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> Discrete Time State Space
jl4945
Posted: March 19, 2011 08:32 pm
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I have been modelling a DC motor using state space, open loop control output feedback and state feedback calculating the relevant terms and then modelling the systems using Matlab.

I have also transformed another continuous time system (the actual system modelled not stated) into a discrete system with my poles set in the unit circle for stability

Now so far so good I end up with 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 for the continuous time system it was simple, the motor speed X2(t) is given as a constant Hence its differential is 0 and I now have a formula telling me that the other state X1(t) is 0 so I can calculate the feed back terms

But I am struggling to do this for a discrete system, I am told that y(n) converges to 3 in steady state

so
Y(n)=X1(n)

X1(n) = 3 as T goes to infinity

X1(n+1)=0.28X1(n) - 0.02288X2(n) + 0.0192V(n)

But X1(n+1) with X1(n) = 3 is what???, it would be zero in continuous time as its a differential of a constant but my senses tell me for this DIFFERENCE equation it would be 3!, the speed has stopped changing one sample time after infinity!!

Can anyone advise me on how to calculate V(n) with the information given?
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MrAl
Posted: December 15, 2011 12:55 pm
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Hi,

A little late i guess but i didnt visit here for a while now.

If you can accept Vn as a constant (for driving a motor for example) then Vn=112.5 gives you the required Y=3 for n going to infinity.


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Sorry i stepped on your T.O.E.
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