## The radio-navigation system VOR example

The system VOR example from the library NAVLIB contains a demonstration of the practical use of the VOR blocks. First, the nominal signals are computed in the block VOR, then, the steady-state error in the VOR signal is taken into account in the block VORerr.

Double-click the subsystem block VOR example to see its internal structure. The blocks VOR and VORerr need to be double-clicked too in order to specify their parameters.

A slightly altered version of this block (which uses somewhat different I/O definitions) is used by the systems APILOT2 and APILOT3.

### Inputvector: x

      x = [V alpha beta p q r psi theta phi xe ye H]' (aircraft states)

     {V    : airspeed [m/s]                                         }
     {alpha: angle of attack [rad]                                  }
     {beta : sideslip angle [rad]                                   }
     {p    : roll rate [rad/s]                                      }
     {q    : pitch rate [rad/s]                                     }
     {r    : yaw rate [rad/s]                                       }
      psi  : yaw angle [rad]
     {theta: pitch angle [rad]                                      }
     {phi  : roll angle [rad]                                       }
      xe   : x-coordinate in Earth-fixed reference frame [m]
      ye   : y-coordinate [m]
      H    : altitude above sea-level [m]

When applied to an autopilot simulation model, these input variables are usually outputs from a non-linear aircraft model. The block VOR which computes the nominal values of the VOR signals does not give correct results if a small-deviations model is used for the aircraft dynamics! Open the Beaver system for an example of such a non-linear aircraft model.

### Output: Gamma_VOR

    Gamma_VOR: Angle between the selected VOR-bearing and the line
               from the aircraft's center of gravity to the VOR antenna [rad]

During simulations, the time-trajectories of the VOR signals and some interim results from the block VOR are sent to the matrix yvor in the Matlab workspace. Each row from this matrix corresponds with the vector yvor_workspace at a certain time t, according the following definition:

    yvor_workspace = [yvor1; yvor2; yvor3; yvor4]'

    yvor1 = Gamma_VOR
    yvor2 = R_VOR
    yvor3 = [Cone-of-silence-flag, Range-flag]'.
    yvor4 = ToFrom

    Gamma_VOR : Angle between selected VOR-bearing and line from the
                aircraft's c.g. to the VOR antenna [rad]
    R_VOR     : 2D-distance from origin of Earth-fixed reference
                frame to VOR (as seen from above) [m]

The Cone-of-silence-flag is set to 1 if the aircraft enters the 'cone of silence'. The Range-flag is set to 1 if the aircraft flies outside the area where the VOR signals can be received with appropriate reliability.

The variable ToFrom is set to 1 if aircraft is flying towards the VOR antenna or 0 if the aircraft flies away from the antenna.

For more info about the definitions of the variables, consult the FDC user-manual.

### References

For more information about the VOR model, consult the FDC user-manual, and/or:

1. M.O. Rauw: A Simulink environment for Flight Dynamics and Control analysis - Application to the DHC-2 'Beaver'. MSc-thesis, Delft University of Technology, Faculty of Aerospace Engineering, Delft, The Netherlands, 1993.