Just to clarify:
You're trying to solve
,
subject to , and .
Is this correct?
Hello all hopefully you can be of help
I have to solve the following difference equation using z transforms
Xq+2 - 5Xq+1 +6Xq = 2
conditions Xo=0 and X1=1
Not to sure how to do it
so far i have took the z transforms and got
(z^2-z) -5zx + 6x = 2z/z-1
I'm not sure if this is correct but even if it is i have no idea of what to do next
Any help would be greatly appreciated
There are different definitions of the z-transform: bilateral, unilateral, and geophysical. Which one are you using? I'm guessing unilateral?
So, when I take the z-transform of the difference equation, , I get the following:
.
As with most transform techniques, the next step is to solve the problem in the new domain (i.e., solve for ), and then perform the inverse z-transform. You might need partial fraction decomposition.
Okay im still not 100% sure
But so far i've got it to this form
2z/(z-1)(z-3)(z-2)
Then using partial fractions got it to,
-4/z-2 +1/z-1 +3/z-3
You mention inverse z-transform, have i missed a stage? or am i heading in the right direction?
(sorry being vague very new to z-transforms)
Many thanks figured it out.
Hmm. That doesn't jibe with what RSolve gives me in Mathematica. Also, you want to be careful with your parentheses. What's being exponentiated?
I got the partial fraction expansion of
.
The inverse z-transform of this is
.
Plugging in the initial conditions yields two simultaneous equations:
.
Solving gives , and . Plugging this into the expression above yields
, which is what RSolve also yields.