## Linear Control System Analysis### OverviewThe block diagram depicted illustrates a linear control system. In this system, \( r(t) \) represents the reference input, while \( n(t) \) signifies the disturbance.### Tasks and Questions1. **Steady-State Error for Unit Ramp Input** - **Task a**: Determine the steady-state value of the error \( e(t) \) as a function of \( K \) when \( n(t) = 0 \) and \( r(t) \) is a unitary ramp. 2. **Conditions for Validity** - **Task b**: Identify conditions on the values of \( K \) to ensure the solution from (a) is valid.3. **Minimum Possible Error** - **Task c**: Evaluate the minimum possible error under the conditions from (a) and (b).4. **Steady-State Output for Unitary Step Disturbance** - **Task d**: Compute the steady-state value of \( y(t) \) when \( r(t) = 0 \) and \( n(t) \) is a unitary step.5. **Steady-State Error for a Specific Input Signal** - **Task e**: Given \( n(t) = 0 \), determine the steady-state value of the error as a function of \( K \) for an input signal of \( 4t \mu_s(t) \).### Block Diagram Components- **R(S)**: Reference input in the Laplace domain.- **2/S**: Integrator block with a gain of 2.- **N(S)**: Input disturbance in the Laplace domain.- **K/((S+2)(S+3))**: Controller/plant transfer function.### Explanation of the Diagram- The diagram exhibits a feedback control system with a disturbance.- The input signal \( R(S) \) is subjected to an integrator with a gain of 2 before being fed into a summation junction, which also takes in the disturbance \( N(S) \).- The resulting signal is then processed by a system described by the transfer function \( \frac{K}{(S+2)(S+3)} \).- The output \( Y(S) \) is generated, representing the controlled system output.This block diagram is crucial for analyzing the control system's response to different inputs and disturbances and for

1.- The block diagram of a linear control system is shown in the Fig., where r(t) is the reference input and n(t), the disturbance. a) Find the steady-state value of e(t), as a function of K, when n(t) = 0 and r(t) is a unitary ramp b) Find the conditions on the values of K so that the solution in a) is valid c) what is the minimum possible error obtained under a) and b) conditions? d) Find the steady-state value of y(t) when r(t) = 0 and n(t) is a unitary step e) Assuming n(t) = 0, what is the steady-state value of the error, as a function of K, for an input signal of 4tµs(t)? N(S) 2/S K/(S+2)(S+3) R(S) +Y(S)

1.- The block diagram of a linear control system is shown in the Fig., where r(t) is the reference input and n(t), the disturbance. a) Find the steady-state value of e(t), as a function of K, when n(t) = 0 and r(t) is a unitary ramp b) Find the conditions on the values of K so that the solution in a) is valid c) what is the minimum possible error obtained under a) and b) conditions? d) Find the steady-state value of y(t) when r(t) = 0 and n(t) is a unitary step e) Assuming n(t) = 0, what is the steady-state value of the error, as a function of K, for an input signal of 4tµs(t)? N(S) 2/S K/(S+2)(S+3) R(S) +Y(S)

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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