Skid Pad Simple 4DOF

Maneuver in circles of a nonlinear simple vehicle model with Pacejka tire model.

A control law (rear-wheel-drive) is used to maintain a CG speed of 8 m/s.

Contents

Code start

clear ; close all ; clc

import VehicleDynamicsLateral.*

Model and parameters

Simulation

% Choosing tire
TireModel   = TirePacejka();
% Choosing vehicle
System      = VehicleSimpleNonlinear4DOF();
% Defining vehicle parameters
System.mF0  = 700;
System.mR0  = 600;
System.lT   = 3.5;
System.nF   = 1;
System.nR   = 1;
System.wT   = 2;
System.muy  = 1;
System.deltaf           = 10*pi/180;
System.FXFRONTLEFT      = 0;
System.FXFRONTRIGHT     = 0;
System.FXREARLEFT       = @VelControl4DOF;
System.FXREARRIGHT      = @VelControl4DOF;
System.K                = 50000000; % Rigidez torcional da massa suspensa
System.C                = 5000000;

System.H    = 0.6;                       % CG height                [m]
System.L    = 0.6;                       % track                    [m]
System.IXX  = 12000;
System.IYY  = 65000;
System.IZZ  = 65000;
System.IXY  = 1000;
System.IXZ  = 1000;
System.IYZ  = 1000;

System.tire = TireModel;

% Choosing simulation
T = 30;                                 % Total simulation time     [s]
resol = 200;                            % Resolution
TSPAN = 0:T/resol:T;                    % Time span                 [s]
simulator = Simulator(System, TSPAN);

simulator.V0 = 8;

% Simulation
simulator.Simulate();

Results

% Retrieving states
XT      = simulator.XT;
YT      = simulator.YT;
PSI     = simulator.PSI;
THETA   = simulator.THETA;
VEL     = simulator.VEL;
ALPHAT  = simulator.ALPHAT;
dPSI    = simulator.dPSI;
dTHETA  = simulator.dTHETA;

% Retrieving data from vehicle (?)
m   = System.mT;
a   = System.a;
b   = System.b;
K   = 50000000;                             % Rigidez torcional da massa suspensa
CC  = 5000000;
h   = 0.6;                                  % CG height             [m]
l   = 0.6;                                  % track                 [m]
g   = 9.81;

FzRight = (m*g*l/2 + K*THETA + CC*dTHETA)/l;
FzLeft = m*g - FzRight;

FzFrontRight = FzRight*b/(a+b);
FzFrontLeft = FzLeft*b/(a+b);
FzRearRight = FzRight*a/(a+b);
FzRearLeft = FzLeft*a/(a+b);

figure
hold on ; grid on ; box on
plot(TSPAN,XT)
xlabel('time [s]')
ylabel('Distance in the x direction [m]')

figure
hold on ; grid on ; box on
plot(TSPAN,YT)
xlabel('time [s]')
ylabel('Distance in the y direction [m]')

figure
hold on ; grid on ; box on
plot(TSPAN,PSI)
xlabel('time [s]')
ylabel('Yaw angle [rad]')

figure
hold on ; grid on ; box on
plot(TSPAN,THETA)
xlabel('time [s]')
ylabel('Roll angle [rad]')

figure
hold on ; grid on ; box on
plot(TSPAN,VEL)
xlabel('time [s]')
ylabel('Velocity [m/s]')

figure
hold on ; grid on ; box on
plot(TSPAN,ALPHAT)
xlabel('time [s]')
ylabel('Vehicle slip angle [rad/s]')

figure
hold on ; grid on ; box on
plot(TSPAN,dPSI)
xlabel('time [s]')
ylabel('Yaw rate [rad/s]')

figure
hold on ; grid on ; box on
plot(TSPAN,dTHETA)
xlabel('time [s]')
ylabel('Roll rate [rad/s]')

figure
hold on ; grid on ; box on
plot(TSPAN,FzFrontRight,'r')
plot(TSPAN,FzRearRight,'g')
plot(TSPAN,FzFrontLeft,'b')
plot(TSPAN,FzRearLeft,'m')
xlabel('time [s]')
ylabel('Vertical force [N]')
legend('Front Right','Rear Right','Front Left','Rear Left')

figure
hold on ; grid on ; box on
plot(TSPAN,FzFrontRight + FzFrontLeft,'r')
plot(TSPAN,FzRearRight + FzRearLeft,'g')
xlabel('time [s]')
ylabel('Vertical force [N]')
legend('Front axle','Rear axle')

mF0

disp(num2str(System.mF0))

700

mR0

disp(num2str(System.mR0))

600

Frame and animation

g = Graphics(simulator);
g.TractorColor = 'r';

g.Frame();

angulo = 0:0.01:2*pi;

[R,XC,YC] = circfit(XT(40:end),YT(40:end));

XX = XC + R*cos(angulo);
YY = YC + R*sin(angulo);

hold on
plot(XX,YY,'k')

g.Animation();
% g.Animation('html/SkidPadSimple4DOF');       % Uncomment to save animation gif

Maneuver radius

disp(num2str(R))

20.0944

See Also

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Published with MATLAB® R2019b