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

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Goutham Sajja
Goutham Sajja on 9 May 2021
Answered: Vimal Rathod on 22 Jun 2021
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
  1 Comment
Goutham Sajja
Goutham Sajja on 16 May 2021
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

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Answers (1)

Vimal Rathod
Vimal Rathod on 22 Jun 2021
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

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