You find that the gain margin of a nominal loop transfer function (with no right-half plane open-loop pole) to be -40 dB. Now answer the following: 1) The closed-loop system is unstable 2) One may increase (or, decrease) the gain up to 100 and still have CL stability (or, instability). 20log_10(100) = 40 ✓

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Recall that:
• If a closed-loop (CL) system is stable, then one may increase the gain (by up to
a certain amount) and still maintain CL stability.
• On the other hand, if the CL system in unstable, then one may decrease the
gain (by up to a certain amount) and still have CL instability.
You find that the gain margin of a nominal loop transfer function (with no right-half
plane open-loop pole) to be -40 dB. Now answer the following:
1) The closed-loop system is unstable
2) One may increase (or, decrease) the gain up to 100
and still have CL stability (or, instability).
20log_10(100) = 40 ✓
NOTE: The second part is dependent on your answer to the first part, i.e.,
• If you answered "stable" to part-1, you will read part-2 as "increase the gain by
up to X and still have CL stability".
• If you answered "unstable" to part-1, you will read part-2 as "decrease the gain
by up to X and still have CL instability".
Transcribed Image Text:Recall that: • If a closed-loop (CL) system is stable, then one may increase the gain (by up to a certain amount) and still maintain CL stability. • On the other hand, if the CL system in unstable, then one may decrease the gain (by up to a certain amount) and still have CL instability. You find that the gain margin of a nominal loop transfer function (with no right-half plane open-loop pole) to be -40 dB. Now answer the following: 1) The closed-loop system is unstable 2) One may increase (or, decrease) the gain up to 100 and still have CL stability (or, instability). 20log_10(100) = 40 ✓ NOTE: The second part is dependent on your answer to the first part, i.e., • If you answered "stable" to part-1, you will read part-2 as "increase the gain by up to X and still have CL stability". • If you answered "unstable" to part-1, you will read part-2 as "decrease the gain by up to X and still have CL instability".
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