Question

MATLAB questions. Please answer everything and explain for question 2.

Using the Following Functions G()1672) and H() - 54 S+1 s(s+2) 1. Enter the G(s) and H(s) functions. (Take advantage of using either symbolic tool or entering vector format with Commands like tf to generate the transfer function.) Your goal is to find the following: a) X(s) G(s) H(s) Y(s) Cascade system b) X1(s) G(s) Y(s) Parallel System X2(s) H(s) c) Feedback System (Hint: Use commands like cascade(tf), parallel(tf) and feedback(tf)) 2. Use the results from question 1, Test your TF functions (la and lb are Open Loop TF, 1<c is ClosedLoop) using the impulse and step forced responses. (Hint: matlab commands impulse(Function) and step (Function)) Explain base on your poles and zeros the behavior of your TF. Is there any difference between OpenLoop (OL) and ClosedLoop (CL)? Explain. What happens to the poles and Zeros of OL and CL TF?

Answer 1

Answer:

Problem-1:

Matlab Code:

clc;
clear all;
close all;
% used to clear screen , clear previous data
%% Given data
G=tf([1 1],[1 2 0])
% tf creates a transverse function with first term numerator and second denominator
H=tf([1 3],[1 4])
%% 1A
% cascade
sys1a=series(G,H)
sysa=zpk(sys1a)
% zpk converts system in zeros and poles form
%% 1B
% parallel
sys1b=parallel(G,H)
sysb=zpk(sys1b)
%% 1C
% feedback system
sys1c=feedback(G,H)
sysc=zpk(sys1c)
%% 2 impulse and step to plot above functions
%% %% 1A
figure
impulse(sys1a)
title('impulse response of cascade')
figure
step(sys1a)
title('step response of cascade')
%% %% 2B
figure
impulse(sys1b)
title('impulse response of parallel')
figure
step(sys1b)
title('step response of parallel')
%% %% 2C
figure
impulse(sys1c)
title('impulse response of feedback')
figure
step(sys1c)
title('impulse response of feedback'

OutPuts:

Impulse Response of Cascade

impulse responce of cascade 0.9 0.8 O 0.7 0.6 0.5 0.4 0.3 1.5 Time (seconds) 0 0.5 2 2.5

Step Response of Cascade:
step responce of cascade 50 45 40 35 a 30 E 25 4 20 15 10 0 20 40 80 100 120 60 Time (seconds)
Impulse response of Parallel:

impulse responce of parallel 0.6 0하 0.4 0.3 0.2 0.1 0 0 2 Time (seconds) 3 4
Step response of Parallel:
step responce of parallel 70 60 50 0 40 30 20 10 0 0 40 80 100 120 60 Time (seconds) 20

Impulse response of feedback

impulse responce of feedback 0.9 0.8 0.7 0.6 E 0.5 0.4 0.3 0.2 0.1 0 5 10 15 Time (seconds)

Impulse response of Feedback

impulse responce of feedback 1.4 1.2 0.8 E 0.6 0.4 0.2 15 20 10 Time (seconds)

Problem-2:

Command window

s 1 sA22 s Continuous-time transfer function. s +3 s + Continuous-time transfer function sysla sA2+4st3 s3 6 s 2+8s Continuous-time transfer function. sysa

sysa s (s+4) (st2) Continuous-time zero/pole/gain model. syslb- s 3 + 6 s 2 + 11 s 4 Continuous-time transfer function. (s+0.4786) (s*2 + 5.521s+ 8.357) s (s+4) (st2) Continuous-time zero/pole/gain model. sys 1c fx

Continuous-time transfer function. sysb- (s+0.4786) (s 2 5.521s8.357) s (s+4) (s+2) Continuous-time zero/pole/gain model syslc- s 2 5 s+4 SA3 7 s 2 + 12 s 3 Continuous-time transfer function (s+4.461) (s+2.239) (s+0.3004) Continuous-time zero/pole/gain model
Result:

Impulse response of Feedback

impulse responce of feedback 0.9 0.8 0.7 0.6 E 0.5 4 0.4 0.3 0.2 0.1 10 15 Time (seconds)
Note: Due to limited time, explanation is not possible this time. if you want explanation re-post question 2 separately and you have any problem with this answer , please comment. i will clear your doubts Thank you.