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      FDC help: Gain block XFIX
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    <h2>
      Gain block <i>XFIX</i>
    </h2>
    <p><i>XFIX</i> is a standard Simulink gain-block, which is used in the
    subsystem <i><a href="eqmotion.htm">Aircraft Equations of Motion (level
    3)</a></i> of the aircraft model <i><a href="beaver.htm">Beaver</a></i> to
    artificially fix states to their initial values.</p>
    <p>The value of the constant
    <i>xfix</i> needs to be defined in the Matlab workspace before starting a
    simulation or any other evaluation of the <i>Beaver</i> model; the utility <i><a href="fixstate.htm">FIXSTATE</a></i> can be used to assist in this definition.</p> 
    <h3>
      Why artificially fix state variables?
    </h3>
    <p>Artificially fixing state variables to their initial values means that one
    deliberately eliminates certain couplings from the simulation model. This
    may for instance be useful if you want to assess the aircraft&#39;s
    longitudinal and lateral motions independently from eachother (thus
    deliberatly neglecting the cross-coupling effects), or to implement the
    &#39;ideal&#39; control-behavior (e.g. pitch attitude hold or speed hold)
    against which a practical control system should be measured.</p> 
    <h3>
      How does it work?
    </h3>
    <p>The gain <i>XFIX</i> multiplies the vector with time-derivatives of the
    state variables, <i>xdot</i>, with the gain-factor <i>xfix</i>. If the user
    does not impose artificial restrictions upon the states, <i>xfix</i> will
    be equal to one, and the outputvector from <i>XFIX</i> is equal to
    <i>xdot</i>, according to the equations of motion. The same result is
    obtained when the constant <i>xfix</i> is equal to a vector of length 12
    with elements that are all equal to one.</p>
     <p>If, however, the user wants to fix some of the twelve states to their
    initial values, <i>xfix</i> needs to be equalled to a vector of length 12
    with elements that are all equal to one, <i>except</i> for the element
    numbers that correspond with the states to be fixed. If, for instance, the
    user wants to fix the first, fifth, and last states to their initial
    values, the first, fifth, and last element of <i>xfix</i> must be set to
    zero. In that case, the input/output structure around the block <i>XFIX</i>
    looks like:</p> 
<pre>
xdot_in = [V dot;      \            /  xdot_out = [ 0
           alpha dot;  |            |              alpha dot;
           beta dot;   |            |              beta dot;
           p dot;      |            |              p dot;
           q dot;      |            |               0
           r dot;      |            |              r dot;
           psi dot;    |&gt; * <i>xfix</i>   &lt;|              psi dot;
           theta dot;  |            |              theta dot;
           phi dot;    |            |              phi dot;
           xe dot;     |            |              xe dot;
           ye dot;     |            |              ye dot;
           H dot]      /            \               0 ]
</pre>
    <p>Since the first, fifth, and last elements of xdot are artificially set to
    zero, the corresponding states will equal their initial values until the
    value of <i>xfix</i> is changed again!</p>
     <p>If the variable <i>xfix</i> is not present in the workspace when the aircraft model is accessed by e.g. a simulation or a linearization process, it will automatically be set to <code>ones(1,12)</code>. Run <i><a href="fixstate.htm">FIXSTATE</a></i> if you want to change this default definition of <i>xfix</i>.</p>
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