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For the system shown below, find the range of K > 0 that yields less than 16% overshoot for a step input. Will the system always be an underdamped system with the computed range of K? R(s) + K s² + 10s C(s)

For the system shown below, find the range of K > 0 that yields less than 16% overshoot for a step input. Will the system always be an underdamped system with the computed range of K? R(s) + K s² + 10s C(s)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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### Problem Statement: For the system shown below, find the range of \( K > 0 \) that yields less than 16% overshoot for a step input. Will the system always be an underdamped system with the computed range of \( K \)? ### System Diagram: - The diagram illustrates a feedback control system. - It includes a summing junction, where \( R(s) \) enters as the reference input and the feedback loop is subtracted. - The difference is passed through a transfer function given by \(\frac{K}{s^2 + 10s}\). - The output is denoted by \( C(s) \), which is fed back into the system. ### Explanation: To solve the problem, you need to calculate the appropriate range of the gain \( K \) that will ensure the system has less than 16% overshoot, a common requirement for ensuring adequate system stability and performance. Overshoot in a control system's response can be associated with the damping ratio, and finding the right \( K \) helps in setting the system into an underdamped state as necessary to meet the criterion while maintaining desirable system dynamics.
Transcribed Image Text:### Problem Statement: For the system shown below, find the range of \( K > 0 \) that yields less than 16% overshoot for a step input. Will the system always be an underdamped system with the computed range of \( K \)? ### System Diagram: - The diagram illustrates a feedback control system. - It includes a summing junction, where \( R(s) \) enters as the reference input and the feedback loop is subtracted. - The difference is passed through a transfer function given by \(\frac{K}{s^2 + 10s}\). - The output is denoted by \( C(s) \), which is fed back into the system. ### Explanation: To solve the problem, you need to calculate the appropriate range of the gain \( K \) that will ensure the system has less than 16% overshoot, a common requirement for ensuring adequate system stability and performance. Overshoot in a control system's response can be associated with the damping ratio, and finding the right \( K \) helps in setting the system into an underdamped state as necessary to meet the criterion while maintaining desirable system dynamics.
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