5. In many industrial and chemical systems, temperature is an important variable to regulate. A basic representation of a thermal control system is shown in Figure 4. The temperature is controlled

using a heater with resistance R. Assume that E₁ (s) = kaEE(s), where ka is the constant of the actuator. When/nthe difference between and the external temperature Te is small, the following relationship holds where I (s): = kika Et TS +1 -E(s) + 1 Ts +1 Te(s), T = MC/P(A), M = mass in tank, A = surface area of tank p = heat transfer constant C = specific heat constant k₁ = a dimensionality constant. Draw a block diagram for the system above (hint: the external temperature is basically a disturbance). What is the transfer function from E(s) to 7(s)? Determine and compare the open-loop and closed-loop systems for a. sensitivity to changes in the constant K = k₁kaEb; b. the ability to reduce the effects of a step disturbance in the environmental tem- perature ATC(s); c. the steady-state error of the temperature for a step change in the input, Edes (s).