An electrically heated, stirred-tank system is shown in figure. Using the given information do the following:

(a) Draw a block diagram for the case where T₃ is the controlled variable and voltage signal V₂ is the manipulated variable. 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 T₀ is constant.

3. A 0.75.gallmln decrease in q₀ ultimately makes T₁ increase by 3 ?F. Two-thirds of this total temperature change occurs in 12min. This change in q₀ 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 lest 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 min.

6. The thermocouple output is amplified to give V₃ = 0,15T₃ + 5, where V₃ [=] volts and T₃ [=] ?F.

7. The pipe connecting the two tanks has a mean residence time of 30 s.

To 90 SCR Power ap T2 90 Tank 1 T3 SCR Power amp T3 TT Tank 2