2020 and uni teachers still don't know how to explain correctly, hopefully there is youtube and these wonderful videos, makes everything easy, thanks you ! I'm gonna end with a master degree in youtube search
I am wondering if you can do this for a second order transfer function. For example, if you had simplified the denominator of the transfer function to s(s+2), can you say that the time constant for the system is 1?
Just look at the form your type of response should be and rearrange your transfer function so that they are of the same form. Then you can just match up the variables
t=5tau seems arbitrary. Why not 4tau, when e^-4 would be 0.018 and could be rounded to zero, or 6tau when e^-6 would be 0.0025 and could be rounded to zero? Is there some significant figures or orders of magnitude argument that is being made that allows you to decide that 5tau is okay to choose, or has it just been agreed upon that for this equation, yprime = KM(1-exp(-t/tau)), 5tau is sufficient to approximate steady state? I guess its easy enough to just remember 5tau, just curious why that value was chosen. And thanks for the video.
I wondered about that too. From wikipedia: en.wikipedia.org/wiki/Time_constant It says: "After a period of one time constant the function reaches e−1 = approximately 37% of its initial value. In case 4, after five time constants the function reaches a value less than 1% of its original. In most cases this 1% threshold is considered sufficient to assume that the function has decayed to zero - as a rule of thumb, in control engineering a stable system is one that exhibits such an overall damped behavior." So when t=5*tau, the value is less than 1% of its original, an can be considered 0.
+samuel kelly Thank you for your question. I think you are asking about the calculation at 7:14. This is where we are calculating only e^(-t/tau). When t approaches tau, t/tau approaches one, so e^(-t/tau) approaches e^(-1), which is approximately 0.368. I hope this helps.
2020 and uni teachers still don't know how to explain correctly, hopefully there is youtube and these wonderful videos, makes everything easy, thanks you !
I'm gonna end with a master degree in youtube search
Thank you for the help. Made my lab for Systems Dynamics a lot easier.
Fantastic, great explanation. Thank you
This was helpful. Thanks!
I am wondering if you can do this for a second order transfer function. For example, if you had simplified the denominator of the transfer function to s(s+2), can you say that the time constant for the system is 1?
Just look at the form your type of response should be and rearrange your transfer function so that they are of the same form. Then you can just match up the variables
What does it mean when a transfer function ends up having multiple K values?
t=5tau seems arbitrary. Why not 4tau, when e^-4 would be 0.018 and could be rounded to zero, or 6tau when e^-6 would be 0.0025 and could be rounded to zero? Is there some significant figures or orders of magnitude argument that is being made that allows you to decide that 5tau is okay to choose, or has it just been agreed upon that for this equation, yprime = KM(1-exp(-t/tau)), 5tau is sufficient to approximate steady state?
I guess its easy enough to just remember 5tau, just curious why that value was chosen. And thanks for the video.
I wondered about that too. From wikipedia: en.wikipedia.org/wiki/Time_constant
It says:
"After a period of one time constant the function reaches e−1 = approximately 37% of its initial value. In case 4, after five time constants the function reaches a value less than 1% of its original. In most cases this 1% threshold is considered sufficient to assume that the function has decayed to zero - as a rule of thumb, in control engineering a stable system is one that exhibits such an overall damped behavior."
So when t=5*tau, the value is less than 1% of its original, an can be considered 0.
Rebirbokaj
1% makes sense. Thanks for the answer.
in that last question where did you get 368 from?
+samuel kelly Thank you for your question. I think you are asking about the calculation at 7:14. This is where we are calculating only e^(-t/tau). When t approaches tau, t/tau approaches one, so e^(-t/tau) approaches e^(-1), which is approximately 0.368. I hope this helps.
jesus this guy's voice is unbearable