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



1

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)



2

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



3

3. Flow control system

Using the experimental data, simulate the following flow control system.

Figure 3 Flow control system



4

4a. Stirred-tank blending system

Figure 4a Stirred-tank blending system

4b. Stirred-tank heating system

Figure 4b Stirred-tank heating system


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



5

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



6

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



7

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)



8


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


h

Q +qo

Y +qd

bax



9

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



10

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



11

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



12


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)



13

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)].



14

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



15

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



16

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)



17

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


h

qo

qi

V

R


Input flow rate q2(t)

q4

hl

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