AircraftPointMassDLM:

Path: ACPro/ACPointMass

% Generate a discrete time-varying linear model of a point-mass aircraft.

   At each time step k, a linearized model of the open-loop aircraft
   dynamics is generated using APMLinMod. This continuous model is then
   discretized at a sampling time equal to the current time step, t(k+1)-t(k).

   The process is repeated to generate a matrix-form expression that
   describes small motion dx(t) about the nominal trajectory x(t).

     dx(t) = H*dx(0) + G*du(t)
   
   The control input to the linear system is du(t), which is small changes
   about the nominal control input u(t). The output is dy(t), which is
   just the position component (east, north, and altitude) of the state
   vector.

     dy(t) = C*dx(t)

   The vectors dx(t) and du(t) are column vectors, stacked over multiple
   time points. The sizes are: 
        dy: 3*N rows, 1 column
        dx: 7*N rows, 1 column
        du: 3*N rows, 1 column
         H: 7*N rows, 7 columns
         G: 7*N rows, 3*N columns
         C: 3*N rows, 7*N columns

--------------------------------------------------------------------------

   State:     x = [V;gama;psi;x;y;h;Tbar]
   --------------------------------------
     V     true airspeed
     gama  air relative flight path angle
     psi   air relative flight heading angle
     x     East position
     y     North position
     h     altitude
     Tbar  normalized excess thrust

   Control:   u = [Lbar;phi;Tcbar]
   -------------------------------
     Lbar    normalized excess lift
     phi     bank angle
     Tcbar   normalized excess thrust command
     
--------------------------------------------------------------------------
   Form:
   [A,B,C,G,H] = AircraftPointMassDLM( x, u, t );
--------------------------------------------------------------------------

   ------
   Inputs
   ------
   x       (7,N)    State trajectory
   u       (3,N)    Control input trajectory
   t       (1,N)    Time vector over which trajectories are defined

   -------
   Outputs
   -------
   A       (7,7)    Discrete linear state transition matrix (at last time)
   B       (7,3)    Discrete linear control effect matrix (at last time)
   C       (3N,7N)  State output matrix
   G       (7N,3N)  Discrete time varying input effect matrix
   H       (7N,7)   Discrete time varying state transition matrix

--------------------------------------------------------------------------

Children:

ACPro: ACPointMass/APMLinMod
Common: Control/C2DZOH

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