# Ask Dr Bob: How can I model a process? What is the FOPDT model?

### Video Transcript:

Hello, I’m Bob Rice, and I’m the Head of Engineering for Control Station. Today we’re going to talk about process modeling and process dynamics. In fact, I’m going to show you a very easy way to be able to hand capture and calculate a first order plus dead time model, which is going to allow us to understand how the controller output impacts our process variable.

So we’ll start with a process, first, we’re gonna do a very, very simple one, we’re going to take a pipe. And we’re going to have a control valve over here, and we’re going to have some sort of sensor over here. Okay, so this is our process, we’ve got a control valve in flow. So what we want to do is we want to go ahead and take our control valve, and we’re going to hold it constant. And then we’re going to open it some amount and be able to see what happens. Okay, so in this case, we’re going to go ahead and open our control valve from, say, 40%. To 50%. So we’ve opened the control valve, Delta CO, 10%. Now, what do you expect the flow to do? Well, odds are the flow is going to start at some value, it’s going to be chattery, it’s going to bounce around. And then when we open the control valve, it’s going to start to increase and then settle out. Again, this is our process variable here, which is flow. Our controller output is down here, this is our valve, we open the control valve, and the flow increases.

The three parameters we’re after here, are known as the process gain, the process time constant, and the process dead time. These numbers tell us how far the process variable goes when we move the output, how fast does it get there, and then with how much delay is the process variable starts to respond when we move the controller output. So how much delay? Well, how do we calculate these?

Well, let’s start with the KP the process gain how far variable? That is? How far does the process variable go when we move the output? So we have to know how far does it go? Where does it start? Well, let’s say the starting average value here is 25 gallons per minute, then it increases to say 30 gallons per minute. So we’ve increased the flow by five. So the change in process variable is five gallons per minute. We open the control valve 10% we increase the flow from 25 to 30, which is five gallons per minute. So what is the process gain? The process gain is the change in the process variable divided by the change in the output. How far does it go? All right. In this case, the change in the process variable is five gallons per minute. The change in the output is 10% CO. So what’s our process game like to keep the math simple? This is 0.5 gallons per minute. Right? 0.5 gallons per minute? What is that percent CO? What does that number mean? It’s the sensitivity of the system. It means that for every 1% we move the control valve, our flow will increase by 0.5 gallons per minute. So for every 1%, we open the valve, the flow increases by point five gallons per minute. If we increase the output by 10% 10 times this is five gallons per minute, our process variable moves five gallons per minute. What happens if we moved it 100%? What’s 100 times this 50 gallons per minute. So the biggest change that we can get for the process in the range in which we modeled this would be 50 gallons per minute. So for looking to get 1000 gallon per minute change. We’re not going to do it with this process. Because if we move the valve 100% we’re only getting 50 gallons per minute change.

The next parameter that we’re after is known is how fast or the process time constant that is going to be how fast does it get there? And here, we’re specifically looking at how fast it takes the process variable to kind of get 63% of the way there. Right? So how long does it take from when the process first starts to change? till it reaches a little more than halfway there? This time is the time constant of the system. Right? So we need to know when did we make the change? When did we cross over 63% of the total change? Maybe this is five seconds. Okay, so it takes five seconds from the time we make a change to the process variable for the process variable starts to respond till it reaches about 63% of the way there.

The dead time, the last number here, the how much delay is from the time you make the change, till something actually starts to happen to a pretty small number here, maybe it’s 0.5 seconds. So we made the valve change, but the flow didn’t instantaneously move. It took about half a second before something started to happen. There was a little bit of hesitation, a little bit of delay, right? That’s the delay of the system.

How far did it go, how fast, and how much delay gives us the understanding and the behavior of the system. How far did it move? What is it sensitivity? How fast did it get there? How much delay? Do these define the dynamics of the system? And the next web series, I’m going to talk a little bit more about how to expand upon the knowledge of these numbers. How can we use that process gain to understand the sizing of the system or the sampling time or the delays or if we’re gonna have other control issues? So the first order plus model is the first order plus dead time model. So the first order plus dead time model is: how far, how fast, with how much delay.

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.