I need help with ode45 function, how to write the code?

I need to write a code to solve the differential equatian but I don't even know how to start, I need to use the ode solver to find the solution

This is the hint they gave to me:

And this is the problem:

I already have all the values on the right side in the form of a vector nx1, only scalar numbers are Cf,Cr,m,la,I and lb.

[Dyuman Joshi]

Please show what you have tried yet.

Also, take a look at the documentation of ode45 for resources, examples and other references. This will help you formulate the equation in terms of the expected input to the ode solver.

[Zlatan]

the problem is I can't even start properly or get something, I always get an error, but I will try again

[Sam Chak]

@Zlatan, Follow the example in the documentation, post your code and error message here. We will assess what went wrong.

Update: I understand now. Your problem is described in state-space form, which involves matrix differential equations. Unfortunately, the ode45 documentation does not provide a specific example using state-space representation. As a result, learning solely from examples may not be possible.

However, if you apply critical thinking skills or seek assistance from your course mates, you can work on resolving the matrix differential equation into individual ordinary differential equations. This process can be challenging, but with the right approach, you can overcome the frustration and find a solution.

Update 2: Moreover, the hint provided may be more confusing than helpful in guiding you. The ordinary differential equation (ODE) is defined as a dxdt vector, but the input arguments mentioned are t and y. Additionally, the usage of '...' is unclear, and it is uncertain what additional parameters should be passed to the function.

function dxdt = yourfunction(t, y, ...)
    dxdt = A*y + B*d;
end

[Zlatan]

Ok I found the better equations to solve, and now I have two of them, but I still think this is wrong. Any idea how to improve the code so it works?

[Torsten]

Please include code as plain ascii text, not as graphics, so that we are able to execute it.

[Zlatan]

clc

maks = xlsread("all_units.xlsx");

a=1.024;

b=1.602;

m=1574.02;

v=maks(:,24);

r=maks(:,20);

u=maks(:,23);

t1=maks(:,25);

cr=-25488;

cf=-184780;

I=1790;

del=(maks(:,18)+maks(:,19))/2;

alfaf= atan((v+r.*a)./u)-del;

alfar= atan((v-r.*b)./u);

Fyf=alfaf*cf;

Fyr=alfar*cr;

% Time span for the simulation

tspan = [min(t1),max(t1)];

% Initial condition

v0 = 0; % replace n with the appropriate size

% Solve the differential equation using ode45

[t,v,r] = ode45(@(t, v,r) myODE(t, v, Fyf,Fyr,m,r,u,tspan, v0);

% Plot the results

figure;

subplot(2, 1, 1);

plot(t, v);

xlabel('Time');

ylabel('v');

title('Solution of dv/dt = (Fyf + Fyr - u*r)/m');

subplot(2, 1, 2);

plot(t, r);

xlabel('Time');

ylabel('r');

title('Solution of dr/dt = (a*Fyf + b*Fyr)/I');

% Define the differential equation function

function dvdt = myODE(t, v, Fyf,Fyr,m,r,u)

% Define the differential equation

dvdt = (Fyf + Fyr - u*r)/m;

drdt = (a*Fyf + b*Fyr)/I;

end

this is the whole code

Answer 1

[Sam Chak]

Hi @Zlatan

It's great that you figured it out. Anyway, here is the code snippet for the state-space version. I would suggest placing certain parameters inside the vehicle ODE function as constants since they remain unchanged for the vehicle. If you need to run the simulation multiple times to analyze the vehicle's responses to the steering angle δ, you will need to pass this parameter (delta) in the vehicle ODE function as shown below:

%% State-space model of your Vehicle
function dxdt = myVehicleODE(t, x, delta)
    % parameters (properties that do not change in the vehicle)
    Cf   = 1;
    Cr   = 1;
    la   = 1;
    lb   = 1;
    m    = 1;
    I    = 1;
    u    = 1;

    % Elements in matrices (that depend on the parameters)
    a11  = 1;
    a12  = 1;
    a21  = 1;
    a22  = 1;
    b1   = 1;
    b2   = 1;
    
    % matrices
    A    = [a11, a12;   % state matrix
            a21, a22];
    B    = [b1;         % input matrix
            b2];
    
    % matrix differential equation (x is the state vector for [v; r])
    dxdt = A*x + B*delta;
end