It is known that G(s) and the closed-loop structure is shown below: R(s) (7 K(s+2) s(s + 1)(s + 4)' E(s) G(s) C(s) Find the range of K for which the closed-loop system will yield a steady-state error range of [0.1, 10] for ramp-type input 5t.
It is known that G(s) and the closed-loop structure is shown below: R(s) (7 K(s+2) s(s + 1)(s + 4)' E(s) G(s) C(s) Find the range of K for which the closed-loop system will yield a steady-state error range of [0.1, 10] for ramp-type input 5t.
Introductory Circuit Analysis (13th Edition)
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Author:Robert L. Boylestad
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![### Closed-Loop System Analysis
**Transfer Function:**
It is given that the transfer function \( G(s) \) is:
\[
G(s) = \frac{K(s + 2)}{s(s + 1)(s + 4)}
\]
**Closed-Loop Structure:**
The block diagram of the closed-loop system is illustrated. It contains:
- \( R(s) \): Reference input
- \( E(s) \): Error signal
- \( G(s) \): Transfer function block
- \( C(s) \): Output of the system
The structure is a typical feedback loop where the reference input \( R(s) \) is compared with the output \( C(s) \) to produce an error signal \( E(s) \). This error signal is processed by the transfer function \( G(s) \).
**Problem Statement:**
Determine the range of the gain \( K \) such that the closed-loop system achieves a steady-state error within the range [0.1, 10] for a ramp-type input of \( 5t \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6e11f595-a40a-4bf3-b7d2-0a0cab1f1556%2Fab2b19b6-4774-474b-963d-bab35a3df2dd%2F4dufmeq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Closed-Loop System Analysis
**Transfer Function:**
It is given that the transfer function \( G(s) \) is:
\[
G(s) = \frac{K(s + 2)}{s(s + 1)(s + 4)}
\]
**Closed-Loop Structure:**
The block diagram of the closed-loop system is illustrated. It contains:
- \( R(s) \): Reference input
- \( E(s) \): Error signal
- \( G(s) \): Transfer function block
- \( C(s) \): Output of the system
The structure is a typical feedback loop where the reference input \( R(s) \) is compared with the output \( C(s) \) to produce an error signal \( E(s) \). This error signal is processed by the transfer function \( G(s) \).
**Problem Statement:**
Determine the range of the gain \( K \) such that the closed-loop system achieves a steady-state error within the range [0.1, 10] for a ramp-type input of \( 5t \).
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