 # Can the Jacobian matrix formed from some equations be converted into the transfer function?

Can the Jacobian matrix formed from some equations be converted into the transfer function? Actually I have 6 equations and got the Jacobian matrix formed from those equations by keeping some parameters as variables and some as constants.Now I want the state space equations and then convert it into transfer function,please can someone help me.

Sounds like homework. Just FYI, we don’t do people’s homework here.

Well, let me just say that I, for one, believe this topic has been addressed so many times in so many threads here that people don’t even get excited about it any more.

In my experience, there are a great many different things which can be called by the title of “transfer function”. I would advise you to go to whoever said those two words to you (teacher, project manager, whatever) and find out from them precisely what it is they want.

You are going to have to fully understand what those words mean…

Hey buddy,thats not my home work.I am a Master’s student and I need this to complete my project.After this doubt is resolved, I have to do a lot more work of simulation on this. Please reply if you know how to do it.Thanks.

Hello friend,can you just give me the link where it is discussed.I need it a lot.Thanks.

Hello friend,can you just give me the link where it is discussed.I need it a lot.Thanks.

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After (finally) getting clarification from the OP, this is not homework. The OP is basically just asking if one form of equations can be converted to another form, and while this may or may not be related to his master’s work (I didn’t receive clarification on that point) it is still basically just a question of mathematics and isn’t directly asking for a homework answer.

Can you post some clarifications as to what you are trying to do ? Generally, the state space representation of the dynamic system is given by :

dX/dt = AX + BY
Y=CX+DY

This can be easily converted to a s function and most textbooks will tell you how. If you are looking to simulate - Matlab has an inbuilt function too.

Yes,you are right that about the state space representation.
But if I have the Jacobian matrix which is calculated from some equations having more than 1 variables,can the A,B,C,D matrices be obtained from it.
The transfer function can be obtained by the formula- C[sI-A]^-1 B
The doubt which I have is that the Jacobian matix itself is the A matrix.Is it correct?
If it is not then can we calculate the A B C matrices from the Jacobian matrix?

Just to satisfy my curiosity, can I ask what textbook you are working off of? Or maybe a rough idea of the application: I’d like to know the context of the problem. I won’t be able to help though.

Sorry for the late reply - I forgot about this post. I think what you are trying to do is to covert a non linear control problem to a localized linear one. If that is the case, then this linktells you all about it. It is shown how to get to A B C and D.

Thanks buddy.Exactly this is what I am trying to do.Converting a non linear system to linear system of equations.I studied in many books that it can be done using Taylor series by taking the values at some particular points.Now. I am having problem in getting these points.

These points are the nominal points which is stated n the reference you gave the link for.

I believe the question is answered - right ?

If not, please understand that not all non-linear systems can be meaningfully linearized around local points. There are global linearization methods that work better for chemical reactions and things like that.

For many mechanical control problems, the nominal value you are seeking is the equilibrium point or sometimes the set point.