Question

1. A closed-loop unity feedback system has the loop gain $L(z)$ as shown below. Use MATLAB to assist you in solving the problems below. (a) Is the system open-loop stable? Why or why not? (b) Assuming the closed-loop system is stable, the Nyquist plot of $L(z)$ should have how many CCW encirclements of the $(-1,0)$ point? (c) Does the Nyquist plot indicate that the closed-loop system is stable? (d) Determine the gain margin in dB of the closed-loop system. (e) From your results above, determine the gain (to at least three significant figures) that makes the closed-loop system marginally stable and show the resulting new loop gain function. $L(z) = \frac{0.7}{z + 0.2z - 0.99}$

          1. A closed-loop unity feedback system has the loop gain $L(z)$ as shown below. Use
MATLAB to assist you in solving the problems below.
(a) Is the system open-loop stable? Why or why not?
(b) Assuming the closed-loop system is stable, the Nyquist plot of $L(z)$ should
have how many CCW encirclements of the $(-1,0)$ point?
(c) Does the Nyquist plot indicate that the closed-loop system is stable?
(d) Determine the gain margin in dB of the closed-loop system.
(e) From your results above, determine the gain (to at least three significant
figures) that makes the closed-loop system marginally stable and show the
resulting new loop gain function.
$L(z) = \frac{0.7}{z + 0.2z - 0.99}$

1. A closed-loop unity feedback system has the loop gain L(z) as shown below. Use
MATLAB to assist you in solving the problems below.
(a) Is the system open-loop stable? Why or why not?
(b) Assuming the closed-loop system is stable, the Nyquist plot of L(z) should
have how many CCW encirclements of the (-1,0) point?
(c) Does the Nyquist plot indicate that the closed-loop system is stable?
(d) Determine the gain margin in dB of the closed-loop system.
(e) From your results above, determine the gain (to at least three significant
figures) that makes the closed-loop system marginally stable and show the
resulting new loop gain function.
L(z) = (0.7)/(z + 0.2z - 0.99)

Added by Domingo H.

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