Thread: [control] need help for state space and representation

Hello,

I'm preparing a practical work for the next week, and I need some help.

Actually this work deals abour the "state feedback compensation",

The system has a transfer function: G(s) =
1
-----------------------
s ( s + 2 ) ( s + 1 )

the state representation is like this:

U(s) -> 1/(s+1) -> X3(s)= Y3(s) -> 1/(s+2)-> X2(s)=Y2(s) ->1/s -> X1(s)=Y1(s)

I've computer the matrix like this:

~X= A X + B U where ~x is the derived of X
Y= C X + D U

and I have:

( ~x1 ) ( 0 1 0 ) ( x1 ) + ( 0 )
( ~x2 ) = ( 0 -2 1 ) ( x2 ) + ( 0 ) u
( ~x3 ) ( 0 0 -1 ) ( x3 ) ( 1 )


( y1 ) ( 1 0 0 ) ( x1 )
( y2 )= ( 0 1 0 ) ( x2 ) + 0 u
( y3 ) ( 0 0 1 ) ( x3 )

Now, I have to do the same thing but with only X1 as state variable (X2 ans X3 would be masked in the system) and U as input.

And, I haven't the slightest idea to do that...
I've tried to write X1 according to U and the TF G(s) but it's not easy and I can't find a good result...

If someone can help me, it'd be very helpful!

thanks in advance!