Show work please. use MATLAB to obtain insight into the system behavior for firs

Question

Show work please. use MATLAB to obtain insight into the system behavior for first-order and second-order when the system has one real pole and no finite zero (first-order system response); real and equal poles and no finite zero (critically damped system); real and unequal poles and no finite zero (overdamped system); imaginary poles and no finite zero (underdamped); and imaginary poles with a damping ratio of 0.707 and different real zero locations. System: G[s] = n[s]/d[s] Let n[s] = 1 and d[s] = (s + 1) = s + 1 Let n[s] = 1 and d[s] = (s + 1)(s + 1) = s^2 + 2s + 1. Let n[s] = 4 and d[s] = (s + 1) = s + 4) = s^2 + 5s + 4. Let n[s] = 1 and d[s] = s^2 + 2 s + 1, with zeta = 0.707, zeta = 0.45, and zeta = 0 1. Let n[s] = (+ 1) with z = 5.0, z = 1.0, z = 0.4, and z = -1.0 and d [s] = s^2 + 2 zeta s + 1, with zeta = 0.707. Example MATLAB Code: t = 0:0.01:10.0; % Introduce a consistent time vector for all of the plots. nc = 4, dc = [1, 5, 4], % Numerator and Denominator for Part (c) gc = tf(nc, dc), % Create the transfer function from the numerator and denominator. figure(3)% open a third figure window (assuming you have already opened two for parts (a) and (b)) step(gc t) % Display the step response in the newly created figure window. title (Part (c): Overdamped System 's Step Response] Notation [A M] = Astrom and Murray, "Feedback systems: An Introduction for Scientists and Engineers. "2008.

Explanation / Answer

clc
close all
clear all
%%%%%%%%%%part A%%%%%%%%%%%%%%%
num1=1;%numerator of the part A
den1=[1 1];% denominatror of the part A
G1=tf(num1,den1)% create transfer of the part A
t=0:0.01:10.0;% introduce a consistent time vector.
figure(1)
step(G1,t)% display step response
title('first order system')
%%%%%%%%%%%%part B%%%%%%%%%%%%%
num2=1;%numerator of the part B
den2=[1 2 1];%denominatror of the part B
G2=tf(num2,den2)% create transfer of the part B
t=0:0.01:10.0;% introduce a consistent time vector.
figure(2)
step(G2,t)% display step response
title('critically damped system')
%%%%%%%%%%%%part C%%%%%%%%%%%%%
num3=4;%numerator of the part C
den3=[1 5 4];%denominatror of the part C
G3=tf(num3,den3)% create transfer of the part C
t=0:0.01:10.0;% introduce a consistent time vector.
figure(3)
step(G3,t)% display step response
title('over damped system')
%%%%%%%%%%%%part D%%%%%%%%%%%%%
zeta1=0.707;
zeta2=0.45;
zeta3=0.1
num4=1;%numerator of the part D
den4=[1 2*zeta1*1 1];%denominatror of the part D WHEN ZETA=0.707
den5=[1 2*zeta2*1 1];%denominatror of the part D WHEN ZETA=0.45
den6=[1 2*zeta3*1 4];%denominatror of the part D WHEN ZETA=0.1
G4=tf(num4,den4)% create transfer of the part D WHEN ZETA=0.707
G5=tf(num4,den5)% create transfer of the part D WHEN ZETA=0.45
G6=tf(num4,den6)% create transfer of the part D WHEN ZETA=0.1
t=0:0.01:10.0;% introduce a consistent time vector.
figure(4)
step(G4,t,'r')% display step response WHEN ZETA=0.707
hold on
step(G5,t,'y')% display step response WHEN ZETA=0.45
hold on
step(G6,t,'b')% display step response WHEN ZETA=0.1
title('under damped system')

RUN MATLAB PROGRAM YOU GET GRAPHS AND TRANSFER FUNCTION.

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