I came across this doubt while reading the Wikipedia page on PID Control. The section on Steady-state error states:

Steady-state error (SSE) is proportional to the process gain and inversely proportional to proportional gain.

First of all I'm not able to understand what "process gain" actually means and how it differs from proportional gain. Secondly, I can't understand the relation between SSE and the two gains.

PS. I haven't taken a formal course on Control Systems and I'm just a hobbyist trying to make a PID controlled line follower at home. So, it might be the case that I've totally missed something important.


To understand this, take a look at this image, also from the Wikipedia article:

Feedback control loop diagram

The “process gain” is not part of your PID controller. Rather, it is a representation of what is actually happening in your process. Consider a heater control. The signal you are measuring is temperature, but the output of your controller would be something to turn your heater on and off (perhaps a pulse width modulation duty cycle). The “process gain” is simply a mathematical representation of how the actual temperature responds to what your heater is doing.

The article is saying that steady state error gets bigger if the process gain gets bigger, but gets smaller as you turn up the proportional gain in your PID controller.

  • $\begingroup$ Thanks for your response. In the example you provided, does "process gain getting bigger" refers to the rise in temperature leading to more heating? $\endgroup$ – TheReal_Skywalker Mar 19 '20 at 18:16
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    $\begingroup$ @TheReal_Skywalker “Process gain getting bigger” would be like if you changed out your heater for a more powerful one, such that the same controller output that you had before would now give you more heat. If you didn’t change your controller gains, then you could expect that steady state error could get worse. $\endgroup$ – Ben Miller - Remember Monica Mar 19 '20 at 18:22
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    $\begingroup$ Okay, now I think I understand this. Tell me if I'm wrong with another example - if I was making a line follower robot, more powerful (more torque, speed) motors without any change in code and tuning, would result in a bigger steady state error. However, if I increase Kp, it will become smaller. $\endgroup$ – TheReal_Skywalker Mar 19 '20 at 18:30
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    $\begingroup$ @TheReal_Skywalker Yes, you’ve got the right idea. However, increasing proportional gain, while it will reduce steady state error, can also give you other effects, such as increasing overshoot or causing instability. Another solution for reducing steady state error is increasing the integral gain. That’s the first thing I’d try if you are happy with the response of your controller otherwise and are simply trying to eliminate steady state error. $\endgroup$ – Ben Miller - Remember Monica Mar 19 '20 at 18:34
  • $\begingroup$ Good to hear that, thanks a lot for making me understand this. As increasing the integral gain will also increase instability, increasing the derivative gain can help here, I guess? $\endgroup$ – TheReal_Skywalker Mar 19 '20 at 18:37

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