How to plot multiple lines (with a varying slope coefficient) in the same graph?

Hi.

I devised a script that runs a rudimentary dynamical simulation of a cornering (hybrid) vehicle, calculating lateral velocity and total time required to perform a full rotation around a circle(hypothesizing that the engine will be producing the exact amount to offset all the longitudinal forces), setting a specific radius of the turn and the steering angle of the front wheel. (I had to initialize lift and drag forces as 1 to make the code run the first iteration of the while circle. I know it gives a wrong result on the first millisecond but i haven't found a solution to that either, for now, help with that would also be appreciated!)

It runs smoothly when i give it a specific value on the steering angle, for example:

delta = deg2rad(5)

My code produces this graph:

However, i want to plot on the same graph multiple curves of space/time that are produced with different values of the steering angle.

I know that i'd be expecting something like this: (Forgive my terrible microsoft paint skills)

Here is the part of the code that works.

clear;

close all;

clc;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% PARAMETERS

rho = 1.225; % Air density standard conditions: kg/m^3

g = 9.81; % Acceleration of gravity: m/s^2

la = 0.85; % Distance center of gravity - front axis: m

lb = 0.7; % Distance center of gravity - rear axis: m

wb = la + lb; % Wheel base: m

h = 0.25; % Height center of gravity: m

laero = 1; % Distance aerodynamic center - front axis: m

haero = 0.35; % Height aerodynamic center: m

SLift = 1.54; % Lift surface: m^2

SDrag = 0.55; % Drag surface: m^2

cL_close= 2.4; % Lift coefficient, DRS closed: /

cD_close= 1.65; % Drag coefficient, DRS closed: /

W_ICE = 60000; % Internal combustion engine power: W

W_EL = 20000; % Electric motor power: W

f = 1.2; % Friction coefficeint: /

m = 290; % Total vehicle mass: kg

dt = 0.001; % Discretization time: s

radius = 8.375; % Curvature Radius: m

kLc = 0.5*cL_close*rho*SLift; % Lift constant DRS closed: kg/m

kDc = 0.5*cD_close*rho*SDrag; % Drag constant DRS closed: kg/m

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% INITIALIZATION

t_3(1) = 0; % Time: s

x_3(1) = 0; % Space: m

front_acc_3(1) = 0; % Frontal Acceleration: m/(s^2)

Nr_3(1) = m*g*la/wb; % Vertical reaction rear axis: N

LD_3(1) = la/wb; % Load distribution wrt rear axis: /

delta = deg2rad(5); % Steering Angle: radians

Lift_3(1) = 1; % -Lift force: N

Drag_3(1)= 1; % Drag force: N

i = 1; % Generic index

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

while x_3 <= 2 * pi * radius

Torque(i) = (2 * sin(delta)) * f * (1-LD_3(i))*(m * g + Lift_3(i))+ Drag_3(i) ;

Front_force(i) = (Torque(i) - Drag_3(i)) / sin(delta) ;

Rear_force(i) = (Front_force(i) * cos(delta))/lb;

vel_3(i) = sqrt((radius*(Rear_force(i) + cos(delta) * Front_force(i)))/m);

Lift_3(i+1) = kLc * vel_3(i)^2;

Drag_3(i+1) = kDc * vel_3(i)^2;

lat_acc_3(i+1) = vel_3(i)^2 / radius;

Nr_3(i) = (m * g * la + haero * Drag_3(i) + laero * Lift_3(i)) / wb;

LD_3(i+1) = Nr_3(i) / (m*g + Lift_3(i));

x_3(i+1) = x_3(i) + vel_3(i)*dt;

t_3(i+1) = t_3(i) + dt;

i = i + 1;

end

plot(t_3,x_3);

legend("Location","eastoutside")

ylim([0,55]);

yline(2 * pi * radius)

grid on

xlabel("Time")

ylabel("Distance")

title("Distance over Time")

I thought of using:

delta = deg2rad(5:1:20)

Which would give me a vector of the range of angles i was planning to study in the Script.

I then planned to replace delta in the code with delta(index).

How can i make it so the code runs with delta(1), produces a graph, holds on the result, then graphs delta(2), and so on until delta(15), all in the same graph?

Thanks in advance.

Answer 1

[ANKUR KUMAR]

You code is producing the same results for all iteration.

You can simply use a for loop, and use hold on to plot multiple plots in a plot.

clear;
close all;
clc;

delta_raw = deg2rad(5:1:20)

delta_raw = 1×16

0.0873 0.1047 0.1222 0.1396 0.1571 0.1745 0.1920 0.2094 0.2269 0.2443 0.2618 0.2793 0.2967 0.3142 0.3316 0.3491

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% PARAMETERS
rho = 1.225;            % Air density standard conditions: kg/m^3
g = 9.81;               % Acceleration of gravity: m/s^2
la = 0.85;              % Distance center of gravity - front axis: m
lb = 0.7;               % Distance center of gravity - rear axis: m
wb = la + lb;           % Wheel base: m
h = 0.25;               % Height center of gravity: m
laero = 1;              % Distance aerodynamic center - front axis: m
haero = 0.35;           % Height aerodynamic center: m
SLift = 1.54;           % Lift surface: m^2
SDrag = 0.55;           % Drag surface: m^2
cL_close= 2.4;          % Lift coefficient, DRS closed: /
cD_close= 1.65;         % Drag coefficient, DRS closed: /
W_ICE = 60000;          % Internal combustion engine power: W
W_EL = 20000;           % Electric motor power: W
f = 1.2;                % Friction coefficeint: /
m = 290;                % Total vehicle mass: kg
dt = 0.001;             % Discretization time: s
radius = 8.375;         % Curvature Radius: m
kLc = 0.5*cL_close*rho*SLift;   % Lift constant DRS closed: kg/m
kDc = 0.5*cD_close*rho*SDrag;   % Drag constant DRS closed: kg/m
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

for index = 1:size(delta_raw,2)
% INITIALIZATION 
t_3(1) = 0;                 % Time: s
x_3(1) = 0;                 % Space: m
front_acc_3(1) = 0;         % Frontal Acceleration: m/(s^2)
Nr_3(1) = m*g*la/wb;        % Vertical reaction rear axis: N
LD_3(1) = la/wb;            % Load distribution wrt rear axis: /
delta = delta_raw(index);         % Steering Angle: radians 
Lift_3(1) = 1;              % -Lift force: N
Drag_3(1)= 1;               % Drag force: N
i = 1;                      % Generic index
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
while x_3 <= 2 * pi * radius 
Torque(i) = (2 * sin(delta)) * f * (1-LD_3(i))*(m * g + Lift_3(i))+ Drag_3(i) ;
Front_force(i) = (Torque(i) - Drag_3(i)) / sin(delta)  ;
Rear_force(i) = (Front_force(i) * cos(delta))/lb;
vel_3(i) = sqrt((radius*(Rear_force(i) + cos(delta) * Front_force(i)))/m);
Lift_3(i+1) = kLc * vel_3(i)^2;
Drag_3(i+1) = kDc * vel_3(i)^2;
lat_acc_3(i+1) = vel_3(i)^2 / radius;
Nr_3(i) = (m * g * la + haero * Drag_3(i) + laero * Lift_3(i)) / wb;
LD_3(i+1) = Nr_3(i) / (m*g + Lift_3(i));
x_3(i+1) = x_3(i) + vel_3(i)*dt;
t_3(i+1) = t_3(i) + dt;
i = i + 1;
end
plot(t_3,x_3);
hold on
end

legend("Location","eastoutside")
ylim([0,55]);
yline(2 * pi * radius)
grid on
xlabel("Time")
ylabel("Distance")
title("Distance over Time")