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Find the following for the system shown in Figure P5.12: [Section: 5:3] a. The equivalent single block that represents the transfer function, T(s) = C(s)/R(s). b. The damping ratio, natural frequency, percent overshoot, settling time, peak time, rise time, and damped frequency of oscillation. R(s) 10 10 s+12 0.2s 20 S C(s)

Find the following for the system shown in Figure P5.12: [Section: 5:3] a. The equivalent single block that represents the transfer function, T(s) = C(s)/R(s). b. The damping ratio, natural frequency, percent overshoot, settling time, peak time, rise time, and damped frequency of oscillation. R(s) 10 10 s+12 0.2s 20 S C(s)

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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**Find the following for the system shown in Figure P5.12: [Section: 5.3]** **a.** The equivalent single block that represents the transfer function, \( T(s) = \frac{C(s)}{R(s)} \). **b.** The damping ratio, natural frequency, percent overshoot, settling time, peak time, rise time, and damped frequency of oscillation. ### Diagram Description: The block diagram represents a control system with the following components: - An summing junction with an input \( R(s) \) and a negative feedback loop. - A forward path consisting of a series of blocks arranged as follows: 1. A gain block with a value of 10. 2. Another gain block with a value of 10. 3. A summing junction with a feedback path. 4. A transfer function block \( \frac{1}{s + 12} \). 5. A gain block with a value of \( \frac{20}{s} \). - There is a feedback loop that transmits the output through a block with a transfer function of \( 0.2s \) back to the summing junction in the forward path. The system aims to determine the transfer function \( T(s) \) and other system parameters, such as damping ratio and natural frequency.
Transcribed Image Text:**Find the following for the system shown in Figure P5.12: [Section: 5.3]** **a.** The equivalent single block that represents the transfer function, \( T(s) = \frac{C(s)}{R(s)} \). **b.** The damping ratio, natural frequency, percent overshoot, settling time, peak time, rise time, and damped frequency of oscillation. ### Diagram Description: The block diagram represents a control system with the following components: - An summing junction with an input \( R(s) \) and a negative feedback loop. - A forward path consisting of a series of blocks arranged as follows: 1. A gain block with a value of 10. 2. Another gain block with a value of 10. 3. A summing junction with a feedback path. 4. A transfer function block \( \frac{1}{s + 12} \). 5. A gain block with a value of \( \frac{20}{s} \). - There is a feedback loop that transmits the output through a block with a transfer function of \( 0.2s \) back to the summing junction in the forward path. The system aims to determine the transfer function \( T(s) \) and other system parameters, such as damping ratio and natural frequency.
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