Determine the analytical expression for a step set point change in the following processes under P-only and PI feedback control. You should select values for the tuning constant that give acceptable performance. (a) Example 3.1 with CA as the controlled variable, Cao as the manipulated variable, and ∆SP = 0.1 mole/m3. (b) Example 3.7 with T as the controlled variable, F as the manipulated variable, and ∆SP = 3°C. (Fc is constant.) (c) Example 3.3 with ∆A2 as the controlled variable, Cao as the manipulated variable, and ∆SP = 0.05 mole/m3. EXAMPLE 3.1. Validation. The mixing tank was built, the experiment was performed, and samples of the outlet material were analyzed. The data points are plotted in Figure 3.4 along with the model prediction. By visual evaluation and considering the accuracy of each data point, one would accept the model as “valid” (or, more accurately, not invalid) for most engineering applications. EXAMPLE 3.3. Two isothermal CSTR reactors A problem similar to the single CSTR is presented, with the only difference that two series reactors are included Each tank is one-half the volume of the tank . EXAMPLE 3.7. Stirred-tank heat exchanger To provide another simple example of an energy balance, the stirred-tank heat exchanger in Figure 3.9 is considered.