.. _template-simple:

Template Simple
********************************************************************************

This template shows how to simulate a simple vehicle and plot the results.

First, we choose the tire and vehicle models. The first one is the Pacejka tire model (:ref:`tire-pacejka`) and the second one is the nonlinear vehicle model (:ref:`vehicle-simple-3dof`).

.. code-block:: matlab
    
    TireModel = TirePacejka();                  % Choosing tire
    VehicleModel = VehicleSimpleNonlinear();    % Choosing vehicle
    
In this case, no parameter is defined. So, the default values are used. The default parameters of the vehicle and tire model can be seen in :mod:`VehicleSimpleNonlinear` and :mod:`TirePacejka`, respectively.

Now, we have two variables defined.

The system is completely defined once we attribute the chosen tire model to the vehicle object.

.. code-block:: matlab
    
    VehicleModel.tire = TireModel;
    
After this, we define the simulation time span

.. code-block:: matlab
    
    T = 6;                              % Total simulation time [s]
    resol = 50;                         % Resolution
    TSPAN = 0:T/resol:T;                % Time span [s]
    
To define a simulation object (:mod:`Simulator`) the arguments must be the vehicle object and the time span. This is,

.. code-block:: matlab
    
    simulator = Simulator(VehicleModel, TSPAN);
    
The default parameters of the simulation object can be found in :mod:`Simulator`. However, we are interested in changing the initial conditions of the simulation object. This can be done running

.. code-block:: matlab
    
    simulator.ALPHAT0 = -0.2;           % Initial side slip angle [rad]
    simulator.dPSI0 = 0.7;              % Initial yaw rate [rad/s]
    
Now, we have everything needed to run the simulation. For this, we use

.. code-block:: matlab
    
    simulator.Simulate();
    
The resulting time response of each state is stored in separate variables:

.. code-block:: matlab
    
    XT = simulator.XT;
    YT = simulator.YT;
    PSI = simulator.PSI;
    VEL = simulator.VEL;
    ALPHAT = simulator.ALPHAT;
    dPSI = simulator.dPSI;
    
The following lines plot the time response of each state of the model.

.. code-block:: matlab
    
    f1 = figure(1);
    grid on ; box on
    plot(TSPAN,XT,'linewidth',1)
    xlabel('time [s]')
    ylabel('Distance in the x direction [m]')
    
    f2 = figure(2);
    grid on ; box on
    plot(TSPAN,YT,'linewidth',1)
    xlabel('time [s]')
    ylabel('Distance in the y direction [m]')
    
    f3 = figure(3);
    grid on ; box on
    plot(TSPAN,PSI,'linewidth',1)
    xlabel('time [s]')
    ylabel('Yaw angle [rad]')
    
    f4 = figure(4);
    grid on ; box on
    plot(TSPAN,VEL,'linewidth',1)
    xlabel('time [s]')
    ylabel('Velocity [m/s]')
    
    f5 = figure(5);
    grid on ; box on
    plot(TSPAN,ALPHAT,'linewidth',1)
    xlabel('time [s]')
    ylabel('Vehicle slip angle [rad/s]')
    
    f6 = figure(6);
    grid on ; box on
    plot(TSPAN,dPSI,'linewidth',1)
    xlabel('time [s]')
    ylabel('Yaw rate [rad/s]')
    
The generated figures can be seen below.

.. figure::  ../illustrations/plot/TemplateSimpleFig1.svg
    :align:   center
    :width: 40%

    Longitudinal position of the center of gravity of the system.

.. figure::  ../illustrations/plot/TemplateSimpleFig2.svg
    :align:   center
    :width: 40%

    Transversal position of the center of gravity of the system.

.. figure::  ../illustrations/plot/TemplateSimpleFig3.svg
    :align:   center
    :width: 40%

    Yaw angle of the vehicle

.. figure::  ../illustrations/plot/TemplateSimpleFig4.svg
    :align:   center
    :width: 40%

    Velocity of the center of gravity

.. figure::  ../illustrations/plot/TemplateSimpleFig5.svg
    :align:   center
    :width: 40%

    Vehicle slip angle

.. figure::  ../illustrations/plot/TemplateSimpleFig6.svg
    :align:   center
    :width: 40%

    Vehicle yaw rate

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

.. code-block:: matlab
    
    g = Graphics(simulator);
    
After that, just run

.. code-block:: matlab
    
    g.Frame();
    g.Animation();
    
Both graphics feature can be seen below.

.. figure::  ../illustrations/frame/TemplateSimpleFrame.svg
    :align:   center
    :width: 60%

    Frame of the simple vehicle model.

.. figure::  ../illustrations/animation/TemplateSimpleAnimation.gif
    :align:   center

    Animation of the simple vehicle model.