I have a MIMO system of order 14 with two inputs and two outputs.
I want to apply feedback linearisation to control it.
I have attempted this, and as a result I have a FBL system with a combined relative degree of 2 and 12 internal dynamic states.
I have attached the equations for the internal dynamics below.
(z1, z2 are the output states)
(z3-z14 are the internal dynamics states)
But I am quite lost at this point on how to proceed from here.
My questions are:
Any insights into this would be much appreicated.
Thank you
1. Do as with any stability analysis: start by investigating the stability around the equilibrium points (eigenvalues of tangent linearizations). It will give you some precious basic information about the behavior of your system.
2. Your question is somewhat vague. It could be understood as: what will be the system behavior if the model is not exactly what you think? In other words, will slightly different systems of equations lead to only slightly different solutions, and for how long? This is the basis of perturbation theory (regular and singular).
3. Robustify in what sense?
Dear Chanditha,
I suggest you to see links in topic.
-Experimental feedback linearisation of a vibrating system with a non ...
https://www.sciencedirect.com/science/.../pii/S0022460X17308271
-Feedback Linearization - University of Nevada, Reno
https://wolfweb.unr.edu/~fadali/EE776/FeedbackLinearization.pdf
-Strategies for Feedback Linearisation: A Dynamic Neural Network Approach
https://books.google.dz/books?isbn=1447100654
-Partial linearization of the PVTOL aircraft with internal stability - Hal
https://hal.archives-ouvertes.fr/hal-00858102/document
-Input-output linearizing control with load estimator for three-phase AC ...
https://ieeexplore.ieee.org/document/1022550/
Best regards
Dear Chanditha,
It seems interesting problem, what is the inputs of your system?
what are the equations for z1 and z2.
Best regards,
@philippe Martin
Thank you for the response.
By "robustifying" what I intended was how can I make this system stable if the parameters were not exactly known, but only known within a certain tolerance.
But I think I have made an error in the equations I posted so I am working on them again. Once I have them I will start looking into the stability with your advice in mind.
@Mohamed-Mourad Lafifi
Thank you for all the resources you posted. I am still new to this so applications on how this theory is used in practice esp for MIMO systems is very useful to me
@Tamir Shaqarin
Tamir I made an error in my equations. I need to work on Z1-Z14 again.
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