Question

Consider two tanks in series. Water flows into the first tank at a rate controlled by a control valve. The height of water in each tank is measured by a transducer at the bottom of the tank. The time constant for these transducers is 5 msec. These heights are sent to a Pl controller that outputs a voltage to the control valve. (You may assume the control ler simply outputs a flowrate.) The flowrate out of each tank is proportional to the height of fluid in that tank. (F1 h1/R, F2 = h2/R2). The diameter of the first tank is 18 inches. The diameter of the second tank is 20 inches. The height of both tanks is 24 inches. At steady state, the flowrate from the control valve is 1.0 gal/min. The height of water in the first tank is 12 inches, the height of water in the second tank is 10 inches. Derivation of Transfer Function Derive the transfer function for each tank to determine the height in each tank as a function of the inlet flowrate. That is, what is H(s)/F/(s) and what is Hz2(s)/F{ (s), where H, H2, and F are the shifted variables? Show all steps, including any shifting of variables necessary to perform a Laplace transform 1. Block Diagram and Transfer Function Simplification 2. Sketch out two block diagrams for the system, including the PI controller. One diagram should be to control the height of the first tank, the second diagram to control the height of the second tank. Include the transfer function for the transducers. For each "stream" on the diagram, list the units of that stream. 3. Determine the overall transfer function for both systems. What order is each system? (There is a lot of algebra that must be done here. Show your work.)

please do 1,2,3

Answer 1

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Above is the problem 1 and it's a non-interacting system as it was given F₁ = H₁ / R₁ and F₂ = H₂ / R_2.

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