Solenoid - Integration of inductance L as a function of plunger position x

Hello All,

I am in the process of evaluating the value of inductance L at each step of the plunger position in a solenoid according to the differential equation:

Force = 0.5*i^2*dL/dx

The value of current is a constant at 8.75 A. The value of force F varies at each step of the plunger position. dL/dx data for each step of the plunger position is available from the manufacturer force-stroke data. I need to integrate dL/dx to get L as a function of x. I tried using the ode45 function.

Lo = 3.8184e-3;                                     % initial value of inductance
i = 8.74;                                           % current in ampere
x = plungerPosition;                                % plungerPosition (984x1 double) data imported from excel
[x,L] = ode45(@(x,L) F/0.5*i^2, x, L0);             % F (984x1 double) data also imported from excel, force in newton

But I get the following error:

Error using odearguments (line 95)

@(X,L)F/0.5*I^2 returns a vector of length 984, but the length of initial conditions vector is 1. The vector returned by

@(X,L)F/0.5*I^2 and the initial conditions vector must have the same number of elements.

Error in ode45 (line 115)

odearguments(FcnHandlesUsed, solver_name, ode, tspan, y0, options, varargin);

Error in IntegrationofdL (line 4)

[x,L] = ode45(@(x,L) F/0.5*i^2, x, L0);

Can you please help me how I can solve this problem?

Thanks and Regards,

Goutham Sajja

[Goutham Sajja]

Dear All,

A little update to the previous query. I modified the ode45 code to obtain the value of inductance for each changing of the plunger position x.

L0 = 3.8184e-3;                                 % initial value of inductance
i = 8.75;                                       % current in ampere
x = plungerPosition;
for j = 1:numel(F)
[x,L] = ode45(@eval, x, L0,[],F(j));            % F is the force at each plunger position
end

function dLdx = eval(x,F,i)
dLdx = (F/0.5*i^2);                             % equation is dL/dx = F/0.5*i^2
end

With this code, I get the value of inductance L for each plunger position x.

Could you please tell me if the code that I have written is correct?

Thanks and Regards,

Goutham Sajja

Answer 1

[Vimal Rathod]

Hi Goutham,

Few things I would like to point out are, you seem to be passing a lot of arguments to the ode45 function call which might not work. Also, "eval" is matlab defined function which already exists, so I would suggest you to use some other name say "eval1". Make sure to define function in a different .m file. I have added a way to store the L values when returned from ode45 in a cell array.

Have a look at the following snippet, hopefully it helps.

L0 = 3.8184e-3;                                 % initial value of inductance
i = 8.75;                                       % current in ampere
x = plungerPosition;
Lval = {};
for j = 1:numel(F)
[x,L] = ode45(@(x,L)eval1(x, F(j), i), x, L0);            % F is the force at each plunger position
Lval{end+1} = L;
end

% Below lines should be in a different file named "eval1.m"
function dLdx = eval1(x,F,i)
dLdx = (F/0.5*i^2);                             % equation is dL/dx = F/0.5*i^2
end

Refer to the following document for more examples on ode45

Solve nonstiff differential equations — medium order method - MATLAB ode45 (mathworks.com)