Question

Consider the liquid-level control system in Figure 2 below. This system has a valve, a controller, a process and a level transmitter. The level transmitter has negligible dynamics, while the control valve has a time constant of 10 seconds. In addition, the following data is available: A = 3$ft^2$, the steady-state flow rate out, $q_3$ = 10 gal/min, $K_v$ = -1.3 gal/min/mA and $K_m$ = 4 mA/ft. $q_1$ h $q_2$ $h_m$ LT LC p $q_3$ Fig. 2: Liquid-level Control System + Pump in Exit Line a) Develop the block diagram (35 points) b) Derive the set-point transfer function (10 points) c) Determine the numerical values of $K_c$ and $\tau_I$ for a Proportional Integral controller that will result in a stable closed-loop system. (20 points)

          Consider the liquid-level control system in Figure 2 below. This system has a valve, a
controller, a process and a level transmitter. The level transmitter has negligible
dynamics, while the control valve has a time constant of 10 seconds. In addition, the
following data is available:
A = 3$ft^2$, the steady-state flow rate out, $q_3$ = 10 gal/min, $K_v$ = -1.3 gal/min/mA and
$K_m$ = 4 mA/ft.
$q_1$
h
$q_2$
$h_m$
LT
LC
p
$q_3$
Fig. 2: Liquid-level Control System + Pump in Exit Line
a) Develop the block diagram (35 points)
b) Derive the set-point transfer function (10 points)
c) Determine the numerical values of $K_c$ and $\tau_I$ for a Proportional Integral controller that
will result in a stable closed-loop system. (20 points)

Consider the liquid-level control system in Figure 2 below. This system has a valve, a
controller, a process and a level transmitter. The level transmitter has negligible
dynamics, while the control valve has a time constant of 10 seconds. In addition, the
following data is available:
A = 3ft^2, the steady-state flow rate out, q3 = 10 gal/min, Kv = -1.3 gal/min/mA and
Km = 4 mA/ft.
q1
h
q2
hm
LT
LC
p
q3
Fig. 2: Liquid-level Control System + Pump in Exit Line
a) Develop the block diagram (35 points)
b) Derive the set-point transfer function (10 points)
c) Determine the numerical values of Kc and for a Proportional Integral controller that
will result in a stable closed-loop system. (20 points)

Added by Anthony M.

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