How to linearize these equations?

Summary:

A brain teaser for all the control pros out there!

How to linearize these equations?

paramsci 24 Jan 2012 00:57

Linearize following system of equations and put them in linear state space format

(1)

\begin{align} m\ddot{x}+\frac{K{{i}^{2}}}{x}=mg \end{align}

(2)

\begin{align} L\frac{di}{dt}+iR=V \end{align}

I am still struggling with it, the thing is if I try to linearize $\frac{1}{x}$, even then the nonlinear part from coupling electrical circuit remains $K{{i}^{2}}$. Any insights? Ideas?

Re: How to linearize these equations?

Flippo789 26 Jan 2012 00:01

Hey Perry,

I think you need to linearize about a set of i & x. Thus you are not really finding a "line" that represents the point, but you are instead finding a "plane" that represents the combination of both variables.

Here is a lecture from an Arkansas Tech University Calculus III class that talks about multivariable linearization:

Local Linearity of Multivariable Functions

I hope this helps answer your question.