Question

R(s) Ts(s) 140 s4 +12s3 39s2 48s 140 Experiment 1 For the system shown in preliminarily: In Matlab, write instructions to create the closed-loop transfer function. Using Matlab find the location of poles for this transfer function (use pzmap Matlab command) Using Routh-Hurwitz criterion principals (preliminarily task) justify the locations of complex (pure imaginary with no real) poles a) b) c) d) Plot the step response for this system e) Considering the location of the poles justify (explain) the result obtained for step response.

I need matlab code

Answer 1

MATLAB code is given below in bold letters.

clc;
clear all;
close all;

% define complex variable s as below
s = tf('s');

% now define T(s) as follows
T = 140/(s^4+12*s^3+39*s^2+48*s+140);

% Now the closed loop transfer function definition named as G
G = feedback(T,1) % Assuming unity feedback loop

% finding the location of poles of this transfer function
p = pole(G); % closed loop poles

% plot the pole and zero locations
figure;pzmap(G);

% plotting the step response of the closed loop system
figure;step(G);title('Step response of the closed loop system');
grid on;

  

RESULTS:

Closed-loop transfer function G:
G =

140
----------------------------------
s^4 + 12 s^3 + 39 s^2 + 48 s + 280

Continuous-time transfer function.

Closed-loop poles:
p =

-6.4113 + 1.3924i
-6.4113 - 1.3924i
0.4113 + 2.5171i
0.4113 - 2.5171i

Closed-loop pole locations plot in complex s plane:

Pole-Zero Map 3 -1 2 3 -7 -65 4 3 2-1 0 Real Axis (seconds)

closed loop step response:

x 10 26 Step response of the closed loop system 2 1.5 0.5 0 兰-0.5 4-1 1.5 -2 2.5 -3 0 50 100 150 Time (seconds)

From the above plot, it is observed that the response is unstable as it goes to infinite. This can be related to the location of closed-loop poles given in the PZ map of the system given before. It is observed that the system has two closed-loop poles lie on the right side of the jw axis. These poles are responsible for the unstable response.