# Error in using ode45 for solution of nonlinear system of three equations which are interlinked to each other

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FAIZ UL HASSAN am 12 Apr. 2023
Kommentiert: FAIZ UL HASSAN am 12 Apr. 2023
% Define the ODE system
f = @(t,x) [-(p1 + x(2)) * x(1) + p1 * Gb + D; -p2 * x(2) + p3 .* x(3) + p3.* Ib; -n * (x(3) - Ib) + u];
% Solve the ODE system
[t,x] = ode45(f, tspan, [x1; x2; x3]);
Error using vertcat
Dimensions of arrays being concatenated are not consistent.
Error in UpdatedTrialsmc>@(t,x)[-(p1+x(2))*x(1)+p1*Gb+D;-p2*x(2)+p3.*x(3)+p3.*Ib;-n*(x(3)-Ib)+u] (line 51)
f = @(t,x) [-(p1 + x(2)) * x(1) + p1 * Gb + D; -p2 * x(2) + p3 .* x(3) + p3.* Ib; -n * (x(3) - Ib) + u];
Error in UpdatedTrialsmc (line 54)
[t,x] = ode45(f, tspan, [x1; x2; x3]);
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### Antworten (3)

Torsten am 12 Apr. 2023
Verschoben: Torsten am 12 Apr. 2023
Check
size(p1)
size(Gb)
size(D)
size(p2)
size(p3)
size(Ib)
size(n)
size(u)
If one of the sizes is not 1x1 (a scalar), your code won't work.
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FAIZ UL HASSAN am 12 Apr. 2023
All are scalar, have single constant value which is defined earlier in the code.
Torsten am 12 Apr. 2023
All are scalar, have single constant value which is defined earlier in the code.
If you get the error message as stated, this can't be true.

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Bjorn Gustavsson am 12 Apr. 2023
Perhaps you need to check the size of each component in your ode-function:
f = @(t,x) [-(p1 + x(2)) * x(1) + p1 * Gb + D; -p2 * x(2) + p3 .* x(3) + p3.* Ib; -n * (x(3) - Ib) + u];
What are the sizes of p1, Gb, D, p2, p3, Ib, n, Ib and u? The error-message you get is what I typically get when I try to concatenate arrays of incompatible sizes.
HTH
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FAIZ UL HASSAN am 12 Apr. 2023
D and u have same size and others are single value constant parameters.

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Sam Chak am 12 Apr. 2023
Bearbeitet: Sam Chak am 12 Apr. 2023
Try this:
% Define the time-varying Disturbance
D = @(t) sin(pi/10*t);
% Define the scalar parameters
Gb = 1;
n = 1;
p1 = 1;
p2 = 1;
p3 = 1;
Ib = 1;
% Define the feedback input u
u = @(x) - x(1) - 2*x(2);
% Define the system dynamics
f = @(t, x) [-(p1 + x(2))*x(1) + p1*Gb + D(t);
- p2*x(2) + p3*x(3) + p3*Ib;
- n*(x(3) - Ib) + u(x)];
% Define the initial conditions
x0 = [1; 0; 0];
% Define the time interval
tspan = [0 20];
% Solve the system using the ode45 solver
[t, x] = ode45(f, tspan, x0);
% Plot the result
plot(t, x); grid on
xlabel('t')
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Sam Chak am 12 Apr. 2023
Bearbeitet: Sam Chak am 12 Apr. 2023
Thanks @FAIZ UL HASSAN. It looks a little complicated to read the equation this way without breaking up the terms. But some parameters are unavailable. Try simplifying u by making up u1, u2, u3, ... This helps troubleshooting later. I guess that the error "Dimensions of arrays being concatenated are not consistent" is caused by u.
Edit: On a second look, I'm just guessing...💡 that u is some kind of a sliding mode forcing input structure and e, ed, edd refers to , respectively. S must be the sliding surface then.
Besides, check if sign(S) is a discontinuous function or just a scalar like this
sign(3.14159)
ans = 1
The ode45() solver does not work well with discontinuous function when .
FAIZ UL HASSAN am 12 Apr. 2023
Thanks @Sam Chak will try this way.

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