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 20 dB. Now answer the following: beta_m> 0, there exists a positive gain margin 1) The closed-loop system is stable If L(s) has a gain margin beta_m, then the CL system 1 + beta L(s) is stable for every beta < beta_m 2) One may increase (or, decrease) the gain up to 10 and still have CL stability (or, instability). 20log_10(10) = 20 ✓ 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"
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 20 dB. Now answer the following: beta_m> 0, there exists a positive gain margin 1) The closed-loop system is stable If L(s) has a gain margin beta_m, then the CL system 1 + beta L(s) is stable for every beta < beta_m 2) One may increase (or, decrease) the gain up to 10 and still have CL stability (or, instability). 20log_10(10) = 20 ✓ 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"
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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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 is 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 20 dB. Now answer the following:
1) The closed-loop system is **stable**.
If L(s) has a gain margin beta_m, then the CL system 1 + beta L(s) is stable for every beta < beta_m.
2) One may increase (or, decrease) the gain up to **10** (20log_10(10) = 20)
and still have CL stability (or, instability).
**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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