2.3 Three-capacitance thermal system A conducting bar (Fig. P2.3(a)) is insulated along its length but exposed to the ambient temperature at one end, and heated at the other end. An approximate electrical equivalent, based on "lumping" the bar into three finite lengths, is shown in Fig. P2.3(b). Write the differential equations for the system using a state variables , 2, and, the capacitor voltages. The input u is the temperature at the heated end, and the output y is the temperature D, al point 3 on the rod, as would be mined by a thermocouple, for example. u=CO Heater Co-M R/2 wwwww U C www U2 =c =C 604 R JOANE Thermometer 93 =c R/2 Metal bar ER Un=fa (6) Figure P2.3 Three-capacitance thermal system. (a) Cross-sectional view; (b) Electrical analog. P2. mat COR foll Prod P2.6