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
--------------------------------------------------------------------------
ACPro: ACPointMass/APMLinMod Common: Control/C2DZOH
Back to the ACPro Module page