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

MATLABodestate-space modelSystem Identification Toolbox

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

Best Answer

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
Related Question