### Block Diagram of a Linear Control SystemThe block diagram of a linear control system is shown below, where $ r(t) $ is the reference input and $ n(t) $ is the disturbance.#### Problem Statement:1. Find the steady-state value of $ e(t) $ when $ n(t) = 0 $ and $ r(t) = u_s(t) $. Find the conditions on the values of $ \alpha $ and $ K $ so that the solution is valid.#### Diagram Explanation:This diagram is a representation of a linear control system comprising two main components: a controller and a process.- **Inputs and Outputs:** - $ R(s) $: Reference input in the Laplace domain. - $ N(s) $: Disturbance input in the Laplace domain. - $ Y(s) $: Output in the Laplace domain. - $ E(s) $: Error signal, representing the difference between the reference input and the feedback.- **Controller Block:** - This block is represented by the transfer function $ \frac{s + \alpha}{s} $. - It processes the error signal $ E(s) $ to generate an appropriate control action.- **Process Block:** - This block is represented by the transfer function $ \frac{KCs + 3}{s^2 - 1} $. - It models the dynamics of the process being controlled, translating the control action into the system output.- **Feedback Loop:** - The diagram includes a feedback loop where the output $ Y(s) $ is fed back to the summing junction at the start, creating a closed-loop system.- **Summing Junctions:** - The error signal $ E(s) $ is computed as the difference between $ R(s) $ and the feedback. - Another summing junction combines the control action with the disturbance $ N(s) $.This setup is typical in control systems where the goal is to regulate the process output $ Y(s) $ to follow the reference input $ R(s) $, despite any disturbances $ N(s) $. The task is to determine the conditions on $ \alpha $ and $ K $ for steady-state accuracy.

Given: Block diagram of a control system, To find: a) Steady state value of error e(t) when…

The block diagram of a linear control system is shown in the Fig, where r(t) is the reference input and n(t) is the disturbance. 1. Find the steady-state VALUE of e(t) when n(t)= 0 and r(t) tus(t). Find the conditions on the values of and K so that the solution is valid N (s) ૨૬) E(s) sta S controller + + K(s+3) (s² -1) Process 9(5) 1)

The block diagram of a linear control system is shown in the Fig, where r(t) is the reference input and n(t) is the disturbance. 1. Find the steady-state VALUE of e(t) when n(t)= 0 and r(t) tus(t). Find the conditions on the values of and K so that the solution is valid N (s) ૨૬) E(s) sta S controller + + K(s+3) (s² -1) Process 9(5) 1)

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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