📄 fixstate.htm
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FDC help: FIXSTATE
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<h2>
The utility <i>FIXSTATE</i>
</h2>
<p><i>FIXSTATE</i> is a Matlab program, which can be used to artificially fix
state variables of the non-linear aircraft model (in this case the Simulink
<i><a href="beaver.htm">Beaver</a></i> model).</p>
<p><i>FIXSTATE</i> sets the
value of the gain vector <i>xfix</i>, which is a multiplication factor for
the time-derivative of the state vector (<i>xdot = dx/dt</i>) within the
non-linear aircraft model. The corresponding gain block <i><a href=
"xfix.htm">XFIX</a></i> can be found in the subsystem <i><a href=
"eqmotion.htm">Aircraft equations of motion</a></i> within the <i>Beaver</i> model.</p>
<p>The gain-factor <i>xfix</i> is applied as follows: the
time-derivative of the state-vector, used by the Simulink integrator, is
equal to: </p>
<pre>
xdot_used = xdot_true .* xfix
</pre>
<p>(where the <code>.*</code> symbol corresponds with the Matlab operator for
element-by-element of vectors). The elements of <i>xfix</i> are either
equal to one or zeros. If <i>xfix = ones(1,12)</i>,
<i>xdot_used</i> will be equal to <i>xdot_true</i>, which means that none
of the state variables will be artificially fixed. If one or more elements
of <i>xfix</i> 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.</p>
<p>For instance: if the true airspeed (that is: the first element of the
state vector <i>x</i>) needs to be kept constant, <i>xfix</i> has to be set equal to
<code>[0 1 1 1 1 1 1 1 1 1 1 1]</code>. 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 <i>FIXSTATE</i>
is the determination of purely longitudinal or lateral dynamics, without
cross-coupling effects.</p>
<p><b>Note:</b> the variable <i>xfix</i> needs to be defined in the workspace
if the system <i>Beaver</i> (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 <i>xfix = ones(1,12)</i> will be used automatically.</p>
<h3>
Definition of the state-vector
</h3>
<pre>
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)
</pre>
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