# Ask Dr Bob: How to calculate the process gain?

### Video Transcript:

Hello, I’m Bob Rice. And in this episode, we’re going to continue our discussion of the process model for first order plus dead time systems. recall in the last video, we talked about trying to understand the relationship between when the controller output moves in the process variable response.

In this episode, I want to talk specifically about how to calculate this term called the process gain. The process gain tells us how far does the process variable booth when we manipulate the output? So we need to calculate that, how do we calculate that? So first, we have to understand how far did we move the controller output? So we have to know when we move the controller output from A to B, how far did that go? So in this example, we’re going to say we move the controller output from 50% to 60%. When we go from 50 to 60%, that means we move the controller output or the valve 10%. Okay, so we move the control valve 10%, how far did the process variable move for that, we’re going to need to be able to measure the process variable. So in this case, let’s say we went from 130 degrees Fahrenheit to 150 degrees Fahrenheit. So we move the controller output 10%, we open the control valve 10%, and our temperature went from 130 degrees to 150 degrees.

So our process gain is how far our process variable moves divided by the change in our controller output, that is our process gain or k p. Okay, so in this example, the process variable goes from 130 to 150. That is a change of 20 degrees Fahrenheit as our change in process variable, so our delta p VI, is 20 degrees F, then we have to look at what our change in the controller output is. So we divide that by the change in the output, which is going to be 10%. So we divide those two together 20 divided by 10. And we get two degrees Fahrenheit per percent. Co. What that means is that for every 1%, we open our control valve or our pump, or whatever it is, our temperature is going to increase by two degrees Fahrenheit. It gives us the sensitivity and the how far.

So for every 1% I move the control valve, my temperature increases by two degrees Fahrenheit, it gives us the how far, so we’re able to take the data for how far the controller output was moved. And understand how far the process variable responded, divide the process variable by the controller output, and we get our process gain. This tells us how far or how sensitive the process variable is to changes in the output. The larger the number, the more sensitive the process variable is to changes in the output. If my process gain was not two degrees Fahrenheit, instead it was 20 degrees Fahrenheit per percent CO would mean that for every 1%, I move the control valve, the temperature increases by 20 degrees Fahrenheit, obviously 10 times further, it’s defining the sensitivity of the process. This gives us a lot of information about how well we can control the process.

Think about this, if I can move a valve accurately at only 1% the best control I’m going to get is probably two degrees Fahrenheit. So if I needed to accurately manipulate the temperature point two degrees, I would have to accurately be able to move the valve point 1% If I cannot accurately move the valve point 1% I’m not going to get that point two degrees control, right? So it helps us understand the controllability of the system, the sensitivity of the system, and all those wonderful things that we can use to better refine our control objective and what is possible. In this web episode, we covered what the process gain was and how to calculate it from process data.

If you have a particular topic or an idea that you would like us to cover, please email us at askus@controlstation.com. Thank you, and I hope you enjoy this video series.