How to solve parametric simultaneous equations in MATLAB?

I have three parametric simultaneous equations as follows:

    I*R + L*s*I + a*s*Y - V = 0
    B*I + m*s^2*Y - k2*X + k2*Y - b2*s*X + b2*s*Y = 0
    -B*I + M*s^2*X + (b1 + b2)*s*X - b2*s*Y + (k1+k2)*X - k2*Y = 0

I am trying to solve these equations using MATLAB. Specifically I am trying to get an output of the form: `X/V = [] / []`

Looking on the mathworks forum and documentation I thought that using `syms` and `solve` would be a good approach.

This is my code:

    clc,clear all;

    % I*R + L*s*I + a*s*Y - V = 0
    % B*I + m*s^2*Y - k2*X + k2*Y - b2*s*X + b2*s*Y = 0
    % -B*I + M*s^2*X + (b1 + b2)*s*X - b2*s*Y + (k1+k2)*X - k2*Y = 0

    syms s Y I R L V B m k1 k2 b1 b2 X a M
    sol = solve([I*R + L*s*I + a*s*Y - V == 0, B*I + m*s^2*Y - k2*X + k2*Y -  b2*s*X + b2*s*Y == 0, -B*I + M*s^2*X + (b1 + b2)*s*X - b2*s*Y + (k1+k2)*X - k2*Y == 0], [X,V]);

    sol.X/V
    sol.X
    sol.V

As can be seen, when I try to solve for `[X,V]` as required, my command window shows:

   ans = *Empty sym: 0-by-1*

This could be because: "the set of equations you are trying to solve does not have a valid symbolic solution" ( Link )

I have also been looking through the official documentation , but I am still getting the same output. When I add `Y` as a symbolic parameter along with `X` and `V` I get the following output:

sol2.X/V

(B*I*m*s^2)/(V*(k1*k2 + b1*m*s^3 + b2*m*s^3 + k1*m*s^2 + k2*m*s^2 + b1*k2*s + b2*k1*s + M*b2*s^3 + M*k2*s^2 + M*m*s^4 + b1*b2*s^2))

sol2.X

(B*I*m*s^2)/(k1*k2 + b1*m*s^3 + b2*m*s^3 + k1*m*s^2 + k2*m*s^2 + b1*k2*s + b2*k1*s + M*b2*s^3 + M*k2*s^2 + M*m*s^4 + b1*b2*s^2)

How can I solve for X and V, and more specifically get an answer in the form of: X/V = [] / [] ?

Any tips or suggestions would be appreciated!

Answer 1

[Walter Roberson]

You are trying to solve three equations for two variables. That is overdetermined and will not generally have a solution.

Question: were you perhaps looking for sol.X/sol.V?

[Ryan Rizzo]

Ah, what a silly mistake. Yes, that is what I am looking for.

Would this be a better implementation?

sol2 = solve([I*R + L*s*I + a*s*Y - V == 0, -B*I == m*s^2*Y - k2*X + k2*Y - b2*s*X + b2*s*Y, B*I ==  M*s^2*X + (b1 + b2)*s*X - b2*s*Y + (k1+k2)*X - k2*Y], [X,V,Y])

sol2.X/sol2.V

[Walter Roberson]

That looks plausible.