Process tank has two input streams - Stream 1 at mass flow rate F1 and Stream 2 at mass flow rate F2. The tank's effluent stream, at flow rate F, discharges through a fixed valve to atmospheric pressure. The pressure drop across the valve is proportional to the flow rate squared. The cross-sectional area of the tank, A, is S m^2, and the mass density of all streams is 940 kg/m^3.
(a) Draw a schematic diagram of the process and write an appropriate dynamic model for the tank level. What is the corresponding steady-state model?
(b) At initial steady-state conditions, with F1 = 2.0 kg/s and F2 = 1.2 kg/s, the tank level is 2.25 m. What is the value of the valve constant (give units)?
(c) A process control engineer decides to use a feed-forward controller to hold the level approximately constant at the set-point value (h_sp = 2.25) by measuring F1 and manipulating F2. What is the mathematical relation that will be used in the controller? If the F1 measurement is not very accurate and always supplies a value that is 1.1 times the actual flow rate, what can you conclude about the resulting level control? (Hint: Consider the process initially at the desired steady-state level and with the feed-forward controller turned on. Because the controller output is slightly in error, F2 ≠ 1.2, so the process will come to a new steady state. What is it?)
(d) What conclusions can you draw concerning the need for accuracy in the steady-state model? For the accuracy of the measurement device? For the accuracy of the control valve? Consider all of these with respect to their use in a feed-forward control system.