📄 hlpfcn.htm

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      FDC help: Hlpfcn
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    <h2>
      Subsystem <i>Hlpfcn</i>
    </h2>
    <p><i>Hlpfcn</i> is used to compute some frequently used
    sines and cosines, which are needed for the calculation of the time
    derivatives of the state variables in the aircraft model. Since the results are, of course, quite
    trivial, it was not necessary to send the outputs from the block
    <i>Hlpfcn</i> to the Workspace, which is why <i>Hlpfcn</i> was placed
    in a feedback loop. The <a href="beaver.htm">aircraft model</a> therefore contains three feedback loops: one for the state vector <i>x</i>, one for its
    time-derivative (this feedback is used for additional output equations
    only, so it does not induce algebraic loops into the system!), and one for
    the outputs from <i>Hlpfcn</i>. </p>
     <p>It is important to notice that these feedback loops are necessary 
    to find a computation order for the simulations: they define an artificial causality that makes simulations possible. In reality, the forces and
    moments depend upon the state variables and there time-derivatives, and
    vice-versa, so the computation order is not necessarily equal
    to the order of occurance in physical reality! </p>
    <h3>
      Inputvector: <i>x</i>
    </h3>
<pre>
  x = [V alpha beta p q r psi theta phi xe ye H]&#39;        (states)

 {V    : 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 in Earth-fixed reference frame [m]        }
 {ye   : y-coordinate &#39;&#39;     &#39;&#39;          &#39;&#39;      &#39;&#39;  [m]        }
 {H    : altitude above sea-level [m]                           }
</pre>
    <p>The signals which are not actually used by <i>Hlpfcn</i> have been put
    between curly braces. </p>
    <h3>
      Outputvector: <i>yhlp</i>
    </h3>
<pre>
  yhlp = [cos(alpha) sin(alpha) cos(beta) sin(beta) ...
          ... tan(beta) sin(psi) cos(psi) sin(theta) ...
          ... cos(theta) sin(phi) cos(phi)]&#39;.
</pre>
    <p>(Notice that this list also contains one tangens, which makes the definition
    of <i>yhlp</i> a little bit confusing. <i>Hlpfcn</i> therefore needs to be
    &#39;fine-tuned&#39; in the future.)</p>
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