B-4-10. Consider the liquid-level control system shown in Figure 4-52. The inlet valve is controlled by a hydraulic integral controller. Assume that the steady-state inflow rate is and steady-state outflow rate is also Q, the steady-state head is H, steady-state pilot valve displacement is X = 0, and steady-state valve position is Y. We assume that the set point R corresponds to the steady-state head H. The set point is fixed. Assume also that the disturbance inflow rate 94, which is a small quantity, is applied to the water tank at = 0. This disturbance causes the head to change from to H+h. This change results in a change in the outflow rate by qo. Through the hydraulic controller, the change in head causes a change in the inflow rate from 0 to + q. (The integral controller tends to keep the head constant as much as possible in the presence of disturbances.) We assume that all changes are of small quantities.
B-4-10. Consider the liquid-level control system shown in Figure 4-52. The inlet valve is controlled by a hydraulic integral controller. Assume that the steady-state inflow rate is and steady-state outflow rate is also Q, the steady-state head is H, steady-state pilot valve displacement is X = 0, and steady-state valve position is Y. We assume that the set point R corresponds to the steady-state head H. The set point is fixed. Assume also that the disturbance inflow rate 94, which is a small quantity, is applied to the water tank at = 0. This disturbance causes the head to change from to H+h. This change results in a change in the outflow rate by qo. Through the hydraulic controller, the change in head causes a change in the inflow rate from 0 to + q. (The integral controller tends to keep the head constant as much as possible in the presence of disturbances.) We assume that all changes are of small quantities.
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![B-4-10. Consider the liquid-level control system shown in
We assume that the velocity of the power piston (valve)
dy
dt
Figure 4-52. The inlet valve is controlled by a hydraulic is proportional to pilot-valve displacement x. or
integral controller. Assume that the steady-state inflow rate
is and steady-state outflow rate is also, the steady-state
head is , steady-state pilot valve displacement is X = 0,
and steady-state valve position is Y. We assume that the set
point R corresponds to the steady-state head H. The set
point is fixed. Assume also that the disturbance inflow rate
94, which is a small quantity, is applied to the water tank at
t = 0. This disturbance causes the head to change from H to
H+h. This change results in a change in the outflow rate
by qo. Through the hydraulic controller, the change in head
causes a change in the inflow rate from Q to Q + q. (The
integral controller tends to keep the head constant as much
as possible in the presence of disturbances.) We assume that
all changes are of small quantities.
=
K₁.x
where K, is a positive constant. We also assume that the
change in the inflow rate q; is negatively proportional to the
change in the valve opening y, or
9i= -Kry
where K, is a positive constant.
Assuming the following numerical values for the system,
C = 2m², R = 0.5 sec/m²,
1 m²/sec
=
a = 0.25 m.
b = 0.75 m.
obtain the transfer function H(s)/Q(s)|
K₂
K₁
=
4 sec¹](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67cb9962-653a-4ebe-9566-d5454f5d6c0d%2F2d78f67a-ddec-4455-bd92-19fb2fa4e7e6%2Fcl8flyt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:B-4-10. Consider the liquid-level control system shown in
We assume that the velocity of the power piston (valve)
dy
dt
Figure 4-52. The inlet valve is controlled by a hydraulic is proportional to pilot-valve displacement x. or
integral controller. Assume that the steady-state inflow rate
is and steady-state outflow rate is also, the steady-state
head is , steady-state pilot valve displacement is X = 0,
and steady-state valve position is Y. We assume that the set
point R corresponds to the steady-state head H. The set
point is fixed. Assume also that the disturbance inflow rate
94, which is a small quantity, is applied to the water tank at
t = 0. This disturbance causes the head to change from H to
H+h. This change results in a change in the outflow rate
by qo. Through the hydraulic controller, the change in head
causes a change in the inflow rate from Q to Q + q. (The
integral controller tends to keep the head constant as much
as possible in the presence of disturbances.) We assume that
all changes are of small quantities.
=
K₁.x
where K, is a positive constant. We also assume that the
change in the inflow rate q; is negatively proportional to the
change in the valve opening y, or
9i= -Kry
where K, is a positive constant.
Assuming the following numerical values for the system,
C = 2m², R = 0.5 sec/m²,
1 m²/sec
=
a = 0.25 m.
b = 0.75 m.
obtain the transfer function H(s)/Q(s)|
K₂
K₁
=
4 sec¹
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