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3. Liquid-level Control System: (30 Points) A liquid level control system (refer to Fig 11.15 and Example 11.2 in Book) uses a computer controller with inputs and outputs in terms of full range (0 to 100%). The tank is 1.5 meters in diameter, with a control valve resistance [R] of 12 min/m². Level transmitter has a span of 2.0 meters [0 to 100% range], valve characteristic is given by: $f = (25)L^{-1}$, where L is the fraction of lift. When the control valve is fully open [L = 1], the flowrate through the valve is 0.35 m³/min. The air-to-open control valve receives a 3 to 15 psi signal from an I/P transducer, which receives a 0 to 100% signal from a proportional-only controller. At nominal operating conditions, the control valve is partially open (L = 0.4). Using an appropriate dynamic model, calculate the closed-loop response to a step change in set point of 0.5 meter, for the following controller gain: $K_c = 10$.

          3. Liquid-level Control System: (30 Points)
A liquid level control system (refer to Fig 11.15 and Example 11.2 in Book) uses a computer controller
with inputs and outputs in terms of full range (0 to 100%). The tank is 1.5 meters in diameter, with a
control valve resistance [R] of 12 min/m². Level transmitter has a span of 2.0 meters [0 to 100%
range], valve characteristic is given by: $f = (25)L^{-1}$, where L is the fraction of lift. When the control valve
is fully open [L = 1], the flowrate through the valve is 0.35 m³/min. The air-to-open control valve
receives a 3 to 15 psi signal from an I/P transducer, which receives a 0 to 100% signal from a
proportional-only controller. At nominal operating conditions, the control valve is partially open (L = 0.4).
Using an appropriate dynamic model, calculate the closed-loop response to a step change in set point
of 0.5 meter, for the following controller gain: $K_c = 10$.

$3. Liquid-level Control System: (30 Points) A liquid level control system (refer to Fig 11.15 and Example 11.2 in Book) uses a computer controller with inputs and outputs in terms of full range (0 to 100%). The tank is 1.5 meters in diameter, with a control valve resistance [R] of 12 min/m². Level transmitter has a span of 2.0 meters [0 to 100% range], valve characteristic is given by: f = (25)L^-1, where L is the fraction of lift. When the control valve is fully open [L = 1], the flowrate through the valve is 0.35 m³/min. The air-to-open control valve receives a 3 to 15 psi signal from an I/P transducer, which receives a 0 to 100% signal from a proportional-only controller. At nominal operating conditions, the control valve is partially open (L = 0.4). Using an appropriate dynamic model, calculate the closed-loop response to a step change in set point of 0.5 meter, for the following controller gain: Kc = 10.$

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