Question

2. Consider the closed-loop transfer function: T(s) a) Obtain the family of impulse responses for K-10, 200 and 500 b) Obtain the family of step responses for K-10, 200 and 500. c Obtain the family of ramp responses for K-10, 200 and 500. b) Co-plot each of the family of responses Explain using the DC-Gain for each of the K and the test signal. Is there any difference between s2+5s+K K's in terms of the natural and forced response?

Please provide the used MATLAB code.

Answer 1

fig:1 fig:2 impulse response impulse response impulse response 500 400 150 200 5D -200 300 -400 2.5 05 15 2.5 time in seconds (seconds) time in seconds (econds time in seconds iseconds) clci clear all; % Declaring the required inputs numl-input('enter the coefficients of numerator:' denl-input ('enter the coefficients of denominator:' %Declaring the transfer function Gl-tf (numi, deni) INPUTS FOR FIG:1:: enter the coefficients of numerator: [10 10] enter the coefficients of denominator:[l 5 10] FOR FIG: 2: : enter the coefficients of numerator: [200 200] enter the coefficients of denominator: [1 5 200] Defining the required function impulse (G1) Label on X axis xlabel ('time in seconds') %Label on Y axis ylabel ('amplitude) Display Title on the figure title('impulse response') FOR FIG :3 Enter the coefficients of numerator [500 500] enter the coefficients of denominator:[ 5 500]

FIG:1 FIG:2 FTG:3 STEP RESPONSE STEP RESPONSE STEP RESPONSE 20 10 .5 15 0.5 25 Tine i seconde econde) Time in scconds (cconds Time in seconds (seconds) clc; clear all; Declare the required inputs num-input ('enter the coefficienta of numerator:) den=input ('enter the coefficients of denominator: " ; INPUTS FOR FIG:1:: enter the coefficients of numerator:110 10] enter the coefficients of denominator: [1 5 10] Declare the transfer function G-LI (num, den) % Returns the step response of the systeem step (G) AT,abel in x-axis xlabel (Time in seconds); %label in y-axis ylabel ('Amplitude) % Display title on the figure title( STEP RESPONSE FOR FIG:2: enter the coefficients of numerator: [200 200] enter the coefficients of denominator: [1 5 200] FOR FIG: :3 enter the coefficients of numerator: [500 500] enter the coefficients of denominator: [1 5 500]

FIG:1 FIG:2 FIG: 3 amp reepDne rsmp esponse 30- 10 time in seconds isecard time in seconds seconca clc; clear all; Declare the required inputs num-input ('enter the coefficients of numerator: den-input ('enter the coefficients of denominator:) %Declaring the transfer function G-t.f (num, den) s-tf('s Defining the function step (G/s) %Label on x axis xlabel('time in seconds) SLabel on y-axis ylabel'amplitude') %Display title for the figure title('ramp response') INPUTS FIG:1: enter the coefficients of numerator: [10 10]; enter the coefficients of denominator: [1 5 10] FIG: :2: enter the coefficients of numerator: [200 200] enter the coefficients of denominator: [1 5 200] FIG:3:: enter the coefficients of numerator: [500 500]; enter the coefficients of denominator: [1 5 500]