The discussion revolves around the concept of time constants in transfer functions, particularly focusing on a third-order transfer function. Participants explore how to express time constants, the implications of adding poles, and the definitions of time constants in various contexts, including integrators and low-pass filters.
Participants do not reach a consensus on the definition of time constants or how to apply them in the context of the given transfer function. Multiple competing views remain, particularly regarding the implications of adding poles and the interpretation of time constants in different systems.
Participants express various assumptions about the nature of the transfer function and the behavior of the system, indicating that the definitions and applications of time constants may depend on specific system characteristics and configurations.
No. In fact, the response to a step input increases without limit as t → ∞. Seems like a really weird question.jaus tail said:
Also, the response to a step input is not oscillatory so there is no wn.
rude man said:
You should have spoken to your instructor about this by now, referring to my remarks in post 2. Hopefully he would then avoid asking such a meaningless question.jaus tail said:
The time response to a unit step input is 6(t/6 - e-3t/9 + e-2t/4 - 5/36). There is no single time constant, just two, and the first term indicates unlimited expansion in time. And there is no oscillatory component as you can appreciate. To what do you disagree?donpacino said:
It looks like it's just a couple of low pass filters followed by an integrator. Its response to a step function should be to integrate to infinity without oscillations.donpacino said:
The response to a unit impulse is also unlimited in time, although there is only one time constant in that case, it being 1/3 sec. Which would give (D), not (C), as the answer.jaus tail said:
Right.FactChecker said:
That definition is meaningless since it depends on the gain of the integrator: k/s with k the gain in sec-1.LvW said:
If you've been taught that T = 1/ζwn, use it in your exam. Main thing is to pass the exam!jaus tail said:
rude man said:
LvW said:
"Physically, the time constant represents the elapsed time required for the system response to decay to zero if the system had continued to decay at the initial rate, because of the progressive change in the rate of decay the response will have actually decreased in value to 1 / e ≈ 36.8 % in this time (say from a step decrease). In an increasing system, the time constant is the time for the system's step response to reach 1 − 1 / e ≈ 63.2 % of its final (asymptotic) value (say from a step increase)."LvW said:
That sounds right.LvW said:
That is a definition that I am familiar with. But I think that definition would not work for an integrator. So I don't know if there is a consistent definition for the different transformation types. That makes it hard to guess what it would mean for 1/(S3+aS2+bS+c).rude man said:
I rather think, I have given my answer already in post#10.rude man said:
LvW said:
That seems as good a guess as any. But the book answer is time_constant=1/2 and the response of this transformation to a unit step input does not reach 1 till about 1.8 seconds. So it doesn't seem like a match. Also, it doesn't reach the 63.2% value till about 1.4 seconds. The book should give a definition of "time constant" that applies to this example. Without that, we are just guessing.LvW said:
In situations where the system can become unstable, maintaining large enough phase and gain margins is one of the top level system requirements. The margins allow for some uncertainty in the modeling and the equipment condition (age, damage, dirt, etc.). In those cases, getting fast response often makes the designs come close to the margin limits. So they become important constraints.LvW said:
What does time scale mean? When T = 0?LvW said:
jaus tail said:
