plotting variables within function

Hi, so I'm trying to plot certain variables in my code, that are calculated in the function with state variables.

Plotting the state variables is working well but when I try to plot other Variables like Fwx over time I get an error saying

Unrecognized function or variable 'Fwx'.

Error in ZUSTANDSRAUM (line 63)

plot(t, Fwx); xlabel('t'); ylabel('Fwx'); % Plot von Fwx gegen t

Here's the code:

clear
close all;
clc;
%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]
Af = 0.3; %[Windanströmfläche]
Jv = 1.245; %[kgm^2]
Jh = 1.245; %[kgm^2]
r = 0.49; %m
%Eingangsgrößen
delta = deg2rad(0);   %[Lenkwinkel°]
%Mav = 100;   %Antriebsmoment [Nm]
Mah = 0;
Mbv = 0;     %Bremsmoment [Nm]
Mbh = 0;
%Zeitbereich
tspan = [0 10];
%Anfangsbedingungen - Zustandsvektor
x =[0;     % x(1): XV - KS X Richtung
    0;     % x(2): YV - KS Y Richtung
    0;     % x(3): PSI - Gierwinkel
    70;    % x(4): XV' - Geschwindigkeit in X Richtung [m/s]
    0;     % x(5): YV' - Geschwindigkeit in Y Richtung [m/s]
    0;     % x(6): PSI' - Giergeschwindigkeit
    145.14;    % x(7): pv' Winkelgeschwindigkeit Vorderes Rad
    0;     % x(8): ph' Winkelgeschwindigkeit hinteres Rad
    204; % x(9): vFv,x Kraft Vorderreifen x-Richtung
    0;     % x(10): vFv,y Kraft Vorderreifen y-Richtung
    0;     % x(11): hFh,x Kraft Hinterreifen x-Richtung
    0];     % x(12): hFh,y Kraft Hinterreifen y-Richtung   

[t,x] = ode45(@(t,x) odefcn(m, lv, lh, iz, cs, ca, cx, cy, cw, pL, Af, Jv, Jh, r, delta,  Mah, Mbv, Mbh,x,t),tspan,x);
subplot(4, 3, 1); plot(t, x(:,1)); xlabel('t'); ylabel('x(1): XV');
subplot(4, 3, 2); plot(t, x(:,2)); xlabel('t'); ylabel('x(2): YV');
subplot(4, 3, 3); plot(t, x(:,3)); xlabel('t'); ylabel('x(3): PSI');
subplot(4, 3, 4); plot(t, x(:,4)); xlabel('t'); ylabel('x(4): XV'' [m/s]');
subplot(4, 3, 5); plot(t, x(:,5)); xlabel('t'); ylabel('x(5): YV''  [m/s]');
subplot(4, 3, 6); plot(t, x(:,6)); xlabel('t'); ylabel('x(6): PSI'' - ');
subplot(4, 3, 7); plot(t, x(:,7)); xlabel('t'); ylabel('x(7): pv''');
subplot(4, 3, 8); plot(t, x(:,8)); xlabel('t'); ylabel('x(8): ph''');
subplot(4, 3, 9); plot(t, x(:,9)); xlabel('t'); ylabel('x(9): vFv,x');
subplot(4, 3, 10); plot(t, x(:,10)); xlabel('t'); ylabel('x(10): vFv,y');
subplot(4, 3, 11); plot(t, x(:,11)); xlabel('t'); ylabel('x(11): hFh,x');
subplot(4, 3, 12); plot(t, x(:,12)); xlabel('t'); ylabel('x(11): hFh,y');
Fwx =0.5*cw*pL*Af*x(:,4).*((x(:,4)).^2+(x(:,5)).^2).^0.5;
plot(t, Fwx); xlabel('t'); ylabel('Fwx'); % Plot von Fwx gegen t

function dxdt = odefcn(m, lv, lh, iz, cs, ca, cx, cy, cw, pL, Af, Jv, Jh, r, delta, Mah, Mbv, Mbh,x,t) 
% Vektorkombination
Mav=15*t;
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))) + 1e-10);
sh = (r * x(8) - rh(1)) / (max(abs(r * x(8)), abs(hrh(1))) + 1e-10);
% Schräglaufschlupf 
av = -(vrv(2) / (abs(x(7)) + 1e-10));
ah = -(hrh(2) / (abs(x(8)) + 1e-10));
% Reifenkräfte
A=1.12;
C=0.625;
D=1;
n=0.6;
K=46;
d=5;
B = (K/d)^(1/n);
%vFvxstat = cs*sv;
%vFvystat = ca*av;
%hFhxstat = cs*sh;
%hFhystat = ca*ah;
vFvxstat =(m/4)*sign(sv).*(A.*(1-exp(-B*abs(sv)))+C*sv.^2-D*abs(sv));
vFvystat = (m/4)*sign(av).*(A.*(1-exp(-B*abs(av)))+C*av.^2-D*abs(av));
hFhxstat = (m/4)*sign(sh).*(A.*(1-exp(-B*abs(sh)))+C*sh.^2-D*abs(sh));
hFhystat = (m/4)*sign(ah).*(A.*(1-exp(-B*abs(ah)))+C*ah.^2-D*abs(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*Af*x(4)*((x(4))^2+(x(5))^2)^0.5;
Fwy =0.5*cw*pL*Af*x(5)*(x(4)^2+(x(5))^2)^0.5;
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]

Recalculate Fwx from the solution (see above).

[Image Analyst]

Looks like he tried that since his code is:

Fwx =0.5*cw*pL*Af*x(:,4).*((x(:,4)).^2+(x(:,5)).^2).^0.5;
plot(t, Fwx); xlabel('t'); ylabel('Fwx'); % Plot von Fwx gegen t

[Marlon]

Okay so now it worked thanks!

[Marlon]

Is there a way to pass variables outside the Function, that I don't have every calculation of the Variables I want to plot two times in the code?

[Walter Roberson]

@Marlon

Yes, there are ways. However, in the context of ode functions, it is almost always the wrong thing to do.