11.8 An electrically heated, stirred-tank system is shown in Fig. E11.8. Using the given information, do the following: (a) Draw a block diagram for the case where T3 is the con- trolled variable and voltage signal V2 is the manipulated vari- able. Derive an expression for each transfer function. (b) Repeat part (a) using V₁ as the manipulated variable. (c) Which of these two control configurations would provide better control? Justify your answer. Available Information 1. The volume of liquid in each tank is kept constant using an overflow line. 2. Temperature To is constant. 3. A 0.75-gal/min decrease in 90 ultimately makes T₁ in- crease by 3 °F. Two-thirds of this total temperature change occurs in 12 min. This change in 90 ultimately results in a 5 °F increase in T3. 4. A change in V₁ from 10 to 12 volts ultimately causes T₁ to change from 70 to 78 °F. A similar test for V2 causes T3 to change from 85 to 90 °F. The apparent time constant for these tests is 10 min. 5. A step change in T2 produces a transient response in T3 that is essentially complete in 50 (= 7 min). 6. The thermocouple output is amplified to give V3 = 0.1573 +5, where V3 [=] volts and T3 [=] °F. 7. The pipe connecting the two tanks has a mean residence time of 30 s. V₁ Το 90 SCR Power amp Figure E11.8 M V2 T1 0 T2 40 Tank 1 SCR Power amp M C T3 90 T3 TT Tank 2