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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!