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Question: (a) The final value theorem seems to demonstrate that the offset tends to zero as the controller gain approaches infinity. Discuss this result, especially with regard to the definition of the Laplace transform and the dynamic responses shown in Figure.

(b) The final value theorem provides one method for calculating the final value of a variable in a control system. Describe another way to determine the final value of variables without using the final value theorem. Use both methods to determine the final value of the manipulated variable in the three-tank mixing process for a step disturbance in the concentration of stream B, (a) without control and (b) with P-only feedback control.

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