causes the valve to move only through a portion of its available stroke as the tank goes from empty to 100% full (assuming proportional only control - Integral and/or derivative action acts in addition to proportional).

Let's assume that we set the lower end of the proportional band at -75% and the upper end at 175%. The gives a PB of 250%. Physically it means that the level would have to fall to below (way below) the bottom of the tank to fully close the valve and above (way above) to fully open the valve. Since the level of our tank can't really go that far, it means that the valve will never fully close or fully open. This occasionally happens when the need for gradual valve movement as the process changes is more important than having a control valve that can close when the level gets low. Tuning is the process of finding the gain or PB that provides the optimal control valve response for controlling the process.

Many process controllers will also have integral and/or derivative actions that act in addition to the proportional control.

Hope this helps,

Kent L. Gerhardt
Gerhardt & Associates

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#### Johan Bengtsson

Assuming you speak about P, PI, PD or PID controllers:

Proportional band=100/gain, that means gain=100/pb

Roughly said:
The higher gain the faster (and less stable) control.
The lower gain the slower (and more stable) control.

Translated to proportional band that means
The higher Pb the slower (and more stable) control.
The lower Pb the faster (and less stable) control.

There are of course more to it than this, like some exceptions and what to do with the other parameters.

I heard some said that the name came from proportional only level control, where Pb is the range in level where the output goes from 0 to 100%. I don't know if that is the orgin of the name, but it is anyway true about how it works.

/Johan Bengtsson

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#### Peter Blyth

Briefly, GAIN=100/Pb,
GAIN=%change in output for equivalent %change in error (typical, but depends on PID algorithm used & controller implementation)
i.e.
Pb=25%, GAIN=100/25 = 4 = very reactive, typical level control, stable PV & linear relationship with output
Pb=250%, GAIN=100/250 = 0.4 = not very reactive, typical flow/pressure, or noisy PV, or non linear (usually high integral)

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#### Dr. Jogy George

Suppose our aim is to control the level of water in a tank. In percentage, we say that when the tank is full, it means 100% and when the tank is empty it is 0%. We put a controller at the outlet pipe to control the flow of water from the tank, and the input is taken as the % of water in the tank.

Now, we want to close the valve completely (controller output =0%) when the water reaches 20% and open the valve completely (controller output =100%) when the water level is above 60%. In this case, the proportional controller will have two parameters as the design criteria: Offset and proportional band PB. In the above case, the offset will be 20%, and the PB will be 60%-20% = 40%. This means, the gain of the circuit is 100%/ 40% = 2.5, and the offset is 20%. Thus, the output of the P controller is given by Pout = 2.5* (e(t) -20%). If one puts the error e(t) as 0% -20%, the output will be <0. If one puts the error e(t) as >60%, the output is >100%. In the band from 20% to 60%, the output linearly varies in the range of 0 to 100%.

This is just a modified version of what is given above, but with offset concept built in.

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