Sketching a zero-input response for an Electrical Engineering problem

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Orlando Salas
Orlando Salas 2016-12-11
编辑： Orlando Salas 2016-12-11
Hi everyone, I'm relatively new to MATLAB, so I don't know if anyone can help me. I'm trying to sketch the zero-input response for a system. The system can be described by
(E^2 - 1.56E + 0.81)y[k] = (E + 3)f[k]
with the following conditions: y[-1]=2, and y[-2]=1.
The following code is what I am trying to trouble shoot:
y=[1 2];
y=y';
k=-2:16;
k=k';
for m=1:length(k)-2
Y=1.56*y(m+1)-0.81 *y(m);
Yzi=[Yzi;Y];
end
stem(k,Yzi)
Does anyone know what I am doing wrong?

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回答（1 个）

Star Strider
Star Strider 2016-12-11
I have no idea how you’re supposed to solve it.
I am not certain what the assignment actually wants you to do. This would be my approach (in terms of powers of 1/z):
a = flip([1 -1.56 0.81]);
b = flip([1 3]);
yi = flip([1 2]);
k=-2:16;
f = filter(b,a,k,yi);
figure(1)
stem(k, f)
grid
But then I’m known to take liberties with problems I don’t understand.
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Star Strider
Star Strider 2016-12-11
The term ‘classical method’ leaves much to the imagination. It would help if you could describe it.
My inclination would be to use the z-transform of your equations, then take the inverse to solve the differential equation. It’s been decades since I‘ve dealt with difference equations and their solutions.
Orlando Salas
Orlando Salas 2016-12-11
编辑：Orlando Salas 2016-12-11
Sorry about that, does the term term "natural-response" help? It's supposed to be similar to the zero-input response. I'm pretty sure that I am looking for yn[k]. My system of equations is supposed to satisfy Q[E](yn[k] + ytheta[k]) = P[E]f[k] when Q[E]yn[k]= 0. I know how to solve it manually, but I am wondering if it is possible to solve via MATLAB....
Edit: I forgot to mention that ytheta[k] represents a forced response rather than a zero-state response.

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