Variables are constant through the integration

Hi, I've got the problem that in the following code, all variable parameters from rv to Fwy are calculated with the initial values of the initial vector x and then set as constant over the integration. However, they should be calculatet with with the new state values of x in each integration step.

The code represents a vehicle dynamics model.

It would be great if somebody could help me with this. Thanks in advance!

clear all

%constant parameters:

m = 1700; % Fahrzeugmasse [kg]

lv = 1.2; % Abstand des Fahrzeugschwerpunkts zum Vorderachsmittelpunkt [m]

lh = 1.8; % Abstand des Fahrzeugschwerpunkts zum Hinterachsmittelpunkt [m]

iz = 500; % Trägheitsmoment um die Hochachse [kg*m^2]

cs = 10000; %Umfangssteifigkeit[N/°]

ca = 50000; %Schräglaufsteifigkeit[N/rad]

cx = 10000; %Reifenlängssteifigkeit

cy = 50000; %Seitetsteifigkeit

cw = 0.23; % CW Wert

pL = 1.2041; % Luftdichte [kg^m3]

A = 0.3; %[Windanströmfläche]

Jv = 1.245; %[kgm^2]

Jh = 1.245; %[kgm^2]

r = 0.49;

%Eingangsgrößen

delta = deg2rad(0); %[Lenkwinkel°]

Mav = 25.444132; %25.444132; %Antriebsmoment [Nm]

Mah = 25.444132;

Mbv = 0; %Bremsmoment [Nm]

Mbh = 0;

%Zeitbereich

tspan = [0 0.1 100];

% Initial Vector

x =[0; % x(1): XV - KS X Richtung

0; % x(2): YV - KS Y Richtung

0; % x(3): PSI - Gierwinkel

0; % x(4): XV' - Geschwindigkeit in X Richtung [m/s]

0; % x(5): YV' - Geschwindigkeit in Y Richtung [m/s]

0; % x(6): PSI' - Giergeschwindigkeit

102.573; % x(7): pv' Winkelgeschwindigkeit Vorderes Rad

102.573; % x(8): ph' Winkelgeschwindigkeit hinteres Rad

51.9268; % x(9): vFv,x Kraft Vorderreifen x-Richtung

0; % x(10): vFv,y Kraft Vorderreifen y-Richtung

51.9268; % x(11): hFh,x Kraft Hinterreifen x-Richtung

0]; % x(12): hFh,y Kraft Hinterreifen y-Richtung

%Variable parameters:

% Vektorkombination

rv = [x(4)-lv*x(6)+sin(x(3));

x(5)+lv*x(6)*cos(x(3));

0];

vrv = [cos(x(3)+delta) sin(x(3)+delta) 0;

-sin(x(3)+delta) cos(x(3)+delta) 0;

0 0 1]*rv;

rh = [x(4)-lh*x(6)+sin(x(3));

x(5)+lh*x(6)*cos(x(3));

0];

hrh = [cos(x(3)) sin(x(3)) 0;

-sin(x(3)) cos(x(3)) 0;

0 0 1]*rh;

% Schlupfwerte

% Längsschlupf

sv = (r* x(7)-rv(1))/(max(abs(r*x(7)),abs(vrv(1))));

sh = (r* x(8)-rh(1))/(max(abs(r*x(8)),abs(hrh(1))));

% Schräglaufschlupf

av = -(vrv(2)/abs(x(7)));

ah = -(hrh(2)/abs(x(8)));

% Reifenkräfte

vFvxstat = cs*sv;

vFvystat = ca*av;

hFhxstat = cs*sh;

hFhystat = ca*ah;

% Radkraft Hinterachse

Fhx = cos(x(3))*x(11)-sin(x(3))*x(12);

Fhy = sin(x(3))*x(11)+cos(x(3))*x(12);

% Radkraft Vorderachse

Fvx = cos(x(3) + delta)*x(9)-sin(x(3) + delta)*x(10);

Fvy = sin(x(3) + delta)*x(9)+cos(x(3) + delta)*x(10);

% Luftwiderstand

Fwx = 0.5*cw*pL*A*x(4)*((x(4))^2+(x(5))^2)^0.5;

Fwy = 0.5*cw*pL*A*x(5)*(x(4)^2+(x(5))^2)^0.5;

[t,x] = ode45(@(t,x) odefcn(x, m, Fvy, Fhy, Fvx, Fhx, Fwx,Fwy, Mav, Mah, Mbv, Mbh, r,iz,delta,lv,lh,Jv,Jh,cs,ca,cy,cx,vFvxstat,vFvystat,t,hFhxstat,hFhystat),tspan,x);

--subplots (..)--

function dxdt = odefcn(x, m, Fvy, Fhy, Fvx, Fhx, Fwx,Fwy, Mav, Mah, Mbv, Mbh, r,iz,delta,lv,lh,Jv,Jh,cs,ca,cy,cx,vFvxstat,vFvystat,t,hFhxstat,hFhystat)

dxdt = zeros(12,1);

dxdt(1) = x(4); %Geschwindigkeit x-Richtung

dxdt(2) = x(5); %Geschwindigkeit y-Richtung

dxdt(3) = x(6); %Gierbeschleunigung

dxdt(4) = (m^-1)*(Fvx+Fhx-Fwx); %Beschleunigung x-Richtung

dxdt(5) = (m^-1)*(Fvy+Fhy-Fwy); %Beschleunigung y-Richtung

dxdt(6) = ((iz^-1)*lv*sin(delta)*x(9)+cos(delta)*x(10)-lh*x(12)); %Gierbeschleunigung

dxdt(7) = (1/Jv)*(Mav-Mbv*sign(x(7))-r*x(9)); %Radwinkelgeschwindigkeit VA

dxdt(8) = (1/Jh)*(Mah-Mbh*sign(x(8))-r*x(11));%Radwinkelgeschwindigkeit HA

dxdt(9) = (cx*(r*x(7))/cs)*(vFvxstat-x(9)); %Radkraft VA X-Richtung

dxdt(10)= (cy*(r*x(7))/ca)*(vFvystat-x(10)); %Radkraft VA Y-Richtung

dxdt(11)= (cx*(r*x(8))/cs)*(hFhxstat-x(11)); %Radkraft VA X-Richtung

dxdt(12)= (cy*(r*x(8))/ca)*(hFhystat-x(12)); %Radkraft VA Y-Richtung

end

Answer 1

[Torsten]

You have to pass only constants to "odefcn", but computations with the unknowns x have to be done within the function. Thus copy the complete computational part after the lines

%Variable parameters:
% Vektorkombination

into your function "odefcn".

[Marlon]

Thanks mate, it worked :)