how to create a state-space model without disturbance and how does the disturbance influence the solution

I would like to identify parameters of an ODE using the system identification toolbox. The sate-space representation in MATLAB is always formulated with a disturbance e, which always influences the solution y due to the equation y = Cx + Dy + e. In my problem, there is no disturbance present. Now, I have two questions: - Of which form is the disturbance e and in which way does it influence the solution (setting K = 0) - Is there the possibility to describe a state-space model in MATLAB without disturbance

Thanks in advance

Manuel

Answer 1

[Rajiv Singh]

The difference between the output of the model and the actual (measured) output is, in general, not going to be zero. So, there will be an error e such that:

 e = ymeasured-ymodel,

where

 ymodel = Cx + Du

which means:

 ymeasured = Cx + Du + e

When you set K = 0 in the idss model, the parameters you get by minimizing |e||| are the ODE coefficients you are interested in. Furthermore, using

 [A, B, C, D] = ssdata(model)

you can extract out the state-space coefficients of the output-reproducing model: xdot = Ax + Bu; y = Cx+du

[Raghav Gopal Rao Netrakanti]

Hi,

I have tried the following experiment to verify this. I modelled a spring-mass-damper system in simulink with (m=10, k(spring constant) = 5, and d(damping coeff) = 2). I took the generated output to my workspace and then tried the systems Identification App to get the state space matrices. My Aim being to verify the mathematically formed state space matrices and the ones from the App.

Now, as mentioned already, the App takes into consideration noise in the system and so the matrices are very different from what was expected. I tried your idss with K=0 approach but it gave me the same matrices(from the App) without any difference. I also tried the ssdata(model) where model was the one from the App and there too i got the same results.( i'm not sure what you actually meant by "output-reproducing model: xdot = Ax + Bu; y = Cx+du" )

I would really appreciate it if you can help me out here.

Thanks,

Gopal

Answer 2

[Azzi Abdelmalek]

you have just to set e to 0

[Manuel]

How can I set e?

[Azzi Abdelmalek]

Is the system you are identifying linear or not?

[Azzi Abdelmalek]

When you identify a linear system, you are looking for the matrix A, B, C and D. the disturbance e is not a part of your dynamic model, it's just an additional input that will disturb your output y