141_1_Midterm

141_1_Midterm - EE 141 Midterm Winter 2010 02/10/10...

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EE 141 – Midterm Winter 2010 02/10/10 Duration: 1 hour and 40 minutes The midterm is closed book and closed lecture notes. No calculators. You can use a single page of handwritten notes. Please carefully justify all your answers. Problem 1: Consider two rooms in a house as depicted in Figure 1 . The temperature in the left room is denoted by x 1 and the temperature in the right room is denoted by x 2 . The left room is equipped with a heater and we are interested in controlling the heater to regulate the x 2 . x 1 x 2 Figure 1: Two rooms in a house. The room in the left is equipped with a heater. We assume that the evolution of x 1 is described by the following differential equation: d dt x 1 = - αx 1 - β ( x 1 - x 2 ) + u (1) where the term - αx 1 describes heat lost to the exterior of the building, - β ( x 1 - x 2 ) represents the heat lost to the room in the right, and u represents the heat generated by the heater. 1. Knowing that the room in the right loses heat to the exterior of the building at the same
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141_1_Midterm - EE 141 Midterm Winter 2010 02/10/10...

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