Find the value of K for the system given below that will place the closed-loop poles as shown.
Find the value of K for the system given below that will place the closed-loop poles as shown.
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Transcribed Image Text:**Description:**
The image presents a control system with the task of finding the value of K that will position the closed-loop poles as depicted.
**System Components:**
- **R(s):** Input signal.
- **Block 1:** Transfer function \( s^2 \).
- **Summation Point 1:** Subtracts feedback from the output of the \( s^2 \) block.
- **Block 2:** Transfer function \( \frac{K}{s^2} \) leading to output \( C(s) \).
- **Block 3:** Transfer function \( \frac{2}{s} \) providing feedback to the summation point.
- **Block 4:** Transfer function \( \frac{1}{s+1} \) also providing feedback to the summation point.
- **Summation Point 2:** Adds the outputs of the feedback transfer functions before returning to the input summation point.
**Pole-Zero Plot:**
- **Axes:**
- Horizontal axis (\( \sigma \)): Represents the real part of the poles.
- Vertical axis (\( j\omega \)): Represents the imaginary part of the poles.
- Two poles (marked with 'X') are situated symmetrically across the real and imaginary axes, indicating desired closed-loop pole positions.
**Objective:**
Identify the value of \( K \) that will adjust the system such that the closed-loop poles align with the given points on the pole-zero plot.
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