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 19<br />
calculated by summing up the contributions <strong>of</strong> all the cabin parts [1]:<br />
����<br />
����<br />
�<br />
����� ���� �<br />
���<br />
�<br />
��������� ��<br />
� ��<br />
�<br />
��<br />
�<br />
���������� (3.3)<br />
While the thermal conductivity � <strong>an</strong>d the material thickness � <strong>an</strong>d area � are usually<br />
known <strong>an</strong>d const<strong>an</strong>t, the convection heat tr<strong>an</strong>sfer coefficients on the outside, ��������, <strong>an</strong>d<br />
inside the cabin, �������, depend on the air speed. Großm<strong>an</strong>n gives approximations <strong>for</strong><br />
these correlations: ������� � �� ���<br />
������, �������� � � ���<br />
���<br />
equation:<br />
The temperature <strong>of</strong> the air blown into the cabin c<strong>an</strong> be expressed with the following<br />
��� � � ����� ¡<br />
�<br />
�������� ¡ ������<br />
� ����� �������� ¡ ���� � ������� ¡ ���� (3.4)<br />
Combining equations 3.1, 3.2 <strong>an</strong>d 3.4, a differential equation <strong>for</strong> <strong>an</strong> estimation <strong>of</strong><br />
the me<strong>an</strong> cabin temperature c<strong>an</strong> be given.<br />
�� �<br />
�<br />
�������� ¡ ������ � � ���� ¡ ��� ¡<br />
�<br />
�������� ¡ ������ ¡ ����<br />
�����<br />
3.1.2 Water mass in the cabin air<br />
����� � ����<br />
¡ �����<br />
����<br />
����� � � �� � � �������<br />
� (3.5)<br />
Water in the cabin has two sources. One is the incoming (moist) air. The other are the<br />
passengers with their respiration, sweat as well as other humidity in the clothes <strong>an</strong>d shoes.<br />
Water leaves the car through the air outlet or is separated at the evaporator.<br />
A basic water equation is found at Großm<strong>an</strong>n [1]. It is however only applicable in<br />
a steady context <strong>an</strong>d does not implement a recirculated air percentage �������. There<strong>for</strong>e,<br />
it is modified in the following:<br />
�������<br />
�� � ������ ������� � ������� �������� (3.6)