Question

Please solve with MATLAB, please solve with MATLAB

PROBLEM 1 A closed loop control system is depicted in Figure 1 where K 2 and the nominal value of a is 1. The goal in this problem is to examine the sensitivity of the whole system in Figure 1 to the parameter a. (a) If a 1, demonstrate explicitly that the steady state value of output is equal to 2 when input is unit step function. Confirm that, after 4 seconds, the unit step response is within 2% of the steady state value. (b) For a 0.5, 2, and 5, obtain the graph of the unit step response. Associate the results to the sensitivity of the closed loop system to deviation of parameter a. RS Figure 1: A system with uncertain parameter a

Answer 1

matlab code for a) and b)

clc;

clear all;

close all;

s=tf('s');

k=2;

a=[0.5 2 5];

g=1/(s-1);

g1=k/(s-a(1));

g2=k/(s-a(2));

g3=k/(s-a(3));

step(feedback(k*g,1));grid % response for a = 1

figure

step(feedback(g1,1));grid % step response for a=0.5

legend(' a=0.5 ')

figure

step(feedback(g2,1));grid % step response for a=2

legend(' a=2 ')

figure

step(feedback(g3,1));grid % step response for a=5

legend(' a=5 ')

File Edit View Insert Tools Desktop Window Help Step Response Tme (3econds):4.0 Ampinde: 1.96 1 6 12 02 Time (seconds)

File Edit View Insert Tools Desktop Window Help Step Response 12 04 Time (seconds)

File Edit View Insert Tools Desktop Window Help Step Response 80 60 10 10 15 25 30 35 Time (seconds)

File Edit View Insert Tools Desktop Window Help Step Response 12 16 18 20 Time (seconds)

with increase in ' a ' the senstivity decreases and the system will become unstable