How do i add a changing input over a interval using ODE45?

I'm trying to intergrate form time 0 to 5000 and at t=1000 i want my y input to rise, modeling a car going up a speed bump. I know when the car is over the speed bump (assuming v is consant in the x direction). I tried to make a liniear line of which represents the speed bump. But it doesnt work.

v = 25/3.6;                 % Speed of the car
Lslope = (0.5/v)*1000;             % Length of the slope in time (assuming v is constant)
Tend = 5000;                % The end
y0 = 0;

global Tslope
Tslope = 999;              % Start time of the slope
global Tlin
Tlin = Tslope + Lslope;     % The end time of the slope (assuming v is constant)

[t, y]= ode45('yslope',[0 Tend],[0, 0, 0, 0]);

figure 
plot(t, y)

My function is:

function dy = yslope(t,y)

% Constants
mb = 36;
mv = 500;
kb = 100000;
kv = 3000;
b = 5000;
a = 0.6;
x0 = 0;

% Aanroepen 
global Tslope
global Tlin

% y input
y_before = 0;
y_slope = linspace(0,0.3,Tlin-Tslope);
y_after = 0.3;

% Checken whick state 

if t <= Tslope                      % Before the slope

    y_in = y_before;

elseif t > Tslope && t <= Tlin      % At slope

   y_in = yslope(t-Tslope);   % t is already at 1001 so minus Tslope to get 1 

elseif t > Tlin                     % After slope

    y_in = y_after;

end

dy1 = y(2);
dy2 = -(kv+kb)/mb *y(1)-b/mb *y(2)+kv/mb *y(3)+b/mb *y(4) +kb/mb *y_in;
dy3 = y(4);
dy4 = kv/mv *y(1) + b/mv *y(2) - kv/mv *y(3) -b/mv*y(4);

dy= [dy1 ; dy2 ; dy3 ;dy4];

end

This is the error i'm getting:

Not enough input arguments.

Error in yslope (line 37)
dy1 = y(2);

Error in yslope (line 29)
   y_in = yslope(t-Tslope);   % t is already at 1001 so minus Tslope to get 1

Error in ode45 (line 308)
        f6 = ode(t6, y6);

Error in Main (line 15)
[t, y]= ode45('yslope',[0 Tend],[0, 0, 0, 0]);

Answer 1

[Torsten]

v = 25/3.6;                 % Speed of the car
Lslope = (0.5/v)*1000;             % Length of the slope in time (assuming v is constant)
Tend = 5000;                % The end
y0 = 0;

global Tslope
Tslope = 999;              % Start time of the slope
global Tlin
Tlin = Tslope + Lslope;     % The end time of the slope (assuming v is constant)

%[t, y]= ode45('yslope',[0 Tend],[0, 0, 0, 0]);
[t, y]= ode45(@yslope,[0 Tend],[0, 0, 0, 0]);

figure 
plot(t, y)

function dy = yslope(t,y)

% Constants
mb = 36;
mv = 500;
kb = 100000;
kv = 3000;
b = 5000;
a = 0.6;
x0 = 0;

% Aanroepen 
global Tslope
global Tlin

% y input
y_before = 0;
%y_slope = linspace(0,0.3,Tlin-Tslope);
y_after = 0.3;

% Checken whick state 

%if t <= Tslope                      % Before the slope

%    y_in = y_before;

%elseif t > Tslope && t <= Tlin      % At slope

%   y_in = yslope(t-Tslope);   % t is already at 1001 so minus Tslope to get 1 

%elseif t > Tlin                     % After slope

%    y_in = y_after;

%end
y_in = y_before*(t<=Tslope) + (y_before*(t-Tlin)/(Tslope-Tlin) + y_after*(t-Tslope)/(Tlin-Tslope))*(t>Tslope)*(t<=Tlin)+y_after*(t>Tlin);

dy1 = y(2);
dy2 = -(kv+kb)/mb *y(1)-b/mb *y(2)+kv/mb *y(3)+b/mb *y(4) +kb/mb *y_in;
dy3 = y(4);
dy4 = kv/mv *y(1) + b/mv *y(2) - kv/mv *y(3) -b/mv*y(4);

dy= [dy1 ; dy2 ; dy3 ;dy4];

end

Answer 2

[Sam Chak]

Hi @Dirk te Brake

I am unsure if I understand your 4-state differential equations. However, a speed bump can be mathematically modeled as a physical disturbance to the car.

For example, the cross-section of a one-part speed bump can be plotted as follows:

https://www.sinoconcept.co.uk/car-park-safety-management/speed-bumps-and-speed-humps/one-part-speed-bump/

Try modifying the state equations to insert the speed bump function.

hw = 150;                               % half-width of the bump (mm)
x  = linspace(-2*hw, 2*hw, 60001);
y1 = exp(-1./(1 - (x/hw).^2));          % component 1
y2 = (sign(x + hw) - sign(x - hw))/2;   % component 2
H  = 50;                                % max height of the bump (mm)
A  = H/0.367879441171442;
y  = A*y1.*y2;                          % Speed Bump function 
plot(x, y, 'linewidth', 1.5), grid on, ylim([0 600])
title('Speed Bump')
xlabel({'$x$/mm'}, 'interpreter', 'latex')
ylabel({'$y$/mm'}, 'interpreter', 'latex')

[Dirk te Brake]

Well my problem isn't really a speed bump. After the car goes up the slope it doesn't come down again. But i do like the function and will give it a try.