Design of an Automatic Control Algorithm for Energy-Efficient ...
Design of an Automatic Control Algorithm for Energy-Efficient ...
Design of an Automatic Control Algorithm for Energy-Efficient ...
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3 System description 25<br />
defrost temperatures <strong>an</strong>d the air speeds on the windscreen. The windscreen const<strong>an</strong>ts are<br />
assumed to be known.<br />
����<br />
�� � � ���������������������������� (3.18)<br />
3.1.5 Time const<strong>an</strong>t considerations<br />
The systems described are <strong>of</strong> first order. A main characteristic <strong>of</strong> such systems is the time<br />
const<strong>an</strong>t giving <strong>an</strong> indication <strong>of</strong> how fast the system reacts to external ch<strong>an</strong>ges. Although<br />
the found systems are not time invari<strong>an</strong>t, boundaries c<strong>an</strong> be given.<br />
For a linear time invari<strong>an</strong>t (LTI) first order system the following c<strong>an</strong> be written<br />
with � being the time const<strong>an</strong>t <strong>an</strong>d � being the gain.<br />
results:<br />
� ¡ ����� ����� �� ¡ ����<br />
Finding the time const<strong>an</strong>ts <strong>for</strong> the four systems presented be<strong>for</strong>e gives the following<br />
������ �<br />
�������� ¡ ������ � � ���� ¡ ���<br />
����� �������� ¡ �������� ¡ ������ � � ���<br />
� ���<br />
(3.19)<br />
The varying parameters here are the air flow <strong>an</strong>d the fraction <strong>of</strong> recirculation. The<br />
minimum time const<strong>an</strong>t is found by using no recirculation <strong>an</strong>d the maximum air flow.<br />
With the parameters found <strong>for</strong> the MUTE car described in Chapter 10 (see also Appendix<br />
C.1), a minimum <strong>of</strong> ���������� � ��� � <strong>an</strong>d a maximum <strong>of</strong> ���������� � ��� � c<strong>an</strong> be<br />
estimated. This is due to the high amount <strong>of</strong> thermal energy stored in the car material.<br />
The air itself will react faster. Without the interior thermal mass these times reduce to<br />
�� <strong>an</strong>d �� seconds.<br />
For the humidity <strong>an</strong>d carbon dioxide concentration the influence <strong>of</strong> the same pa-<br />
rameters c<strong>an</strong> be seen.<br />
�� �<br />
���� �<br />
� �������<br />
����� ��������¡ �� ������<br />
�������� ����� ��������¡ �� ������<br />
(3.20)<br />
(3.21)
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