Question

Sample Code and Models

Run each of the models below and explain the code function and your findings for each system, do they agree/disagree with what you understand and why ??

Matlab Code

% Winter 2018 Control Engineering

% Lab No.3 - Root Locus problems

% Mark Clarke

clear

s = tf('s')

K = 1150; %Proportional Controller Gain, May need to be altered?

% Enter Model 1

% This is a model of a simple 2^nd order with no zeros

g1 = 1/((s+2)*(s+4));

h1 = feedback(K*g1,1);

figure(1)

rlocus(g1) % Plot the root locus of system g1

figure(2)

step (h1,5)% plot the step response of system h1

% Enter Model 2

% This is a model of a simple 2^nd order with one zeros

g2 = (s+3)/((s+2)*(s+4));

h2 = feedback(K*g2,1);

figure(1)

rlocus(g2) % Plot the root locus of system g2

figure(2)

step (h2,5)% plot the step response of system h2

% Enter Model 3

g3 = 1/((s*(s^2 + 15*s + 60)));

h3 = feedback(K*g3,1);

g4 = 1/((s+1)*(s^2 + 15*s + 60));

h4 = feedback(K*g4,1);

figure(1)

rlocus(g3)   % run the root locus on the g3 an g4 above

figure(2)

step(h3,10) % run the step response on the h3 an h4 above

PART 2 Findings and Conclusion

Answer 1

u can directly run the below code on matlab:

clc;

clear all;

close all;

s=tf('s');

k=1150; % gain

% model 1

g1=1/((s+2)*(s+4));

h1=feedback(k*g1,1);% closed loop transfer function

rlocus(g1);% root locus of g1 (open loop)

figure

step(h1,5);grid % step response

% model 2

g2=(s+3)/((s+2)*(s+4));

h2=feedback(k*g2,1);% closed loop transfer function

figure

rlocus(g2);% root locus of g2 (open loop)

figure

step(h2,5);grid % step response

% model 3

g3=1/(s*(s^2+15*s+60));

h3=feedback(k*g3,1);% closed loop transfer function

g4=1/((s+1)*(s^2+15*s+60));

h4=feedback(k*g4,1);% closed loop transfer function

figure

rlocus(g3,g4);% root locus of g3 and g4 (open loop)

figure

step(h3);grid % step response of h3

figure

step(h4);grid % step response of h4

from the responses;

h1,h2 are  stable systems and h3 and h4 are unstable systems