how to simulate an impusles response of a transfer function?

how to simulate an impulse response of transfer function?

which is T(s)= 15/(s^2+8s+15)

simulink should be used to find the impulse response

Answer 1

[Aquatris]

An impulse signal is a signal that has a certain magnitude that is applied for a small time. So you can use transfer function block to model your T(s) and use sum of 2 step functions to create impulse signal input. Use scope or toWorkspace block to obtain the response.

Impulse magnitude = x

Impulse time = t

Step function 1: step time 1, initial value 0, final value x

Step function 2: step time 1+t, initial value x, final value 0

Answer 2

[Aryan Ritwajeet Jha]

For definition (construction) of impulse signal: https://fr.mathworks.com/help/signal/gs/impulse-step-and-ramp-functions.html

If you are looking for a time domain response, then MATLAB has some easy to use functions:

%construction of transfer function
numerator=15;
denominator=[1,8,15];%(s^2+8*s+15)
transferFunction=tf(numerator,denominator);  
impulseplot(transferFunction);

If you are looking for a Fourier Spectrum of the impulse response of a transfer function:

%construction of transfer function
numerator=15;
denominator=[1,8,15];%(s^2+8*s+15)
transferFunction=tf(numerator,denominator);

%construction of impulse signal
dt=1e-3;
t = -1:dt:1;
impulse= t==0;

%computing fourier spectrum of impulse response
impulseResponse=fftshift(fft(lsim(transferFunction,impulse,t)));
len=length(impulseResponse); %to take the frequency axis of the harmonics.
q=-(len-1)/2:(len-1)/2;  %divide the frequency components
fimpulseResponse=sqrt(impulseResponse.*conj(impulseResponse)); 
plot(q,[fimpulseResponse]);
title(['Fourier Spectrum Plot']);
axis([-10 10 0 1]);
xlabel('Frequency');
ylabel('Amplitude');

Answer 3

[Ahmad Alkadri]

Just run a stepplot, but multiply the numerator of your transfer function by s to turn the step function into a dirac delta function (recall that that the integral of the step function is the dirac delta).

This corresponds to adding another entry of '0' in your numerator. So instead of

% unit step response
sys = tf([15],[1,8,15])
stepplot(sys)

You can write:

% unit impulse response
sys = tf([15,0],[1,8,15])
stepplot(sys)

Answer 4

[babou babi]

hi,

try this two lines

>> sys = tf (15,[1 8 15])

>> impulse(sys)

best regards,

[yousaf muzafar]

thk