Ask Dr Bob: How can I find dead-time with the FOPDT model?
Hello, I’m Bob Rice. And in today’s episode, we’re going to continue our discussion of the FOPDT model, and how you can use it to describe the dynamics of a system. Today, we’re going to introduce the idea of dead time. The dead time is the model characteristic that tells us the delay of the system. Right? This is the most observable model parameter that you have, and one that you often just know intrinsically by working with the process.
So what is dead time, that time is the time it takes from when you make a change to the output. So if this is our controller output, and we’ve got a process variable, it’s the time it takes from when you make a change, till something actually starts to occur in the process, it’s the difference from the time you made the change, till something actually started to happen. This difference is known as theta, or the dead time of a system, it is the delay, dead time is the killer of control, the larger this number is, that means there’s more delay from the time you make a change, to something actually starts to happen.
Think about how difficult it would be to control the speed in your car. Every time you move the gas pedal, it took five seconds for the speed monitoring a change, right? So you push it down. And you wait. You wait, you wait. You wait, you wait, then you move. Right? How annoying would that be? Well, your PID controllers have to deal with that all the time with your different systems, they make a change, and nothing happens, right? This delay is really difficult for the PID controller to deal with, in times where the time constant is quick, right? If it takes five seconds for this to respond, but 50 minutes for the process to continue its response. You know, that’s, that’s not a big deal, right. But if this dead time, is say, you know, three seconds and my process time constant here is also three seconds, that’s actually a significant dead time related to the time constant of the system.
So even though this may be small, compared to the time constant of the system, it’s actually kind of large. So as the dead time starts to approach that time constant, you start to get difficult control scenarios becomes difficult to control the process quickly, you become what is known as a dead time dominant system, the time factor in the process is limited by the dead time and not the time constant. Okay, so the dead time is related to the delay of the system, you measure from the time the controller output is changed. So either the time you change here or complete, this change doesn’t matter which just be consistent.
That time you read the time off your process where it actually started to show a response. And you look at the difference, right? If it takes three seconds or five seconds, that’s your dead time. It is the delay of the loop. The larger your dead time is relative to your process time constant, the more difficult tight control fast control becomes. Okay, so thank you for joining me in today’s episode, we talked about the process dead time and how it’s the time it takes from when you move the output to the process variable response.
If you have a particular topic or an idea that you would like us to cover, please email us at firstname.lastname@example.org. Thank you, and I hope you enjoy this video series.