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Creating Structured models with Orders Higher than Measurement Data

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I am working on identifying a system. I have 3 measured states which are all related, essentially over determining the system, since they are all the integral or derivative of one another. There is only one unique state. I have done this for ease of hooking up to a control system later.
Which brings me to my next point. The main thing I want to do here is to make the C matrix equal to identity, so that I can hook the controller up to the feedback signals, just as I will in the nonlinear model (an aircraft simulation) where I got the model data from. This nonlinear aircraft model includes some closed loop control which I am not directly privy to (black box). So I am having to go higher order than I usually would for a regular aircraft model.
I was able to achieve what I want with idgrey() , in terms of implementation, but I could not get close enough on the initial parameter guess.
So is there a way that I can use pem() or n4sid(), etc, to go to work on a structured model of order higher than the number of states in my iddata() object? I have 3 states but need a 5th+ order model. Mainly I would like to have the C matrix be identity, but secondly I would really like to also tell it how X and X_dot are known to be related in the A matrix.

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