Template Simple Simulink

This template shows how to simulate a simple vehicle in Simulink using a s-function. The graphics are also plotted.

This model uses the s-function SimpleVehicleSFunction.m in Simulink. The package and this s-function must be in Matlab path.

The “SimpleVehicleSimulink.slx” available in the repository (“docs/examples/TemplateSimpleSimulink”) is illustrated below:

Fig. 59 Simple vehicle simulink S-Function

It can be seen that the longitudinal forces of the tire are zero for the entire simulation. The steering angle recieve a step input.

Template

To simulate the model run

sim('SimpleVehicleSimulink');

Each vehicle state variable goes to a scope. And the output of the model is saved in the workspace.

To generate the graphics, the same model used in Simple Vehicle S-Function must be defined.

Todo

Improve generation of graphics. Define parameters once -> Run Simulink -> Retrieve responses -> Graphics

First, define the tire model.

TireModel = TirePacejka();          % Choosing tire model

Defining the tire parameters to match the parameters used in the S-Function.

TireModel.a0 = 1;
TireModel.a1 = 0;
TireModel.a2 = 800;
TireModel.a3 = 3000;
TireModel.a4 = 50;
TireModel.a5 = 0;
TireModel.a6 = 0;
TireModel.a7 = -1;
TireModel.a8 = 0;
TireModel.a9 = 0;
TireModel.a10 = 0;
TireModel.a11 = 0;
TireModel.a12 = 0;
TireModel.a13 = 0;

The vehicle model is defined as

VehicleModel = VehicleSimpleNonlinear();

Defining the vehicle parameters to match the parameters used in the S-Function.

VehicleModel.mF0 = 700;
VehicleModel.mR0 = 600;
VehicleModel.IT = 10000;
VehicleModel.lT = 3.5;
VehicleModel.nF = 2;
VehicleModel.nR = 2;
VehicleModel.wT = 2;
VehicleModel.muy = .8;
VehicleModel.tire = TireModel;

Defining the simulation object.

simulator = Simulator(VehicleModel, tout);

Retrieving state responses from Simulink model

simulator.XT = simout.Data(:,1);
simulator.YT = simout.Data(:,2);
simulator.PSI = simout.Data(:,3);
simulator.VEL = simout.Data(:,4);
simulator.ALPHAT = simout.Data(:,5);
simulator.dPSI = simout.Data(:,6);

Frame and animation can be generated defining a graphic object (Graphics). The only argument of the graphic object is the simulator object after the simulation.

g = Graphics(simulator);

To change the color of the vehicle run

g.TractorColor = 'r';

After that, just run

g.Frame();
g.Animation();

Both graphics feature can be seen below.

Fig. 60 Frame of the simple vehicle model in Simulink.

Todo

Include Template Articulated Simulink Animation

As expected the vehicle starts traveling in a straight line and starts a turn at (t = 1 , s) because of the step function.

Simple Vehicle S-Function

The simple vehicle S-Function is depicted below.

function [sys,x0,str,ts] = SimpleVehicleSFunction(t,x,u,flag)
% This file is a s-function template for simulating the simple vehicle model in Simulink.

% Choosing tire model
TireModel = TirePacejka();
% Defining tire parameters
TireModel.a0 = 1;
TireModel.a1 = 0;
TireModel.a2 = 800;
TireModel.a3 = 3000;
TireModel.a4 = 50;
TireModel.a5 = 0;
TireModel.a6 = 0;
TireModel.a7 = -1;
TireModel.a8 = 0;
TireModel.a9 = 0;
TireModel.a10 = 0;
TireModel.a11 = 0;
TireModel.a12 = 0;
TireModel.a13 = 0;

% Choosing vehicle model
VehicleModel = VehicleSimpleNonlinear();
% Defining vehicle parameters
VehicleModel.mF0 = 700;
VehicleModel.mR0 = 600;
VehicleModel.IT = 10000;
VehicleModel.lT = 3.5;
VehicleModel.nF = 2;
VehicleModel.nR = 2;
VehicleModel.wT = 2;
VehicleModel.muy = .8;
VehicleModel.tire = TireModel;

switch flag,

  %%%%%%%%%%%%%%%%%%
  % Initialization %
  %%%%%%%%%%%%%%%%%%
  case 0,
    [sys,x0,str,ts]=mdlInitializeSizes();

  %%%%%%%%%%%%%%%
  % Derivatives %
  %%%%%%%%%%%%%%%
  case 1,
    sys=mdlDerivatives(t,x,u,VehicleModel);

  %%%%%%%%%%%
  % Outputs %
  %%%%%%%%%%%
  case 3,
    sys=mdlOutputs(t,x,u,VehicleModel);

  %%%%%%%%%%%%%%%%%%%
  % Unhandled flags %
  %%%%%%%%%%%%%%%%%%%
  case { 2, 4, 9 },
    sys = [];

  %%%%%%%%%%%%%%%%%%%%
  % Unexpected flags %
  %%%%%%%%%%%%%%%%%%%%
  otherwise
    DAStudio.error('Simulink:blocks:unhandledFlag', num2str(flag));

end
% end csfunc

%
%=============================================================================
% mdlInitializeSizes
% Return the sizes, initial conditions, and sample times for the S-function.
%=============================================================================
%
function [sys,x0,str,ts]=mdlInitializeSizes()

% Definitions
sizes = simsizes;
sizes.NumContStates  = 6;
sizes.NumDiscStates  = 0;
sizes.NumOutputs     = 6;
sizes.NumInputs      = 3;
sizes.DirFeedthrough = 1;
sizes.NumSampleTimes = 1;

sys = simsizes(sizes);

% Setting initial conditions
x0  = [0 0 0 20 0 0];
str = [];
ts  = [0 0];

% end mdlInitializeSizes
%
%=============================================================================
% mdlDerivatives
% Return the derivatives for the continuous states.
%=============================================================================
%


function sys = mdlDerivatives(t,x,u,vehicle)

% Defining input
vehicle.deltaf = u(1);
vehicle.Fxf = u(2);
vehicle.Fxr = u(3);

% Getting the vehicle model function (state equations)
ModelFunction = @vehicle.Model;

sys = ModelFunction(t,x,0);

% end mdlDerivatives
%
%=============================================================================
% mdlOutputs
% Return the block outputs.
%=============================================================================
%
function sys=mdlOutputs(~,x,~,~)

% Output are all state variables
sys = x;

% end mdlOutputs