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Why the Need for Bias in Proportional Only Control?
Can anyone advise me on why in a Proportional only control, we need to add a Bias term?

Can anyone advise me on why in a Proportional only control, we need to add a Bias term?

The equation for "P" only control is

Controller Output = Error*Gain + Bias

Hence when the measured variable (PV) equals to the setpoint (SP), the error is zero, hence the equation above becomes;

Controller Output = 0*Gain + Bias = Bias

I do understand that this offset (Bias) is an inherent problem with "P" only control when error is zero. The controller output will keep adjusting the control valve and the PV will never be equal to the SP! (Assuming a level control loop in a water tank)

Why is it that we need this Bias since it introduces this offset problem? Can't we just do away with it?

Help in any form is appreciated.

If you have any other info, please email me at


Hello Roy!

Bias term is used in proportional control to set the level of controller output to an appropriate value. If you take a look at the equation of P controller as you wrote it, you find out that when the control error is zero, the controller output is also zero. For example, if you had a control valve, you would be closing it every time (controller output = 0) when the control error (PV equals to SP) was zero! This is hardly what you wanted. Therefore, you might wish that when there is no control error (PV equals to SP), the controller output is non-zero such as 50% when the control valve range is from 0% (closed) to 100% (fully open). Therefore, you set the bias term to 50%.

By the way, this is how the integral control (=automatic reset) was born. It was troublesome to set the bias term of P controller to have such a controller output so that PV would always follow SP (zero control error). An automatic way to do this was found out and this invention was called automatic reset. Nowadays we better know it as a PI controller.

You may set your bias term anywhere between 0-100%. So, if you find it confusing, set bias to 0.

With regards,
-Pasi A.

Hi there Pasi A.

Wow. That's for clearing my doubts!

Can I contact U for some other discussion/advices on control loop tunning? I am just 2 yrs into the instrument & control line and am picking up all these things slowly.

my email is

By Pasi Airikka on 29 July, 2003 - 10:54 pm

Sorry for the delay, Roy ;=) My e-mail is:


By Friedrich Haase on 5 July, 2003 - 8:18 am

Moin Roy, moin all,

Your process needs a non-zero Controller Output to resume at a non-zero PV. Without the bias a Proportional Only Controller cannot deliver a non-zero Controller Output.

That's the very first reason for an integral part.

Sometimes the plant incorporates an integral part, e.g. a positioning drive, which could serve as well. It depends on how/where disturbancies are introduced in your control loop.

Hope this helps.

regards Friedrich Haase

By Timo Tuokkola on 5 July, 2003 - 8:30 am

As I understand it, the reason for the Bias term in a proportional only control is the fact that most controllers do not have a bi-polar output. A proportional only controller with a unipolar output requires a Bias term in order to be able to respond to a negative error. Typically, the bias term is adjusted so that the controller output sits at the midpoint of its range when the error is zero.

By Anonymous on 5 July, 2003 - 9:12 am

The Bias term (b) in the equation m = (Kc)(e) + b is the live zero of the controller output. For example, for a 4-20mA controller output, b is 4mA. Thus this bias term is required for all control modes including PI, PID, PD, etc.

By Ade Tracy on 5 July, 2003 - 9:31 am

You are intrested in a zero error condition. The system requires some output to maintain the system at the Set Point. That output is the bias. At Set Point there is no offset.

Make Bias = 0 if you don't need it. What if your water tank had a small constant "Blow down"? In that case, you would adjust the bias to equal this constant load so that the level would be maintained evenly when SV = PV. Or maybe the device being controlled requires a positive value to hold a zero setting. Say your controlling a device that is bi-directional from a -5 to +5 volt signal and the output of your controller is 0 to 10. Setting the Bias to 50% would make the output "zero" = zero.

By Peter Whalley on 9 July, 2003 - 1:21 am


The offset in the controller output is not the problem with Proportion Control. The problem is that the Error is not always equal to zero as you may wish. That is the controlled variable (not the controller output) does not always equal the set point. The Bias is introduced into the equation to give zero error at some suitable operating point and generally so that the error varies around the set point (above and below) as the system operates. Without the Bias, the error may always be either +ve or -ve rather than close to zero.

Setting the Bias to zero is likely to result in a larger error than would be the case with a suitably selected Bias value.


Peter Whalley
Magenta Communications Pty Ltd
Melbourne, VIC, Australia
e-mail: peter*no-spam*
delete *no-spam* before sending

you can decrease P controller error offset by adding additional signals from process disturbance to bias. Bias only adjust error offset only for one operation point. you have to multiple this signals by small coefficient before adding to bias

By Steve Myres on 31 March, 2014 - 11:26 am

Think of it as "poor man's integral". For one specific value of load, you can control to setpoint (and will do better at other, similar load values than without the bias).

By Hans H. Eder on 1 April, 2014 - 2:18 pm

The equation you presented gives you the answer:

"The equation for "P" only control is Controller Output = Error*Gain + Bias"

It simply means: The bias is the value of the OP when the PV = SP , i.e. the error = 0.

Consider a temperature control loop, e.g. the product outlet temperature of a furnace : Whenever the PV equals the SP, in other words: when the error = 0, the controller OP simply cannot be 0 this would mean zero heat input.