.. _template-articulated-simulink:

Template Articulated Simulink
********************************************************************************
    
This template shows how to simulate an articulated vehicle in Simulink using a s-function. The graphics are also plotted.

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

The "ArticulatedVehicleSimulink.slx" available in the repository ("examples/TemplateArticulatedSimulink") is illustrated below:

.. figure:: ../illustrations/misc/ArticulatedVehicleSimulink.png
    :align:   center

    Articulated 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

.. code-block:: matlab
    
    sim('ArticulatedVehicleSimulink');
    
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 :ref:`vehicle-articulated-sfunction` must be defined.

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

First, define the tire model.

.. code-block:: matlab

    TireModel = TirePacejka();          % Choosing tire model
    
Defining the tire parameters to match the parameters used in the S-Function.

.. code-block:: matlab
    
    TireModel.a0 = 1;
    TireModel.a1 = 2;
    TireModel.a2 = 700;
    TireModel.a3 = 5000;
    TireModel.a4 = 80;
    TireModel.a5 = 0;
    TireModel.a6 = 0;
    TireModel.a7 = 0.6;
    TireModel.a8 = 0;
    TireModel.a9 = 0;
    TireModel.a10 = 0;
    TireModel.a11 = 0;
    TireModel.a12 = 0;
    TireModel.a13 = 0;
    
The vehicle model is defined as

.. code-block:: matlab
    
    VehicleModel = VehicleArticulatedNonlinear();
    
Defining the vehicle parameters to match the parameters used in the S-Function.

.. code-block:: matlab
    
    VehicleModel.mF0 = 5200;
    VehicleModel.mR0 = 2400;
    VehicleModel.mF = 6000;
    VehicleModel.mR = 10000;
    VehicleModel.mM = 17000;
    VehicleModel.IT = 46000;
    VehicleModel.IS = 450000;
    VehicleModel.lT = 3.5;
    VehicleModel.lS = 7.7;
    VehicleModel.c = -0.3;
    VehicleModel.nF = 2;
    VehicleModel.nR = 4;
    VehicleModel.nM = 8;
    VehicleModel.wT = 2.6;
    VehicleModel.wS = 2.4;
    VehicleModel.muy = 0.8;
    VehicleModel.deltaf = 0;
    VehicleModel.Fxf = 0;
    VehicleModel.Fxr = 0;
    VehicleModel.Fxm = 0;
    VehicleModel.tire = TireModel;
    
Defining the simulation object.

.. code-block:: matlab
    
    simulator = Simulator(VehicleModel, tout);
    
Retrieving state responses from Simulink model

.. code-block:: matlab
    
    simulator.XT = simout.Data(:,1);
    simulator.YT = simout.Data(:,2);
    simulator.PSI = simout.Data(:,3);
    simulator.PHI = simout.Data(:,4);
    simulator.VEL = simout.Data(:,5);
    simulator.ALPHAT = simout.Data(:,6);
    simulator.dPSI = simout.Data(:,7);
    simulator.dPHI = simout.Data(:,8);
    
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);
    
To change the color of the tractor and the semitrailer run

.. code-block:: matlab
    
    g.TractorColor = 'r';
    g.SemitrailerColor = 'g';
    
After that, just run

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

.. figure:: ../illustrations/frame/TemplateArticulatedSimulinkFrame.png
    :align:   center
    :width: 60%

    Frame of the simple vehicle model in Simulink.

.. todo:: Include Template Simple 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.

.. _vehicle-articulated-sfunction:

Articulated Vehicle S-Function
================================================================================

The articulated vehicle S-Function is depicted below.

.. literalinclude:: ../../docs/examples/TemplateArticulatedSimulink/ArticulatedVehicleSFunction.m