How to solve and write system of differential equations?

Question

pml_28 2018-3-28

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https://ww2.mathworks.cn/matlabcentral/answers/391270-how-to-solve-and-write-system-of-differential-equations

编辑： Abraham Boayue 2018-3-30

采纳的回答： Abraham Boayue

edo.png

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Hi, I am trying to solve this system through ODE45, and I tried two ways:

First:

function dxdt = rlcf(t,x)
I4 = (V - R1 * x(1)) / R4;
I3 = (V - R1 * x(1) - R2 * x(2)) / R3;
I5 = x(1) - x(2) - I4;
I6 = x(2) - I3;
dxdt(1,1) = (1/R1)*((V)-(I5/C1));
dxdt(2,1) = (1/R2)*((I5/C1)-(I6/C2));

I don't now how i write dVdt in this case... and my code enter in continuous loop.

Second:

    function dxdt = rlcf(t,x)
    dxdt(1,1) = (1/R1)*((V)-((x(1) - x(2) - ((V - R1 * x(1)) / R4))/C1));
    dxdt(2,1) = (1/R2)*(((x(1) - x(2) - ((V - R1 * x(1)) / R4))/C1)-(((V - R1 * x(1) - R2 * x(2)) / R3)/C2));

In this case, the results in vector are 'NaN'.

How I write dVdt in this case?

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Answer 1

Abraham Boayue 2018-3-29

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https://ww2.mathworks.cn/matlabcentral/answers/391270-how-to-solve-and-write-system-of-differential-equations#answer_312517

编辑：Abraham Boayue 2018-3-29

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RLCi_1.pdf

   R1 = 500; R2 = 800; R3 = 1000; R4 = 200; C1 = 0.1;
    C2 = 0.1; V = 180;
    F = @(t,y)[y(1);  
                 (y(1)/R1 -(y(2)-y(3)-V/R4-R1*y(2))/(R1*C1));
        ((y(2)-y(3)-V/R4-R1*y(2))/(R2*C1)-(y(3)-V/R3-R1*y(2)-R2*y(3))/(R2*C2))];
    tspan = [1 2];
  yin  = [0 0 0];
  [t,y]=ode45(F,tspan,yin);
  plot(t,y(:,2),'linewidth',1.5,'color','b')
  hold on
  plot(t,y(:,3),'linewidth',1.5,'color','r')
  grid;
  a = title('I_1 and I_2');
  legend('I_1','I_2');
  set(a,'fontsize',14);
  a = ylabel('y');
 set(a,'Fontsize',14);
  a = xlabel('t [0 1]');
  set(a,'Fontsize',14);

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pml_28 2018-3-30

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Hi Abraham Boayue,

Thank you for your help! I'll check your code! On those days, I thought of this solution, I do not know if it's correct, I still have to check ... but look!

function dxdt = rlcf(t,x)
global R1 R2 R3 R4 C1 C2 V;
      I4 = ((x(5) - R1 * x(1))) / R4;
      I3 = ((x(5) - R1 * x(1) - R2 * x(3))) / R3;
      I5 = x(1) - x(3) - I4;
      I6 = x(2) - I3;
  dxdt (1,1) = x(1);
      dxdt (2,1) = (x(5) - (I5/C1)) / R1;
            dxdt (3,1) = x(3);
            dxdt (4,1) = ((I5/C1) - (I6/C2))/R2;
            dxdt (5,1) = x(5);
            dxdt (6,1) = R1*x(1) + (I5/C1);

dxdt (1,1) is I1
dxdt (2,1) is dI1/dt
dxdt (3,1) is I2
dxdt (4,1) is dI2/dt
dxdt (5,1) is V
dxdt (6,1) is dV/dt

I don't know this way is correct! What do you think? I do this, after you say for me, to separate V..

Abraham Boayue 2018-3-30

编辑：Abraham Boayue 2018-3-30

You are welcome, you have two systems of ODE with three unknown quantities (I1, I2 and v ). It is not possible to solve for three variables given two equations. I made up the third equation to be able to get a solution. Your new function above is invalid because you haven't got that many ode in your problem. You actually have two 1st order equations which can not be further reduced. Check and see if you can obtain a third equaton involving dv/dt from the circuit diagram that you are working with. My solution is based on an assumption that dv/dt is as defined in the paper attached and may not be correct with respect to your problem. See this link on a similar problem : https://www.mathworks.com/matlabcentral/answers/391390-how-to-solve-nonlinear-coupled-dgl-second-order

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Answer 2

Abraham Boayue 2018-3-28

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https://ww2.mathworks.cn/matlabcentral/answers/391270-how-to-solve-and-write-system-of-differential-equations#answer_312444

编辑：Abraham Boayue 2018-3-28

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ÌCheck your function dxdt, it has two inputs but uses othe variables that aren't defined. Some of these are V, R1, R2. t is an input but never used. Your use of I1 to I6 is quite good. Here is my recommendation

function [dx1 dx2] = rlcf(x1,x2, R1, R2, R3, R4, V)

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pml_28 2018-3-28

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Hi Abraham Boayue,

firstly thanks for the help!

the code above, is only my function. I am trying this:

global R1 R2 R3 R4 C1 C2 V;
R1 = 0.0001; R2 = 0.0001; R3 = 0.0001; R4 = 200; C1 = 0.0001;
C2 = 0.0001; V = 180;
x0=[0; 0];
tf=20;
deltat=1;
[tt,xt]=ode45('rlcf',[0:deltat:tf],x0);