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# Help! watch

1. I have been working on an assignment and have done some head damaging stuff, feedback control with Matlab modelling mostly with continuous time systems

Now I have gotten a bit stuck on something I think should be easy

To cut a long story short I am designing a state feedback control I have done some tricky stuff I have set the poles at 0.5 and -0.5 (for stability) and gotten the K values to give the system

X(n+1)= (F+GK)X(n) + GV(n)
Y(n)=CX(n)

X1(n+1)=0.28X1(n) - 0.02288X2(n) + 0.0192V(n)
X2(n+1)=-7.5X1(n) -0.28X2(2) +0.2(Vn)

Y(n)=[1 0]X(n)

Y(n)=X1(n)

Now I am asked to find the values of V(n) so that Y(n) converges to 3 in the steady state

Hence

X1(n) = 3

Now for a continuous time system it was easy the X1 was a constant so that X(dot)1 = 0 (differential of a constant = 0) and I could easily work the rest out and simulate my result

My problem is I am used to differential equations not difference so I am unsure if X1(n) = 3 what does X1(n+1) =?????

My senses tell me it would be 3 also as the output will not have changed anymore one sample time after infinity!!!

So in a nutshell what do I need to do to calculate V(n)???, obviously set up two simultaneous equations but I don't know what to put in for the X(n+1)

Any help much appreciated
2. is this physics or maths?
3. Its engineering, but its really maths!

I can do everything else except because I know little about difference equations

I think X1(n+1) is the same as X1(n) in steady state but I still end up with 2 equations and 3 unknowns
4. (Original post by Turbo-Dee)
I have been working on an assignment and have

X1(n+1)=0.28X1(n) - 0.02288X2(n) + 0.0192V(n)
X2(n+1)=-7.5X1(n) -0.28X2(n) +0.2(Vn)
I can't believe its so easy!!

X(n+1) tends to X(n) as n approaches inf

1.28X2(n) = -22.5 + 0.2V(n)

V(n) = 112.5

For Y(n) to have steady state 3

Surely that wasn't too hard for this forum!

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Updated: March 21, 2011
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