1) Consider the liquid-level system shown in the figure, where the free surfaces are indicated by...

  

Transcribed Image Text:

1) Consider the liquid-level system shown in the figure, where the free surfaces are indicated by the triangles. Assume constant ambient pressure, ideal (frictionless) pipes and incompressible fluid. reservoir A qA(t) C Pi(t) V 9B (t) reservoir B R C2 Po P2(t) 92(t) Determine the following: a) The list of all the inputs and outputs (unknowns). b) Derive the system equations and express them in Laplace domain. (Note: Assume gauge pressures (p), for p and P2. where, p p Po) c) Express the ODEs obtained in part (b) in the matrix form: A(s)X(s) = U(s). 91(t) SYMBOL: INTERPRETATION: Po Ambient pressure. R1, R2 C1,C2 Flow resistances of the valves #1 and #2. Capacitances of the tanks #1 and #2. 91(t), 92(t) Flow rates through valves #1 and #2. qa(t), 98(t) Pi(t). P2(t) Flow rates entering through the reservoirs A and B. Pressures at the bottom of tanks #1 and #2. Table 1: Model parameters and variables. d) Assuming: C = 2, C = 1, R = 1, R2 = 2, solve for the unknown X(s) in MATLAB, and obtain the transfer function for the pressure at the bottom of the tank #2, i.e., P(s). (Attach your MATLAB code). e) Using the transfer function from part (d), and taking constant flow rates: Q = 10, Q = 5, simulate the system in SIMULINK up to 50 sec., and plot the variation of the gauge pressure in the tank 2, i.e., p2(t). (Attach your SIMULINK block diagram and the generated plot). 1) Consider the liquid-level system shown in the figure, where the free surfaces are indicated by the triangles. Assume constant ambient pressure, ideal (frictionless) pipes and incompressible fluid. reservoir A qA(t) C Pi(t) V 9B (t) reservoir B R C2 Po P2(t) 92(t) Determine the following: a) The list of all the inputs and outputs (unknowns). b) Derive the system equations and express them in Laplace domain. (Note: Assume gauge pressures (p), for p and P2. where, p p Po) c) Express the ODEs obtained in part (b) in the matrix form: A(s)X(s) = U(s). 91(t) SYMBOL: INTERPRETATION: Po Ambient pressure. R1, R2 C1,C2 Flow resistances of the valves #1 and #2. Capacitances of the tanks #1 and #2. 91(t), 92(t) Flow rates through valves #1 and #2. qa(t), 98(t) Pi(t). P2(t) Flow rates entering through the reservoirs A and B. Pressures at the bottom of tanks #1 and #2. Table 1: Model parameters and variables. d) Assuming: C = 2, C = 1, R = 1, R2 = 2, solve for the unknown X(s) in MATLAB, and obtain the transfer function for the pressure at the bottom of the tank #2, i.e., P(s). (Attach your MATLAB code). e) Using the transfer function from part (d), and taking constant flow rates: Q = 10, Q = 5, simulate the system in SIMULINK up to 50 sec., and plot the variation of the gauge pressure in the tank 2, i.e., p2(t). (Attach your SIMULINK block diagram and the generated plot).