P4.15 Figure P4.15 shows the model of a two-tank system containing a heated liquid, where To(s) is the tempera- ture of the fluid flowing into the first tank and T₂(s) is the temperature of the liquid flowing out of the second tank. The system of two tanks has a heater in the first tank with a controllable heat input Q. The time con- stants are ₁ = 10s and 72 = 50 s. (a) Determine T₂(s) in terms of To(s) and Tza(s). (b) If Tza(s), the desired output temperature, is changed instantaneously from Tza(s) A/s to Tza(s) = 2A/s, where To(s) = A/s, determine the transient response of T₂(s) when Ge(s) = K = 500. (c) Find the steady-state errores, for the system of part (b), where E(s) = Tza(s) - T₂(s). 71 To(s) 1 (715+ 1)(728 + 1) Q(s) 1/100 Ge(s) (718+ 1)(728+1) + FIGURE P4.15 Two-tank temperature control. + T₂(s) E(s) T2d(s)