Differential equation to find activation voltage

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Anniken 2023-10-17

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2034654-differential-equation-to-find-activation-voltage

评论： Anniken 2023-10-18

采纳的回答： Torsten

在 MATLAB Online 中打开

I am trying to calculate the activation voltage, with the following code:

i = 100 ;
t = [0 0.2 0.01];
R = 8.314;
G = 9.648*10^4;
T = 303.15; %Conductivity reference temperature
i_0dob = 0.67;
A_m = 232e-4;
b_ca = 0.55 ;
b_an = 1-b_ca ;
C_dl = 3.15e-2*A_m ;
syms u(t)
ode = diff(u,t) == (i-A_m * i_0dob * (exp(((b_an*G)/(R*T))*u)-exp((-(b_ca*G)/(R*T))*u)))/C_dl;
cond = u(0) == 0; 
uSol(t) = dsolve(ode,cond)  %This - is line 19
Warning: Unable to find symbolic solution.
 
uSol(t) =
 
[ empty sym ]
 

I get the warning:

Warning: Unable to find symbolic solution

In dsolve (line 209) %i dont have a line 209??

In Problem43 (line 19)

Can anybody help?

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Anniken 2023-10-18

Yes! Its this one!

Sam Chak 2023-10-18

Thanks @Anniken Hagen.

Could you also take a screenshot of the parameters and post it here super quickly? In the problem image, the values of the parameters are not displayed. It would be helpful for us to cross-check because selected values often impact the transient behavior of the system.

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采纳的回答

Torsten 2023-10-17

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2034654-differential-equation-to-find-activation-voltage#answer_1334759

编辑：Torsten 2023-10-17

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Matlab cannot find an analytical expression for u. You have to use a numerical approach.

I'm not sure about the term exp(b_an*G/(R*T)*u). Shouldn't it be exp(-b_an*G/(R*T)*u) ?

i = 100 ;

R = 8.314;

G = 9.648*10^4;

T = 303.15; %Conductivity reference temperature

i_0dob = 0.67;

A_m = 232e-4;

b_ca = 0.55 ;

b_an = 1-b_ca ;

C_dl = 3.15e-2*A_m ;

fun= @(t,u) (i-A_m * i_0dob * (exp(b_an*G/(R*T)*u)-exp(-b_ca*G/(R*T)*u)))/C_dl;

tspan = [0 0.01];

u0 = 0;

[T,U] = ode15s(fun,tspan,u0);

plot(T,U)

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Sam Chak 2023-10-18

在 MATLAB Online 中打开

Hi @Anniken Hagen

I believe I've found the typo in C_dl. However, I'm struggling to plot the piecewise current i and

using an anonymous function. Maybe I should ask @Torsten for help.

i = [100, 10, 100];

t = [0, 0.2, 0.4, 0.5];

R = 8.314; % looks like gas constant (does gas mix with electric?)

G = 9.648e4;

Temp = 303.15; % Conductivity reference temperature

i_0dob = 0.67;

A_m = 232e-4;

b_ca = 0.55;

b_an = 1 - b_ca;

C_dl = (3.15e2)*A_m; % affect the transient

T = [];

U = [];

u0 = 0;

for j = 1:numel(i)

fun = @(t,u) (i(j) - A_m*i_0dob*(exp(b_an*G/(R*Temp)*u) - exp(- b_ca*G/(R*Temp)*u)))/C_dl;

tspan = [t(j) t(j+1)];

[Tstep,Ustep] = ode15s(fun, tspan, u0);

T = [T; Tstep];

U = [U; Ustep];

u0 = Ustep(end,:);

end

% Plot Voltage

subplot(211)

plot(T, U, 'linewidth', 1.5), grid on

xlabel('t, [s]')

ylabel('u, [V]')

% Plot Currents

im = A_m*i_0dob*(exp(b_an*G/(R*Temp)*U) - exp(- b_ca*G/(R*Temp)*U));

% i =

% id = i - im;

subplot(212)

plot(T, im, 'r'), grid on, ylim([-100 100])

xlabel('t, [s]')

ylabel('i, [A]')

Anniken 2023-10-18

Yes!Had typo in C_dl and the G and F.... The bug was fixed and also a function was implemented and the resolution was found! Thank you so much for all the help:D

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