Thread Subject: State space

How do we write the MIMO state space representation of the model? For example given the below MIMO ARX model:

y1(k) = -a1*y1(k-1) - a2*y2(k-1) + b1*u1(k-1) + b2*u2(k-1) + b3*u1(k-2) + b4*u2(k-2)

y2(k) = -a3*y1(k-1) - a4*y2(k-1) + b5*u1(k-1) + b6*u2(k-1) + b7*u1(k-2) + b8*u2(k-2)

How do we write them in state space representation? This is a 2 inputs 2 outputs system.

Make the z-transform out of it and glue it together.

help tf
help ss

Regards,
Stefan

"Joseph Ho" <hoyoku@yahoo.com> wrote in message <gesnib$6ot$1@fred.mathworks.com>...
> How do we write the MIMO state space representation of the model? For example given the below MIMO ARX model:
>
> y1(k) = -a1*y1(k-1) - a2*y2(k-1) + b1*u1(k-1) + b2*u2(k-1) + b3*u1(k-2) + b4*u2(k-2)
>
> y2(k) = -a3*y1(k-1) - a4*y2(k-1) + b5*u1(k-1) + b6*u2(k-1) + b7*u1(k-2) + b8*u2(k-2)
>
> How do we write them in state space representation? This is a 2 inputs 2 outputs system.

Is this going to work? Cos I don't think with a mimo system, this can work. Output1 is dependent upon the delay of output2. And there are 3 inputs with delays altogether. I do not know how can I put them in state space form.

"Stefan" <gonseaw@yahoo.com> wrote in message <gesr9q$qpr$1@fred.mathworks.com>...
> Make the z-transform out of it and glue it together.
>
> help tf
> help ss
>
> Regards,
> Stefan
>

If you want a minimal representation and are not working symbolically, it
may be good to follow the IDARX->minreal(SS) path. If you are working
symbolically, this may be a difficult exercise since it requires operator
inverses (and I don't know a good solution to that).

See documentation on IDARX objects on how to create these objects to
represent MIMO ARX equations. Once you have an IDARX model M, you may do
minreal(ss(M('m'))).

For your example:
A(:,:,1) = eye(2);
A(:,:,2) = [a1 a2; a3 a4];

B(:,:,1) = zeros(2);
B(:,:,2) = [b1 b2; b5 b6];
B(:,:,3) = [b3 b4; b7 b8];

M = idarx(A, B);
sys = minreal(ss(M('m')))

Rajiv

"Joseph Ho" <hoyoku@yahoo.com> wrote in message
news:getm2t$kag$1@fred.mathworks.com...
> Is this going to work? Cos I don't think with a mimo system, this can
> work. Output1 is dependent upon the delay of output2. And there are 3
> inputs with delays altogether. I do not know how can I put them in state
> space form.
>
> "Stefan" <gonseaw@yahoo.com> wrote in message
> <gesr9q$qpr$1@fred.mathworks.com>...
>> Make the z-transform out of it and glue it together.
>>
>> help tf
>> help ss
>>
>> Regards,
>> Stefan
>>
>