Understanding Sampling Period 'T' in Digital Control Systems: Tips and Tricks

[rizwanibn]

< Mentor Note -- thread moved to HH from the technical engineering forums, so no HH Template is shown >[/color]

Hi.
Please see question no. 1 in the attachment.
If i take the inverse Laplace transform or the Z transform, how can i actually get the value of sampling period 'T'.
or is there any other way to solve this?
Thanks...

 

[rizwanibn]

Ok i took the inverse Laplace transform.
I got

20sin(1.3t) /2.7e^(t/2)
Is the frequency of the wave (2pi f)=1.3 ?

Or do i have to consider the exponential term as well?

 

[donpacino]

Do you know what the nyquist theorem is?

 

[rizwanibn]

Well what i am trying to do is,
Finding out the frequency of the continuous signal.
Two times this frequency is the minimum sampling frequency,and inverse of that is the maximum time period.
Please correct me if i am wrong.
Thank you.

 

[donpacino]

Almost. You need to take into account the frequency of your transient, as well as your steady state signal. . The initial function you are given is your function in the frequency domain. If you get a bode plot, or look at the poles, you should get an idea of what the frequencies will be.

 

[rude man]

< Mentor Note -- thread moved to HH from the technical engineering forums, so no HH Template is shown >

Hi.
Please see question no. 1 in the attachment.
If i take the inverse Laplace transform or the Z transform, how can i actually get the value of sampling period 'T'.
or is there any other way to solve this?
Thanks...

Is F(s) a transfer function or a response to a delta (impulse) or step input? I'm guessing it's the former even though f(t) looks like a response. But if it's a response you'd have to know what the input is, remove it from F(s), then proceed as below. (You could assume a delta function input of course, in which case the response and transfer functions would be the same.)

In either case there is no transient to consider. You have a low-pass filter with either two real poles or one complex-conjugate pair (hint: which is it?). Draw the Bode frequency plot, then use the Nyquist theorem to come up with the min. sampling rate by picking the rolloff frequency off the plot. (NOTE: that rate will be an approximation. Theoretically, any finite frequency is passed by the network to some extent so an infinitely high sampling rate would be required for 100% accuracy in restoring to the time domain, but you have to cut off at some point in reality.)