Question

20 2. G(s) = \frac{20}{s(s^2+4s+4)} is in a closed loop, unity gain system as shown above. ander. a. Use Matlab to make the Bode plots for the closed loop system and find the gain margin (GM) and phase margin (PM). b. Is the system stable? Why? c. Use Matlab to design a lead compensator D(s) to raise the phase at the crossover frequency (the frequency where you measure the PM) by 30 Degrees. Use the recipe we saw in Lecture 18. Let Matlab calculate alpha and the zero and pole locations of the compensator. Do not round the pole and zero frequencies Matlab calculates. Matlab does not care if we do not have pretty, integer frequencies. What alpha, zero location and pole location does Matlab find? d. Use Matlab to make the Bode plot of the lead compensator you found in 2.c. Does it look like the compensator will change the phase of G(s) by 30 degrees at the correct frequency? e. Use Matlab to make the Bode plot of the compensated system D(s)G(s). Is the compensated system stable? Why? f. You bumped the phase at the original crossover frequency by 30 degrees. Did the phase margin (PM) change by 30 degrees? Why?

          20
2. G(s) = \frac{20}{s(s^2+4s+4)} is in a closed loop, unity gain system as shown
above. ander.
a. Use Matlab to make the Bode plots for the closed loop system
and find the gain margin (GM) and phase margin (PM).
b. Is the system stable? Why?
c. Use Matlab to design a lead compensator D(s) to raise the
phase at the crossover frequency (the frequency where you
measure the PM) by 30 Degrees. Use the recipe we saw in
Lecture 18. Let Matlab calculate alpha and the zero and pole
locations of the compensator. Do not round the pole and zero
frequencies Matlab calculates. Matlab does not care if we do
not have pretty, integer frequencies. What alpha, zero location
and pole location does Matlab find?
d. Use Matlab to make the Bode plot of the lead compensator
you found in 2.c. Does it look like the compensator will change
the phase of G(s) by 30 degrees at the correct frequency?
e. Use Matlab to make the Bode plot of the compensated system
D(s)G(s). Is the compensated system stable? Why?
f. You bumped the phase at the original crossover frequency by
30 degrees. Did the phase margin (PM) change by 30 degrees?
Why?

20
2. G(s) = (20)/(s(s^2+4s+4)) is in a closed loop, unity gain system as shown
above. ander.
a. Use Matlab to make the Bode plots for the closed loop system
and find the gain margin (GM) and phase margin (PM).
b. Is the system stable? Why?
c. Use Matlab to design a lead compensator D(s) to raise the
phase at the crossover frequency (the frequency where you
measure the PM) by 30 Degrees. Use the recipe we saw in
Lecture 18. Let Matlab calculate alpha and the zero and pole
locations of the compensator. Do not round the pole and zero
frequencies Matlab calculates. Matlab does not care if we do
not have pretty, integer frequencies. What alpha, zero location
and pole location does Matlab find?
d. Use Matlab to make the Bode plot of the lead compensator
you found in 2.c. Does it look like the compensator will change
the phase of G(s) by 30 degrees at the correct frequency?
e. Use Matlab to make the Bode plot of the compensated system
D(s)G(s). Is the compensated system stable? Why?
f. You bumped the phase at the original crossover frequency by
30 degrees. Did the phase margin (PM) change by 30 degrees?
Why?

Added by Melissa M.

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