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

% 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]);

Answer 1

[Torsten]

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.

[FAIZ UL HASSAN]

All are scalar, have single constant value which is defined earlier in the code.

[Torsten]

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.

Answer 2

[Bjorn Gustavsson]

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

[FAIZ UL HASSAN]

D and u have same size and others are single value constant parameters.

Answer 3

[Sam Chak]

Hi @FAIZ UL HASSAN

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')

[FAIZ UL HASSAN]

D and u have equations of equal size, others are single value constant.

[Sam Chak]

Can you show the math of your D and u?

I have edited the code. Does it look something like that?

[Sam Chak]

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]

Thanks @Sam Chak will try this way.