- #1
Logio
- 4
- 0
Hi,
Just wondering if anyone could give me a few pointers in the right direction for this... thanks!
Incredibly long problem statement so I'll summarise and ask more about the concept:
I have a Plant and Controller set up in the form of a usual control system. The controller is a proportional gain in series with a time delay.
a) What is the Laplace transform of this controller.
b) Draw a bode plot (using a computer package)
c) Estimate the phase margin
d) How much extra time delay can be added to the control loop before instability.
e) Using the bode plot, draw a Nyqiust diagram.
N/A
a) Transfer function = k exp(-iD) where D is the time delay in seconds
b) Done on a computer
c) Phase margin read off the graph as the phase between -180 and the phase for the frequency with 0db gain (fairly confident this is accurate)... ANSWER = 75 degrees (for a given k and D)
d) Not sure where to start... I suspect I could consider another series delay of duration say, P, and then use some form of analysis to find P.
e) I know the phase margin and gain margin from the bode plot... is this enough to plot the Nyq. diagram or can I get more information simply?
Many thanks for any pointers on this!
Just wondering if anyone could give me a few pointers in the right direction for this... thanks!
Homework Statement
Incredibly long problem statement so I'll summarise and ask more about the concept:
I have a Plant and Controller set up in the form of a usual control system. The controller is a proportional gain in series with a time delay.
a) What is the Laplace transform of this controller.
b) Draw a bode plot (using a computer package)
c) Estimate the phase margin
d) How much extra time delay can be added to the control loop before instability.
e) Using the bode plot, draw a Nyqiust diagram.
Homework Equations
N/A
The Attempt at a Solution
a) Transfer function = k exp(-iD) where D is the time delay in seconds
b) Done on a computer
c) Phase margin read off the graph as the phase between -180 and the phase for the frequency with 0db gain (fairly confident this is accurate)... ANSWER = 75 degrees (for a given k and D)
d) Not sure where to start... I suspect I could consider another series delay of duration say, P, and then use some form of analysis to find P.
e) I know the phase margin and gain margin from the bode plot... is this enough to plot the Nyq. diagram or can I get more information simply?
Many thanks for any pointers on this!