Question

1. Suppose that the step response of a 2nd order underdamped system has been measured and recorded in Table I, where the first column denotes the time in second and the second column denotes the measured output. Obtain the transfer function for this system. Graph the response using an Excel graph or chart. Table I: Step Response of a 2nd Order Underdamped System Time (seconds) Step Response 0 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 1.1000 1.2000 1.3000 1.4000 .5000 1.6000 1.7000 1.8000 1.9000 2.0000 2.1000 2.2000 2.3000 2.4000 2.5000 2.6000 2.7000 2.8000 2.9000 3.0000 0.0694 0.2370 0.4487 0.6623 0.8494 0.9961 1.0927 1.1468 1.1631 1.1533 1.1266 1.0923 1.0572 1.0270 1.0023 0.9862 0.9766 0.9735 0.9743 0.9790 0.9878 0.9998 0.9954 0.9994 1.0025 1.0036 1.0041 1.0042 1.0035 1.0026 Hint: You can first compute the percentage overshoot (OS %) from the given data, from where you can find the parameter . then, you can choose to use either the settling time or the peak time to find the other parameter wn

Please answer all of the above question.

Answer 1

CODE FOR ABOVE GRAPH:

clc;
clear all;
s=tf('s');
g=(16.246/(s^2+4.0306*s+16.246));
a=step(g);
step(g)
hold on
b=0:0.1:3;
respon=[0 0.0694 0.2370 0.4487 0.6623 0.8494 .9961 1.0927 1.1468 1.1631 1.1533 1.1266 1.0923 1.0572 1.0270 1.0023 0.9862 0.9766 0.9735 0.9743 0.9790 0.9878 0.9998 0.9954 0.9994 1.0025 1.0036 1.0041 1.0042 1.0035 1.0026];
plot(b,respon,'r');
grid on