Ask Dr Bob: What is the time constant and how do I calculate it?

Video Transcript:

Hello, I’m Bob Rice. And in this episode, we’re going to continue our discussion on the fo PDT model for describing process dynamics and characteristics. Specifically, we’re going to introduce and talk more about this idea of a time constant. A time constant is going to allow us to understand the speed of response of a process.

So the time constant is going to allow us to say, hey, if we have a controller output that moves our valve or pump or whatever it may be, and we see that our process variable starts here, and then it responds and finishes off its response, a time constant is going to tell us the speed of that response, or how fast or how slow it is, specifically, a time constant is the time it takes from when the process first starts to respond till it reaches about 63% of the way there. So if this is 100% of the way there, this is halfway there. 63 is a little more than halfway, so we’re going to call that 63% of the way there, the time it takes from where the process started to respond to it reach 63% of the way there is known as a time constant or a tau p, that is the speed of the response.

Okay, so if this is our process variable, right? How fast does it get there? How fast does it start to respond? If I were to tell you that the process had a small time constant, that would mean it’s very fast, a process with a small time constant, may look something like this, right? Where it moves very, very quickly, fast-moving loops are still going to end at the same point. But it’s actually going to reach that 63% of the time. They’re faster, right? What are some examples of fast loops, things like flow loops, or pressure loops, where when you move the output, the process variable gets to its final position, very, very quickly, within seconds, right, you can have a very slow loop like a temperature controller, right? Whereas if I had a slow process, it would still start at the same position, and take off at the same time. But it may take a while to actually steady out. which case the time it reaches 63% Is there. And so you can see that’s a much longer time constant.

So the time constant is related to how fast does it get there, a smaller time constant is a faster process. A larger time constant is a slower process, it’s how fast does it take to get there it is the clock of the system, the faster the process, the faster things like sample time on your PID Loop need to be because it’s moving very, very quickly. Think about this as the clock of your system. If you’re trying to drive a car, and you’re trying to accelerate and maneuver your way through traffic, that’s a very fast process, right? You need your input to be coming very, very quickly to you, right, you can’t close your eyes for seven out of 10 seconds and expect not to miss something, right? It’s the same thing with your process, the faster your process is, the faster your controller needs to be, be able to pick up all the characteristics of the system, you can’t have a flow loop that has a one-second process time constant executes every 10 seconds, you’re gonna miss, a lot of the dynamics in your control will not be very stable.

All right, so the time constant is the how fast, right? And so if my process started to respond at say, you know, let’s make the numbers easy. One o’clock, and zero seconds. And let’s say this one here, reached 63% of the way there at one o’clock, and three seconds. This one was one o’clock, and say eight seconds, and say this one’s a little bit slower at 105 and zero seconds. Okay? So our time constant would be the difference. So the fastest loop with this was three seconds after this. So our time constant would be three seconds. For this example, for this example, it took eight seconds to get there, right? So this was zero, this was eight seconds. This would mean that your process time constant for this one is eight seconds.

What about this very slow one? Well, it took five minutes to get there. So your time constant would be five minutes. Okay, so the time constant is the how fast is the clock of the system. Understanding the speed really helps you understand how well you can control the process. As we start to get into pi and PID control. We’re going to start using this information to help us dictate the control objective and how fast we can tune it. If we’ve got a five minute process time constant, it would be difficult to expect this loop to be able to get to a set point in five seconds, right? It’s unnatural for the process to move significantly faster than its process time constant. You can force it in some ways, but you’d reduce the stability and robustness right? So use this to stop to to help yourself understand the speed of the system.

Thank you for joining me today. In this episode we talked about the process time constant, and how it can be used to understand the speed and the clock of the system.

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