help wtih plotting ode function

something is wrong, it plots empty result

all_units = 'all_units.xlsx';

maks = xlsread(all_units);

% Vehicle parameters

a = 1.024;

b = 1.602;

m = 1574.02;

cr = -25488;

cf = -184780;

I = 1790;

% Extract relevant columns from the data

v = maks(:, 24);

r = maks(:, 20);

u = maks(:,23);

t1 = maks(:, 25);

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

% Time span for the simulation

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

% Initial condition

x0 = [0; 0]; % Initial values for v and r

% Solve the differential equation using ode45

[t, x] = ode45(@(t, x) myVehicleODE(t, x, t1, del), tspan, x0);

% Plot the results

figure;

subplot(2, 1, 1);

plot(t, x(:, 1), 'b', 'LineWidth', 2);

title('Longitudinal Velocity (v)');

xlabel('Time');

ylabel('Velocity');

subplot(2, 1, 2);

plot(t, x(:, 2), 'r', 'LineWidth', 2);

title('Yaw Rate (r)');

xlabel('Time');

ylabel('Yaw Rate');

% Define the function myVehicleODE at the end of the script

function dxdt = myVehicleODE(t, x, t1, del)

% Parameters

a = 1.024;

b = 1.602;

m = 1574.02;

cr = -25488;

cf = -184780;

I = 1790;

% Interpolate the input function 'del' with respect to time 't'

del_interpolated = interp1(t1, del, t, 'linear', 'extrap');

% System matrices

a11 = (-cf - cr) / (m * x(1));

a12 = (((-cf * a) + (cr * b)) / (m * x(1))) - x(1);

a21 = ((-cf * a) + (cr * b)) / (I * x(1));

a22 = ((-cf * a^2) - (cr * b^2)) / (I * x(1));

b1 = cf / m;

b2 = (cf * a) / I;

% State-space matrices A and B

A = [a11, a12;

a21, a22];

B = [b1;

b2];

% System of differential equations

dxdt = A * x + B * del_interpolated;

end

Answer 1

[Star Strider]

There are two problems:

First, ‘x0’ is initially identically zero, and that creates an Inf result for the first value of ‘A’ and NaN for the rest, none of which will be plotted, so I added eps to ‘x0’.

Second, the system is ‘stiff’ so you need a ‘stiff’ solver, such as ode15s or ode23s (that I chose here, for no particular reason other than it being a stiff solver, either one would work here).

Then using both of those changes, it works —

all_units = 'all_units.xlsx';
maks = xlsread(all_units);
% Vehicle parameters
a = 1.024;
b = 1.602;
m = 1574.02;
cr = -25488;
cf = -184780;
I = 1790;
% Extract relevant columns from the data
v = maks(:, 24);
r = maks(:, 20);
u = maks(:,23);
t1 = maks(:, 25);
del = (maks(:, 18) + maks(:, 19)) / 2;
% Time span for the simulation
tspan = [min(t1), max(t1)];
% Initial condition
x0 = [0; 0]; % Initial values for v and r
x0 = x0 + eps;
% Solve the differential equation using ode45
[t, x] = ode23s(@(t, x) myVehicleODE(t, x, t1, del), tspan, x0);
% Plot the results
figure;
subplot(2, 1, 1);
plot(t, x(:, 1), 'b', 'LineWidth', 2);
title('Longitudinal Velocity (v)');
xlabel('Time');
ylabel('Velocity');
subplot(2, 1, 2);
plot(t, x(:, 2), 'r', 'LineWidth', 2);
title('Yaw Rate (r)');
xlabel('Time');
ylabel('Yaw Rate');

% Define the function myVehicleODE at the end of the script
function dxdt = myVehicleODE(t, x, t1, del)
    % Parameters
    a = 1.024;
    b = 1.602;
    m = 1574.02;
    cr = -25488;
    cf = -184780;
    I = 1790;
    % Interpolate the input function 'del' with respect to time 't'
    del_interpolated = interp1(t1, del, t, 'linear', 'extrap');
    % System matrices
    a11 = (-cf - cr) / (m * x(1));
    a12 = (((-cf * a) + (cr * b)) / (m * x(1))) - x(1);
    a21 = ((-cf * a) + (cr * b)) / (I * x(1));
    a22 = ((-cf * a^2) - (cr * b^2)) / (I * x(1));
    b1 = cf / m;
    b2 = (cf * a) / I;
    % State-space matrices A and B
    A = [a11, a12;
         a21, a22];
    B = [b1;
         b2];
    % System of differential equations
    dxdt = A * x + B * del_interpolated;
end

.

[Sam Chak]

Hi @Zlatan,

Based on your previous 'unresolved' question, it appears that your vehicle is a linear system. However, unless I misunderstood, the symbol u is assumed to be constant. I noticed that you assigned , but at the same time, is also represented by v in the state vector. It would be helpful if you could clarify this inconsistency.

Note that if and the vehicle comes to a halt (), the system will become singular due to division by zero.

a11 = (-cf - cr) / (m * x(1));
a12 = (((-cf * a) + (cr * b)) / (m * x(1))) - x(1);
a21 = ((-cf * a) + (cr * b)) / (I * x(1));
a22 = ((-cf * a^2) - (cr * b^2)) / (I * x(1));
...
% State-space matrices A and B
A   = [a11, a12;
       a21, a22];
dxdt = A * x ...