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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
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Solution

Break Down the Problem

  1. Identify Key Terms: Understand what gain margin and phase margin indicate in control systems.
  2. Choose the Appropriate Option: Analyze the given options in relation to stability margins.

Relevant Concepts

  1. 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.
  2. 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

  1. 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.
  2. 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.

This problem has been solved

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