xdotcorr.hlp

MATLAB在飞行动力学和控制中应用的工具

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XDOTCORR is a masked Simulink subsystem, which is contained in
the subsystem 'Aircraft Equations of Motion (Beaver)' of the
S-function BEAVER. XDOTCORR is the only block of this subsystem
which depends upon the aircraft model considered, in this case
the aerodynamic model of the DHC-2 'Beaver' from ref.[1].

XDOTCORR is used to convert the state equations of the 'Beaver'
dynamic model, which are implicit due to the contributions of the
time-derivative of beta-dot to the aerodynamic sideforce, into
explicit state equations. The resulting equations consist of a
part which is independent of the aircraft considered, and a
correction part, which is implemented in XDOTCORR.

XDOTCORR can be changed to implement models of other aircraft,
in cases where it is necessary to bring into account contribu-
tions of time-derivatives of states to the aerodynamic forces
and moments, which would otherwise result in implicit state equa-
tions. Such implicit state equations most often involve alpha-
dot and beta-dot terms.

Inputvectors (the variables which are not used in the block
XDOTCORR are displayed between accolades):
===========================================================
  xdot = dx/dt = [Vdot alphadot betadot pdot qdot rdot ...
                  psidot thetadot phidot xedot yedot Hdot]'
        (state derivatives, without corrections which make impli-
         cit equations explicit, coming from subsystem '12 ODEs')

  yhlp = [cos(alpha) sin(alpha) cos(beta) sin(beta) ...
          ... tan(beta) sin(psi) cos(psi) sin(theta) ...
          ... cos(theta) sin(phi) cos(phi)]'
            (frequently used sines & cosines, coming from HLPFCN)

  yatm = [rho ps T mu g]',  (atmospheric properties, computed in
                                               the block ATMOSPH)

where:

 {Vdot    : time-derivative of airspeed [m/s^2]                 }
 {alphadot: time-derivative of angle of attack [rad/s]          }
  betadot : time-derivative of sideslip angle [rad/s]
                                                (uncorrected!)
 {psidot  : time-derivative of yaw angle [rad/s]                }
 {thetadot: time-derivative of pitch angle [rad/s]              }
 {phidot  : time-derivative of roll angle [rad/s]               }
 {pdot    : time-derivative of roll rate [rad/s^2]              }
 {qdot    : time-derivative of pitch rate [rad/s^2]             }
 {rdot    : time-derivative of yaw rate [rad/s^2]               }
 {xedot   : time-derivative of x-coordinate in Earth-fixed
                                         reference frame [m/s]  }
 {yedot   : time-derivative of y-coordinate in Earth-fixed
                                         reference frame [m/s]  }
 {Hdot    : time-derivative of altitude above sea-level [m/s]   }

  rho  : airdensity [kg/m^3]
 {ps   : static pressure [N/m^2]                                }
 {T    : temperature [K]                                        }
 {mu   : dynamic viscosity [kg/(m*s)]                           }
 {g    : acceleration of gravity [m/s^2]                        }

 Of the vector yhlp, only cos(beta) is used.

Outputvector: xdot with beta-dot correction.
============================================
  xdot = [Vdot alphadot betadot pdot qdot rdot psidot ...
          ... thetadot phidot xedot yedot Hdot]'

 Here, betadot is corrected for the beta-dot influence upon the
 aerodynamic sideforce Ya!

Parameters, which must be set in the Matlab Workspace.
======================================================
  AM  = matrix with stability and control derivatives of the
        'Beaver' (valid only for the nonlinear aerodynamic model
        of the DHC-2 'Beaver', see ref.[1]). Here, the stability
        derivative CYbdot is extracted (influence of beta-dot
        upon aerodynamic sideforce Ya).

  GM1 = vector with some important geometrical properties of the
        'Beaver' aircraft, and the mass of the aircraft (which is
        assumed to be constant during the motions of interest).
        In XDOTCORR, the wing span b, wing area S, and mass m are
        extracted from GM1.

The vector GM1 and the matrix AM can be loaded into the workspace
from file by applying the routine LOADER.M. Run MODBUILD.M first
if the datafile does not yet exist. Type HELP LOADER or HELP MOD-
BUILD for more info.

References.
===========
[1]  R.T.H. Tjee and J.A. Mulder. Stability and Control Deriva-
     tives of the De Havilland DHC-2 "Beaver" aircraft. Report
     LR-556, Delft University of Technology, 1988.

More Info.
==========
More info about the implicitness of the beta-dot equation for
the 'Beaver' can be found in AEROMOD.HLP, and 12ODES.HLP. See also
VABDOT.HLP, PQRDOT.HLP, EULERDOT.HLP, and XYHDOT.HLP, for more
info about the time-derivatives of other state variables. The
block XDOTCORR uses the outputs of the masked subsystem HLPFCN as
inputvariables; see HLPFCN.HLP for more info.

See also EQMOTION.HLP for more details about the subsystem 'Air-
craft Equations of Motion (Beaver)'.

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