MATLAB: How can i plot a impulse response based on z-transfer function or difference equation

control theory

Hey guys,

i have the followeing z-transfer function:

G(z) = z^4 + 2z^3 + 3z^2 / z^4 – 1

I tried to reproduce the impuls response which can be seen in the figure. But i dont know how to do it. I tried a lot but always fail. Can anybody tell me how can i reproduce the impulse response ?

Best Answer

G = tf([1 2 3 0 0],[1 0 0 0 -1],-1);
impulse(G,20)

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MATLAB: Impulse response from transfer function in matlab

This is how I would do it:

% H(z)= 1-z^(-1)/1-z^(-1)+z^(-2)
b = [1 -1];
a = [1 -1  1];
figure(1)
impz(b,a)

MATLAB: Effect of sampling time on the time-domain response of discrete systems

There is a difference between the results from R2011a and R2014b. It is however expected.

In the release notes of Controls Systems Toolbox R2012a, you can find the following:

Rescaled Impulse Response and Impulse-Invariant Time Domain Conversion

For discrete-time dynamic system models, the input signal applied by impulse is now a unit area pulse of length Ts and height 1/Ts. Ts is the sampling time of the discrete time system. Previously, impulse applied a pulse of length Ts and unit height.

( http://www.mathworks.com/help/control/release-notes.html )

That is to say, before R2012a, the magnitude of the impulse response is always 1, but after R2012a, the magnitude is changed to Ts. Therefore, by specifying different sampling times, you end up with different results. What you can do in your use case is to multiply the results with 1/Ts. Then, you will have consistency in the results with different sample times.

For example, instead of

>> y = impulse(G, 3*0.05)

Please do

y = impulse(G, 3*0.05)*(1/0.05)

Hope this helps!

-Yu

Best Answer

Related Solutions

MATLAB: Impulse response from transfer function in matlab

MATLAB: Effect of sampling time on the time-domain response of discrete systems

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