Reduced Order (Luenberger) Observer in Control Systems

[Javi_Rome]

Hello,

I am trying to implement a simulation of a control system (in state space formalism) in which one of the strategies is to estimate various states and build a Luenberger (reduced/minimum order) observer. First I should simulate the continuous time model, and then discretize it in order to implement later in real time module.

Although I have already done a full order observer using the Control, Design and Simulation Module, I have no idea how to build a reduced order observer.  Anyone could provide some ideas?

Best regards,

Javi.

[AndyClegg]

Are you wondering how to reduce the model order that is used in the observer ? Surely the observer is structured the same wether it uses a full order model or a reduced one.

If you wanting to reduce the model order automatically, without your intervention,then try searching for a command "minreal" - there may be others in the toolkit. But it depends upon what you want to achieve with your model reduction - eliminate near cancelling pole zeros, reduce to a certain order etc. I would always want to manually check that any model reduction method works - as it is easy to simplify a model and loose information that you really want to preserve and compare both the time and frequency responses of the reduced model with the original.

[Javi_Rome]

It is like I do not have all of the state variables fully accesible to meassure and feedback, and I have to estimate the ones that I cannot meassure with enough accuracy. Thus, in the theory, there is a way to construct a minimum order observer to estimate these variables and feedback them with the meassured ones.

I have checked the help of the Control, Design & Simulation manual and says something like you have to implement the usual observer structure (If I am understood that well) and state the variables you cannot access putting some zero value at their place in a diagonal matrix... but I am not totally sure about if that

is the correct way to do it.

Another way I am thinking is to construct the state space or the transfer function of the observer model and try to implement the block diagram that appears

in the theory part.

Also I am going to check the minreal command.

Thanks and best regards!

[Javi_Rome]

This was an old question, but just wanted to know if anyone has attempt a valid approach. Regards.