Exercise 3 Consider the system shown in Figure 4. It includes a block with thermal capacitance C that is heated at the r

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Exercise 3 Consider The System Shown In Figure 4 It Includes A Block With Thermal Capacitance C That Is Heated At The R 1 (144.26 KiB) Viewed 35 times

Exercise 3 Consider the system shown in Figure 4. It includes a block with thermal capacitance C that is heated at the rate qi(t), a second block with temperature 0B (t) that's controlled using a second heating/cooling coil, and three thermal resistances (R₁, R₂ and one that is not specified). The system is perfectly insulated above and below- assume that heat only flows horizontally. Assume that the ambient temperature, a, is a constant. Find an incremental state-variable model for the system, measuring the temperatures relative to the ambient temperature. Include the derivation in your report. Note that you have been given all the information you need to find the necessary equation/s. Find the transfer function, H₁ (s) = that it equals where T₁ = R₁C and T₂ = 0₂ R₁ R₂C² C, OA R₂ OB(t) m m qi(t) Figure 4 A(S), for the situation where qi(t) = 0 and 04 (0) = 0₁. Show @B(S)' T2 (S+T₁+T₂) Include the derivation in your report. H₁(s) = There are two inputs to the system, qi(t) and 0B (t), and so there are two possible transfer functions. Find the other transfer function, H₂ (s) = Include that derivation in your report. A(S) Qi(s)