Polar plots moving toward the imaginary axis makes the system:a)Stable...
Answer: d
Explanation: Polar plots moving toward the imaginary axis makes the system unstable.
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Polar plots moving toward the imaginary axis makes the system:a)Stable...
Introduction:
The question is related to the stability analysis of a system using polar plots. A polar plot is a graphical representation of the transfer function of a system in the complex plane. It shows the frequency response of the system and helps in analyzing its stability.
Explanation:
When a polar plot moves towards the imaginary axis, it means that the magnitude of the transfer function is increasing as the frequency increases. This indicates that the system has an increasing gain with increasing frequency.
Unstable System:
An unstable system is one where the output of the system grows without bound in response to a given input. In the context of polar plots, an unstable system is represented by a plot that moves towards the imaginary axis as the frequency increases.
Reasoning:
When the polar plot moves towards the imaginary axis, it indicates that the magnitude of the transfer function is increasing with frequency. This means that the system gain is increasing, which can lead to instability. As the gain increases, the output of the system can become larger and larger, eventually becoming unbounded. Therefore, when a polar plot moves towards the imaginary axis, the system is considered unstable.
Example:
For example, consider a system with a transfer function H(s) = (s + 1) / s. The polar plot of this system shows that as the frequency increases, the magnitude of the transfer function increases and the plot moves towards the imaginary axis. This indicates that the system is unstable.
Conclusion:
In conclusion, when a polar plot moves towards the imaginary axis, it indicates that the system has an increasing gain with increasing frequency. This can lead to instability, where the output of the system grows without bound. Therefore, the correct answer is option 'D' - Unstable.
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