groups topics 2006
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Assessment 2
Group AssignmentDue Date: 16 October 2006
List of Groups
No
1 Shaun O'connell Ismail Ibrahim Naser Al Hadabi Ankit Munjal Alan
2 Kain Buren Ahmed Iruhas Francis Ally Phillip Murdoch Christop
3 Ben Taylor Abdulla Lugmann Waleed Al Saidi Landon Kibby
4 Mohamed Nishan William West Benjamin Fitzegerald
Topic 2 5 4b 3
Group 1 Group 2 Group 3 Group 4
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Control Systems
1. L iquid-level control system
Design and simulate the following liquid level control system. Consider the effect of a
disturbance qd(t).
Figure 1 Liquid level system
(Seborg et al, Process Dynamics and Control)
h
qo
qi
V
R
Cross-sectional area A
Input flow rateDisturbance qd(t)
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2. Temperature control system
Figure 2 shows an arrangement of an industrial heating and cooling system. Analyse the system
into its component parts and identify the function of each.
Figure 2 Air-conditioning system
Recorder &
controller
Thermocouple
Cold water
Hot water
Fan
Three
way
valve
Drain
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3. Flow control system
Using the experimental data, simulate the following flow control system.
Figure 3 Flow control system
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4a. Stirred-tank blending system
Figure 4a Stirred-tank blending system
4b. Stirred-tank heating system
Figure 4b Stirred-tank heating system
(Seborg et al, Process Dynamics and Control)
x, V
x2
w2
x1
w1
V
QT
w
Ti
wi
Heater and
SCR
Thermocouple
TT TC
SCR = silicon controlled rectifier p
x, w
TT AC
I/P
xsp
xm
pt
p
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5. Liquid level control system
Suppose that two liquid surge tanks are placed in series so that the outflow from the first tank is
the inflow to the second tank, as shown in the following figure. If the outlet flow rate from eachfunction is linearly related to the height of the liquid (head) in that tank, find the transfer function
relating the changes in flow rate from the second tank, Q2(s), to changes in flow rate into the firsttank, Qi(s). Show how this transfer function is related to the individual transfer function,
H1(s)/Qi(s), Q1(s)/H1(s), H2(s)/Q1(s) and Q2(s)/H2(s). H1(s) and H2(s) denoted the deviations in
Tank 1 and Tank 2 levels, respectively. Assume that the two tanks have different areas A1 and A2,and that the valve resistances are fixed at R 1 and R 2.
Figure 5 Liquid level two tank system
Make a simulation program for the system. Suppose if the system is added a disturbance qd, use
the simulation program to analyse how the disturbance gives affect on the system response.
D1 = 0.75 m (diameter of Tank 1), C1 = 2.5 m2, R 1 = 0.5 sec/m2, D2 = 0.5 m (diameter of Tank 2),C2 = 2.0 m
2, R 2 = 0.75 sec/m
2, qi = 0.1 m
3/sec.
Units: V [m3], A [m
2], R [sec/m
2], C [m
2], q[m
3/sec], h[m]
h1
qi
V1 R 1
Cross-sectional area A1
qd
h2
q2 V2
R 2
Cross-sectional area A2
q1
Controller
LT
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6. Steel-rolling process control system
Propose a control system to maintain the thickness of plate produced by the final stand of rollers
in a steel rolling mill as shown in Figure 6a.
a) The input will be desired plate thickness and the output will be the actual thickness. b) The required thickness will be set by a dial control incorporating a position transducer which
produces an electrical signal proportional to the desired thickness. The output thickness will
have to be measured using a device such as β-ray thickness gauge with amplification to provide a suitable proportional voltage.
c) With two voltage signals, an operational amplifier will be suitable as a comparison element.d) The desired power for moving the nip roller will require hydraulic actuation.
e) A power piston regulated by an electro-hydraulic servo-valve will be suitable.
Figure 6a Thickness control system
(pp. 137, Automatic Control Systems, Kuo and Golnaraghi)
Electro-hydraulic
servo valve
Power
piston
β-gauge
Input
Rotary
potentiometer Amplifier
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The schematic diagram of a steel-rolling system is shown in the following figure. The steel plate
is fed through the rollers at a constant speed of v m/sec. The distance between the rollers and the
point where the thickness is measured is d m. The rotary displacement of the motor, m (t)θ , is
converted to the linear displacement y(t) by the gear box and linear actuator combination. y(t) =
mn (t)θ , where n is a positive constant in m/rad. The equivalent inertia of the load that is reflected
to the motor shaft is JL.
Figure 6b Steel-rolling control system
Amplifier
K
R a La
M
TmK i, K b, Jm, Bm
ea e
mθGear train
nController
Gc(s)ia
Linear
actuator
vy(t)
Thickness
sensor K s
r(t) e(t)
d
b(t)
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7. Liquid level control system
Consider the liquid level control system shown in the following figure. The inlet valve is
controlled by a hydraulic integral controller. Assume that the steady state pilot valve
displacement is 0X = , 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 disturbanceinflow rate qd, which is small quantity, is applied to the water tank at t = 0. This disturbance
causes the head to change from H to hH + . This change results in a change in the outflow rate
by qo. Through the hydraulic controller, the changes in head causes a change in the inflow rate
from Q to iqQ + . (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.
Assume the following numerical values for the system: C = 2 m2, R = 0.5 sec/m
2, K v = 1 m
2/sec,
a = 0.25 m, b = 0.75 m, K 1 = 4 sec-1
,
Figure 7 Liquid level control system with hydraulic valve
obtain the response h(t) when the disturbance input qd is a unit-step function. Also obtain this
response h(t) with MATLAB or Simulink.
H +h
Q +qi
VR
Cross-sectional area A
h
Q +qo
Y +qd
bax
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8. Servo control system
Simulate the following servo control system:
Figure 8 Servo control system
K 1 ev
R a La
K 1ev ia
r
er ec
c
T θ
c
Input
device
Reference input Input potentiometer
Output potentiometer
Feedback signal
Error measuring device Amplifier Motor Gear train Load
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9 Speed Control System
Simulate the following speed control system:
Figure 9 Speed control system
Oil under
pressure
k
b
Engine
z
y
e
ω
a2 a1
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10. DC motor remote position control system
Simulate the following DC motor remote position control system:
Figure 10 A remote position control system
Error Amplifiers
Input position
Potentiometer
Potentiometer
Output
position
D.C. motor
Load
Reduction
gearbox
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11. Liquid level control system
The following figure shows the closed-loop control system ‘liquid-level control system’ with the
following parameters and equations:
Motor resistance R a = 10 Ω
Torque constant K i = 10 oz-in./ABack-emf constant K b = 0.0706 V/rad/sec
Load inertia JL = 10 oz-in.-sec2
Amplifier gain K a = 50
Motor inductance La = 0 H
Rotor inertia Jm = 0.005 oz-in.-sec2
Gear ratio n = N1/N2 = 1/100
Load and motor friction = negligible
Area of tank A = 50 ft2
Figure 11 Liquid level control with a dc motor
a a a b me (t) R i (t) K (t)ω+
Amplifier
K a
R a La
MJm
R s
eu
Es
e e
θ
yθ
ei
One turn pot
K s
Gear train
n
qo
h
R
Reservoir
h(t)
Tank
r(t) Float
Nqi(t)
N inlet
valves
Controller
G(s)
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mm
d (t)(t)
dt
θω =
2 mm i a m L
d (t)T K i (t) (J n J )
dt
ω
= = +
y m(t) n (t)θ θ
The number of valves connected to the tank from the reservoir is N = 10. All the valves have the
same characteristics and are controlled simultaneously by yθ . The equations that govern the
volume of flow are as follows:
i I yq (t) K N (t)θ
o oq (t) K h(t)
volume of tank hare of tank
= = i o1 [q (t) q (t)]dtA
−∫
The error detector is modelled as: K s = 1 V/ft, e(t) = K s[r(t) – h(t)].
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12 Electro-hydraulic servo system
Figure 12 shows the arrangement of an electro-hydraulic servo system for manually operating an
aerodynamic control surface.a) The input and output resistance potentiometers are transducers for converting linear
displacement into a voltage. b) The differential amplifier is the comparison element generating the error signal.
c) The amplifier is the controller producing an amplified error signal.
d) The electro-hydraulic servo valve is the control element, controlling the flow of high pressureoil to the actuator which moves the load.
Figure 12 An electro-hydraulic servo system
Potentiometer
Potentiometer
Required
motion
Differential
amplifier Amplifier
Electro-hydraulicservo valve
Load
Output
motion
Feedback
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13 DC motor control system
The schematic diagram of a feedback control system using a dc motor is shown in Figure 11-6.
The torque developed by the motor is Tm(t) = K iia(t), where K i is the torque constant. Theconstants of the system are:
K s = 2 R = 2 Ω R s = 0.1 Ω K b = 5 V/rad/s K i = 5 Nm/A La = 0 H
Jm + JL = 0.1 Nms2
Bm = 0 Nms
Assume that all the units are consistent so that no conversion is necessary.
Figure 13 DC motor control system
K
R a La
M
JmR s
LOADeu
Es
Lθ
r θ
e e
yθ
yθ
ea
es
One turn pot
K s
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14 Permanent magnet dc motor control system
The following schematic diagram shows a permanent magnet dc motor control system with a
viscous inertia damper. The system can be used for the control of the print wheel of an electronicword processor. A mechanical damper such as the viscous inertia type is sometimes used in
practice as a simple and economical way of stabilising a control system. The damping effect isachieved by a rotor suspend in a viscous fluid. The differential and algebraic equations that
describe the dynamics of the system are as follows:
[ ]s r me(t) K (t) (t)= ω − ω sK = 1 V/rad/sec
a a a be (t) Ke(t) R i (t) e (t)= = + K = 10
b b me (t) K (t)= ω K b = 0.0706 V/rad/sec
[ ]m
m D m D
d (t)T (t) J K (t) (t)dt
ω
= + ω − ω J = Jh + Jm = 0.1 oz-in-sec2
m i aT (t) K i (t)= K i = 10 oz-in/A
[ ] DD m D R
d (t)K (t) (t) J
dt
ωω − ω = JR = 0.05 oz-in.sec
Ra = 1 Ω K D = 1 oz-in-sec
Figure 14 Permanent magnet dc motor control system
Controller Amplifier
R a M
DC motor
ea
e(t)
e
JR , Dω
mTK
ia
Jm ωm
ROTOR
Viscous fluid
K D
Viscous inertia damper
Housing
Jh
Controller
G(s)Controller
Amplifier
R a M
DC motor
ea
e(t)e
mTK
ia
Jm
ωm
ROTOR
Damper
ωr (t)
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15 Liquid level control system (2.13, pp. 49-50 Seborg et al)
Design and simulate the liquid level control for the following tank that has a leakage q 4.
Figure 15 Liquid level control system with the disturbance and leakage
(Seborg et al, Process Dynamics and Control)
h
qo
qi
V
R
Cross-sectional area A
Input flow rate q2(t)
q4
hl