AIM:-(a) Plot step response of
given TF and 2nd order system with different values of damping ratio
in MATLAB software.
(b) Plot ramp response.
SOFTWARE
USED: -MATLAB (R2021a)
PROCEDURE:-
Step response is the time behaviour of the outputs of a
general system when its inputs change from zero to one in a very short time.
Mathematically,
the step signal is represented as given below:
u(t)= 1 ; t
> 0
= 0 ; t < 0
num =
input(‘enter the numerator of the transfer function’)
den =
input(‘enter the denominator of the transfer function’)
step(num,den)
EXAMPLE:-
T(s)= (s + 1)/
(s3 + s2 + 2s + 1)
num=[1 1]
num = 1
1
>>
den=[1 1 2 1]
den =
1
1 2 1
>>
sys1=tf(num,den)
sys1 =
s + 1
-------------------
s^3 + s^2 + 2 s + 1
Continuous-time
transfer function.
>> step(sys)
EXAMPLE:-
T(s) = 25 / ( s2
+ 2s+ 25)
num=[25]
num =
25
>>
den=[1 2 25]
den =
1
2 25
>>
sys=tf(num,den)
sys =
25
--------------
s^2 + 2 s + 25
Continuous-time
transfer function.
>>wn= 5;
>>
d=0.4;
>>
[num,den]= ord2(wn,d)
num =
1
den =
1
4 25
>>
num1=5^2*num;
>>printsys(num1,den)
num/den =
25
--------------
s^2 + 4 s + 25
>>
step(num1,den)
n=[0 0 36];
d=[1 3 36];
t=0:0.005:2;
u=t;
plot(t,y)
title('Ramp response')
Result: Step response with different values of damping ratio
and ramp response have been plotted and verified using MATLAB for given
transfer function.
