Symbolic Toolbox, implicit function as implicit function argument.

Hello,

I'm working on small project for my studies - magnetic levitation system.

I wanted to check if my linearization calculations were correct. In order to do that I wanted to use Symbolic Toolbox, therefore I need to define:

• t - time,
• z(t) - position (time-dependant),
• L(z(t)) - inductance of coil, which depends on the position of a levitating object

In following lines I'll try to explain what is incomprehensible to me. I will declare syms objects and validate them with following formula:

• 

I imagine I should write script as follows:

%(1)
syms t
syms z(t)
syms L(z(t))

But it results in error: Invalid variable name.

Next I've written script:

%(2)
syms t
syms z(t)
syms L(z)

diff(L,t)

Script results in t being sym object. After 2nd line z is being defined as symfun object, but 3rd line: syms L(z); overrides z(t) as z, thus at the end of script z is a sym object. Result of the script is 0, therefore it's not a good way to define "my symbols".

After some random coding I've came up with:

%(3)
syms t 
syms z(t)
syms L(t)
L = L(z); 

diff(L,t)

Result of the (pretty) script is:

d

L'(z(t)) -- z(t)

dt

Which I interpretate as...:

L'(z(t)) = dL(z(t)) / dz(t)

This result is compatible with:

And I assume that code (3) is correct. My question is: why? Is it the only way to define such a function in Symbolic Toolbox? Moreover - is it a correct way?

Answer 1

[Charan Jadigam]

Hi,

I feel that you need to find chain rule using symbolic variables and it could be done in 2 other ways.

First method,

syms t z(t) L
L=str2sym('l(z(t))');
diff(L,t)

Second method,

syms t z(t) L(z)
L = L(z); 
diff(L,t)