If you have a system whose response is a first order lag, and you force it with a step function, its output gradually approaches a final value, and the remaining difference between the output present value and that final value is decaying exponentially, right?
Thanks! This should be easy to answer, I thought, but after hunting around a while I didn’t get an answer that was clear to me.
I had to look up “first-order lag”, but yes, you’re right. In the language of differential equations, you can write the output as a superposition of a particular solution and a homogeneous solution; the particular solution is just a constant (whose value is determined by the height of the step function), and the homogeneous is a decaying exponential (either positive or negative.) Add the two together and you get a solution that asymptotically exponentially approaches a particular constant value.
Hope this wasn’t too jargon-filled. Further clarification/obfuscation available upon request.
No, MikeS, beautiful. I found so many items that probably confirmed what I thought but did it in such a powerful and generalized way that it didn’t help me at all. You’re perfect.