The unity-feedback system in Figure P7.1 has the transfer function \( G(s) = \frac{K(s + \alpha)}{(s + \beta)^2} \).**Description of the Figure:**- The diagram shows a block diagram of a unity-feedback control system.- The input signal is denoted as \( R(s) \).- A summation junction is shown, where \( R(s) \) is added positively, and feedback is subtracted.- The error signal \( E(s) \) is fed into the system block \( G(s) \).- The output from the block, \( C(s) \), is fed back to the summation junction to complete the loop.**Specifications:**The system is designed to meet the following criteria:- **Steady-State Error**: For a unit step input, the steady-state error is 0.1.- **Damping Ratio**: 0.5- **Natural Frequency**: \(\sqrt{10}\)**Objective:**Find the values of \( K \), \( \alpha \), and \( \beta \) that satisfy these specifications.

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R(S) + E(s) FIGURE P7.1 G(s) G(s) The unity-feedback system of Figure P7.1,where K(s + a) (s+B)² = C(s) is to be designed to meet the following specifications: steady-state error for a unit step input = 0.1; damping ratio = 0.5; natural frequency = √10. Find K, a, and p.

R(S) + E(s) FIGURE P7.1 G(s) G(s) The unity-feedback system of Figure P7.1,where K(s + a) (s+B)² = C(s) is to be designed to meet the following specifications: steady-state error for a unit step input = 0.1; damping ratio = 0.5; natural frequency = √10. Find K, a, and p.

Introductory Circuit Analysis (13th Edition)

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ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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The unity-feedback system in Figure P7.1 has the transfer function \( G(s) = \frac{K(s + \alpha)}{(s + \beta)^2} \).

**Description of the Figure:**
- The diagram shows a block diagram of a unity-feedback control system.
- The input signal is denoted as \( R(s) \).
- A summation junction is shown, where \( R(s) \) is added positively, and feedback is subtracted.
- The error signal \( E(s) \) is fed into the system block \( G(s) \).
- The output from the block, \( C(s) \), is fed back to the summation junction to complete the loop.

**Specifications:**
The system is designed to meet the following criteria:
- **Steady-State Error**: For a unit step input, the steady-state error is 0.1.
- **Damping Ratio**: 0.5
- **Natural Frequency**: \(\sqrt{10}\)

**Objective:**
Find the values of \( K \), \( \alpha \), and \( \beta \) that satisfy these specifications.

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