A system with gain margin close to unity or a phase margin close to zero isSelect one:a. oscillatoryb.highly stablec. unstabled. relatively stable
Question
A system with gain margin close to unity or a phase margin close to zero is
Select one:
- a. oscillatory
- b. highly stable
- c. unstable
- d. relatively stable
Solution
Break Down the Problem
- Identify Key Terms: Understand what gain margin and phase margin indicate in control systems.
- Choose the Appropriate Option: Analyze the given options in relation to stability margins.
Relevant Concepts
- Gain Margin: Describes how much gain can be increased before the system becomes unstable. A gain margin close to unity indicates the system is on the verge of instability.
- Phase Margin: Indicates how much the phase can change before the system reaches instability. A phase margin close to zero suggests that the system is also nearing instability.
Analysis and Detail
- Gain Margin Close to Unity: This suggests that the system is nearing the point of oscillation. If the gain increases even slightly, the system may become unstable.
- Phase Margin Close to Zero: This implies that there is very little room before the system experiences sustained oscillations, indicating instability.
Verify and Summarize
- Both characteristics suggest that the system is not stable and is instead on the threshold of oscillation or instability.
Final Answer
The correct answer is c. unstable.
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