## The utility FIXSTATE

FIXSTATE is a Matlab program, which can be used to artificially fix state variables of the non-linear aircraft model (in this case the Simulink Beaver model).

FIXSTATE sets the value of the gain vector xfix, which is a multiplication factor for the time-derivative of the state vector (xdot = dx/dt) within the non-linear aircraft model. The corresponding gain block XFIX can be found in the subsystem Aircraft equations of motion within the Beaver model.

The gain-factor xfix is applied as follows: the time-derivative of the state-vector, used by the Simulink integrator, is equal to:

      xdot_used = xdot_true .* xfix

(where the `.*` symbol corresponds with the Matlab operator for element-by-element of vectors). The elements of xfix are either equal to one or zeros. If xfix = ones(1,12), xdot_used will be equal to xdot_true, which means that none of the state variables will be artificially fixed. If one or more elements of xfix is (are) equal to zero, the time-derivatives of the corresponding states will remain zero, hence, these states will remain equal to their initial condition.

For instance: if the true airspeed (that is: the first element of the state vector x) needs to be kept constant, xfix has to be set equal to `[0 1 1 1 1 1 1 1 1 1 1 1]`. This example may, for instance, be useful if one wants to compare a speed hold autopilot mode with the 'ideal' response with artificially fixed airspeed. Another practical purpose for FIXSTATE is the determination of purely longitudinal or lateral dynamics, without cross-coupling effects.

Note: the variable xfix needs to be defined in the workspace if the system Beaver (or a subsystem equivalent thereof) is evaluated for simulation, trimming, and/or linearization purposes. If this variable can't be found when such a task is started, the default value xfix = ones(1,12) will be used automatically.

### Definition of the state-vector

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

      V     = true 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 of aircraft's c.g. [m]
      ye    = Y-coordinate of aircraft's c.g. [m]
      H     = altitude of aircraft's c.g. [m] (above sea level)