Question

Consider the control structure for the overhead section of a distillation column shown in the figure. The composition controller (CC) controls the heavy key impurity in the distillate by adjusting the setpoint of the reflux flow controller in a cascade arrangement. The sign of the controller gain for the pressure controller (PC) and that for the composition controller (CC) are, respectively: \includegraphics[width=0.5\linewidth]{q23 CE.PNG}

• A. negative, negative
• B. negative, positive
• C. positive, positive
• D. positive, negative

Hint:

For cascade control systems, analyze the corrective action needed for each controller in the loop. Positive gain increases the controlled variable, while negative gain reduces it based on the error signal.

Answer 1

The Correct Option is D

Step 1: Analyze the function of the pressure controller (PC). The pressure controller (PC) is responsible for maintaining the column pressure. If the pressure increases, the controller adjusts the valve to reduce the pressure. Hence, a positive gain is required for the pressure controller to provide the correct action (i.e., increase valve opening when pressure increases). Step 2: Analyze the function of the composition controller (CC). The composition controller (CC) adjusts the setpoint of the reflux flow controller to control the heavy key impurity in the distillate. If the impurity concentration increases, the controller increases the reflux flow to reduce the impurity. This requires a negative gain for the composition controller to ensure the proper corrective action. Step 3: Conclusion. The pressure controller (PC) has a positive gain, and the composition controller (CC) has a negative gain.