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Unformatted text preview: EE221A Linear System Theory Problem Set 8 Professor C. Tomlin Department of Electrical Engineering and Computer Sciences, UC Berkeley Fall 2010 Issued 11/16; Due 11/23 Problem 1: Stability. T H T C f f H C T H T C i i , , V H V C Figure 1: A simple heat exchanger, for Problem 1. Consider the simple heat exchanger shown in Figure 1, in which f C and f H are the flows (assumed constant) of cold and hot water, T H and T C represent the temperatures in the hot and cold compartments, respectively, T Hi and T Ci denote the temperature of the hot and cold inflow, respectively, and V H and V C are the volumes of hot and cold water. The temperatures in both compartments evolve according to: V C dT C dt = f C ( T Ci T C ) + ( T H T C ) (1) V H dT H dt = f H ( T Hi T H ) ( T H T C ) (2) Let the inputs to this system be u 1 = T Ci , u 2 = T Hi , the outputs are y 1 = T C and y 2 = T H , and assume that f C = f H = 0 . 1 ( m 3 / min), = 0 . 2 ( m 3 /min) and V H = V C = 1 (...
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- Fall '10
- Electrical Engineering, LTI system theory, Tci, simple heat exchanger