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state space system identification problem

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```Hi everybody,

I`m trying to use Grey-Box modeling with &#8222;pem&#8220;  to do parameter
identification for a SISO state space system in the following form;

dx/dt = Ax(t)+Bu(t);
dy/dt = Cx(t)+Du(t);

with 3x3 system-matrix

A = [-a1 1.5*a1 0; 1 -1 &#8211;1; 0 0 &#8211;a1];
B = [b1; 0; b2];
C = [1 0 0];
D = 0;

The systems has three unknown parameters, namely a1, b1, and b2.

Here is what I have done so far:
Build the state space system m and initialize the values for each
matrix, state and sample time:

m = idss(A,B,C,D,K,x0,'Ts',0)

Set up Grey-Box model:

m.As = [NaN NaN 0; 1 -1 -1; 0 0 NaN];
m.Bs = [NaN; 0; NaN];
m.Cs = m.c;
m.Ds = m.d;
m.Ks = m.k;
m.x0s = m.x0;

Estimate parameters:

m_new = pem(data,m);

The estimates for m_new do not fit the above mentioned system matrix A,
consisting of unknown parameter a1 only.

So here is my question:
Does anyone know, how to make sure that "pem" calculate the same value
for the &#8220;-a1&#8221; in the A matrix (by defining constraints, linkings, etc.)?
Or any other ideal for doing the state space identification for a system
like the upper one?
Any help would be appreciated.

Derek
```
 0

```Hi Jin,
Use the IDGREY objects which requires you to write a MATLAB function that
would take "a1" as an input argument and return A, B, C, D as output

http://www.mathworks.com/products/sysid/demos.html?file=/products/demos/shipping/ident/iddemo7.html

http://www.mathworks.com/help/toolbox/ident/ug/bqs6lf8.html

HTH,
Rajiv

"Jin Derek" <jinxin09@hotmail.com> wrote in message
news:ienvo9\$pne\$1@fred.mathworks.com...
> Hi everybody,
>
> I`m trying to use Grey-Box modeling with &#8222;pem&#8220;  to do
> parameter identification for a SISO state space system in the following
> form;
>
> dx/dt = Ax(t)+Bu(t);
> dy/dt = Cx(t)+Du(t);
>
> with 3x3 system-matrix
>
> A = [-a1 1.5*a1 0; 1 -1 &#8211;1; 0 0 &#8211;a1];
> B = [b1; 0; b2];
> C = [1 0 0];   D = 0;
>
> The systems has three unknown parameters, namely a1, b1, and b2.
>
> Here is what I have done so far:
> Build the state space system m and initialize the values for each matrix,
> state and sample time:
>
> m = idss(A,B,C,D,K,x0,'Ts',0)
>
> Set up Grey-Box model:
>
> m.As = [NaN NaN 0; 1 -1 -1; 0 0 NaN];
> m.Bs = [NaN; 0; NaN];
> m.Cs = m.c;
> m.Ds = m.d;
> m.Ks = m.k;
> m.x0s = m.x0;
>
> Estimate parameters:
>
> m_new = pem(data,m);
>
> The estimates for m_new do not fit the above mentioned system matrix A,
> consisting of unknown parameter a1 only.
>
> So here is my question:
> Does anyone know, how to make sure that "pem" calculate the same value for
> the &#8220;-a1&#8221; in the A matrix (by defining constraints, linkings,
> etc.)? Or any other ideal for doing the state space identification for a
> system like the upper one?
> Any help would be appreciated.
>
>
> Derek

```
 0

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7/23/2012 10:26:14 PM