BCT-Module 04.pdf

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Lecture Notes

BASIC CONTROL THEORY

Module 4Control Elements

SEPTEMBER 2005

Prepared by Dr. Hung Nguyen


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TABLE OF CONTENTS

Table of Contents..............................................................................................................................i

List of Figures..................................................................................................................................ii

List of Tables ................................................................................................................................. iii

References ......................................................................................................................................iv

Objectives ........................................................................................................................................v

1. General Structure of a Control System........................................................................................1

2. Comparison Elements..................................................................................................................2

2.1 Differential Levers (Walking Beams)...................................................................................22.2 Potentiometers ......................................................................................................................3

2.3 Synchros................................................................................................................................4

2.4 Operational Amplifiers .........................................................................................................5

3. Control Elements .........................................................................................................................7

3.1 Process Control Valves .........................................................................................................7

3.2 Hydraulic Servo Valve ........................................................................................................11

3.3 Hydraulic Actuators ............................................................................................................15

3.4 Electrical Elements: D.C. Servo Motors.............................................................................163.5 Electrical Elements: A.C. Servo Motors.............................................................................18

3.6 Hydraulic Control Element (Steering Gear) .......................................................................18

3.7 Pneumatic Control Elements ..............................................................................................194. Exampples of Control Systems..................................................................................................22

4.1 Thickness Control System ..................................................................................................22

4.2 Level Control System .........................................................................................................23Summary of Module 4...................................................................................................................23

Exercises........................................................................................................................................24


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LIST OF FIGURES

Figure 4.1.........................................................................................................................................1

Figure 4.2.........................................................................................................................................3

Figure 4.3.........................................................................................................................................3Figure 4.4.........................................................................................................................................4

Figure 4.5.........................................................................................................................................5

Figure 4.6a.......................................................................................................................................6

Figure 4.6b.......................................................................................................................................6

Figure 4.7.........................................................................................................................................8Figure 4.8.........................................................................................................................................9

Figure 4.9.......................................................................................................................................10

Figure 4.10.....................................................................................................................................11

Figure 4.11.....................................................................................................................................12Figure 4.12.....................................................................................................................................13

Figure 4.13.....................................................................................................................................14

Figure 4.14.....................................................................................................................................15

Figure 4.15.....................................................................................................................................15

Figure 4.16.....................................................................................................................................17

Figure 4.17.....................................................................................................................................18

Figure 4.18.....................................................................................................................................19Figure 4.19.....................................................................................................................................20

Figure 4.20.....................................................................................................................................21Figure 4.21.....................................................................................................................................22

Figure 4.22.....................................................................................................................................22Figure 4.23.....................................................................................................................................24

Figure 4.24.....................................................................................................................................24

Figure 4.25.....................................................................................................................................25

Figure 4.26.....................................................................................................................................25

Figure 4.27.....................................................................................................................................26


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LIST OF TABLES


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iv

REFERENCES

Chesmond, C.J. (1990),Basic Control System Technology, Edward Arnold, UK.

Haslam, J.A., G.R. Summers and D. Williams (1981),Engineering Instrumentation and Control,London, UK.

Kou, Benjamin C. (1995),Automatic Control Systems, Prentice-Hall International Inc., Upper

Saddle River, New Jersey, USA.

Ogata, Katsuhiko (1997),Modern Control Engineering, 3rd Edition, Prentice-Hall International

Inc., Upper Saddle River, New Jersey, USA.

Richards, R.J. (1993), Solving in Control Problems, Longman Group UK Ltd, Harlow, Essex,UK.

Seborg, Dale E., Thomas F. Edgar and Duncan A. Mellichamp (2004),Process Dynamics and

Control, 2nd

Edition, John Wiley & Sons, Inc., Hoboken, New Jersey, USA.

Taylor, D.A. (1987),Marine and Control Practice, Butterworths, UK.


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AIMS

1.0 Explain general structure of a control system and its components.

LEARNING OBJECTIVES

1.1 Describe a general structure of a control system by a block diagram.

1.2 State function of each block in a control system

1.3 Describe components of a control system: process, transducers, recorders, comparison

elements, controllers and final control elements


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1. General Structure of a Feedback Control System

Automatic control systems, including their recording elements, may be represented by a general

block diagram as shown in the following figure.

Figure 4.1 General structure of a feedback control system

Input: The input signal is also called reference signal or set-point signal. It is a desired signal that

is kept stable. The set-point signal can be set by an operator or by a control program.

Output: The output signal is also called process variable (PV). It is an actual signal. The output

signal is often measured by a transducer or transmitter and fed back to the comparison element in

the closed-loop control system. The output is indicated by a recorder or a display.

Error: The error signal is also called an actuating error. It is the difference between the set-point

signal and the measured output signal.

Process: The process block represents the overall process. All the properties and variables that

constitute the manufacturing or production process are a part of this block. The process is also

called a plant or a dynamic system in which the controlled variable is regulated as desired. The

dynamic behaviour of the process can be expressed by an ordinary differential equation. SeeModules 1 through 3.

Transducer: The transducer block represents whatever operations are necessary to determine the

present value of the controlled variables. The transducer block is also called the measurementblock. The transducer is used to measure the process variable or output and feedbacks the

measured output to the comparator. The output of this block is a measured indication of the

controlled variable expressed in some other form, such as voltage, current, or a digital signal.

Recorder: The recorder or indicating device indicates or displays the measured output.

Comparison Element: The comparison element is also called a comparator that detects an error,

a difference between the set-point signal and the measured output signal. The comparison

elements compare the desired input with the output and generate an error signal. The comparison

Controller+_Input r(t) Output y(t)Control

elementProcess

Transducer Recorder

Error e(t)

Comparison

element

u(t)

Feedback signal


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element may be one of the following types: mechanic types such as differential levers, electric

types such as potentiometer, operational amplifier and synchros.

Controller: The control block is the part of the loop that determines the changes in thecontrolling variable that are needed to correct errors in the controlled variable. This blockrepresents the brains of the control system. The output of this block will be a signal, called thefeedback signal, that will change the value of the controlling variable in the process (plant or

dynamic system) then thereby the controlled variable. The controller acts on the actuating error

and uses this information to produce a control signal that drives the process. The controller often

has two tasks 1) being able to compute control signal/s and 2) being able to drive the system

being controlled. There are many types of controller such as pneumatic controller, hydraulic

controller, electrical and electronic controller and hybrid controller that is a combination of two

or more than two of the above types. In traditional analogue control systems, the controller is

essentially an analogue computer. In the computer-based control systems, the controller function

is performed using software. There are several algorithms for controller such as PID control,optimal control, self-tuning control, optimal control, neural network control and so on.

Control Element: The control element block is the part that converts the signal from the

controller into actual variations in the controlling variable. The control element is also called an

actuating element or an actuator in which the amplified and conditioned control signal is used to

regulate some energy source to the process. In practice, the control element is part of the processitself, as it must be to bring about changes in the process variables.

2. Comparison Elements

Comparison elements compare the output or controlled variable with the desired input orreference signal and generate an error or deviation signal. They perform the mathematical

operation of subtraction.

2.1 Differential Levers (Walking Beams)

Differential levers are mechanical comparison elements which are used in many pneumatic

elements and also in hydraulic control systems. They come in many varied an complex forms, atypical example being illustrated in Figure 4.2, which shows a type used in a Taylors Transcope

pneumatic controllers.

For purposes of analysis a differential lever can be considered as a simple lever which is free topivot at points R, S and T as illustrated in Figure 4.3. From Figure 4.3 for small movements:

i) considering R fixed: if x moves to the right then

xba

b

+= (4.1)

ii) considering T fixed: if y moves to the left then


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y)ba(

a

+= (4.2)

The total movement can be found by using the principle of superposition, which states that, for

a linear system, the total effect of several disturbances can be obtained by summation of the

effects of each individual disturbance acting alone. The total movement due to the motion of x

and y is therefore given by sum of (i) and (ii):

y)ba(

ax

)ba(

b

+

+= (4.3)

In many cases it is arranged that a = b, so that the lever is symmetrical, and then

)yx(21 = (4.4)

i.e. error2

1= or deviation

2

1=

It is important that the output movement at y is arranged to always be in the opposite direction to

the input x, i.e. a negative-feedback arrangement.

2.2 Potentiometers

Potentiometers are used in many d.c. electrical positioning servo-systems. They consist of a pair

of matched resistance potentiometers operating on the null-balance principle. The sliders aredriven by the input and output shafts of the control system as illustrated in Figure 4.4.

Figure 4.2 The motion plate for a

Taylors Transcope controllerFigure 4.3 The differential lever


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Figure 4.4 Error detection by potentiometers

If the same voltage is applied to each of potentiometer windings, an error voltage is generated

which is proportional to the relative positions. We have

( )0iPK = (4.5)

where1 = input-shaft position

0 = output-shaft position

KP = potentiometer sensitivity (volts/degree)

When the input and output shafts are aligned and,0i= , and the error voltage is zero, i.e.

null balance is achieved.

2.3 Synchros

Synchros are the a.c. equivalent of potentiometers and are used in many a.c. electrical systems for

data transmission and torque transmission for driving dials. They are also used to compare inputand output rotations in a.c. electrical servo-systems and rotating hydraulic systems.

To perform error detection, two synchros are used: one in the mode of a control transmitter, andthe other as a control transformer, as shown in Figure 4.5.

The synchros have their stator coils equally spaced at 120o

intervals. An a.c. voltage (often 115V

at 400Hz) is applied to the transmitter rotor, producing voltages in the stator coils (by transformer

action) which uniquely define the angular position of the rotor. These voltages are transmitted tothe stator coils of the transformer, producing a resultant magnetic field aligned in the same

direction as the transmitter rotor.


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The transformer rotor acts as a search coil in detecting the direction of its stator field. The

maximum voltage is induced in the transformer rotor coil when the rotor axis is aligned with the

field. Zero voltage is induced when the rotor axis is perpendicular. The in-line position of the

input and output shafts therefore requires the transformer rotor coil to be at 90 o to the transmitterrotor coil.

Figure 4.5 Error detection by synchros

The output voltage is an amplitude-modulated signal which requires demodulating to produce thefollowing relationship for small misalignment angles:

Output = K (input-shaft position output-shaft position)

= )(K 0i

where K = voltage gradient (volts/degree)

Compared to d.c. potentiometers, synchros have the following advantages:

a) a full 360o

of shaft rotation is always available;b) since they have no sliding contacts, their life expectancy is much higher, resolution is infinite,and hence they do not have noise problems;c) a.c. amplifiers can be employed and therefore are no drift problems.

However, phase-sensitive rectifiers are necessary to sense direction.

2.4 Operational Amplifiers

Operational amplifiers, or op. ams, are direct-coupled (d.c.) amplifiers with special

characteristics as


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High gain, 200000 to 106;

Phase reversal, i.e. the output voltage is of opposite sign to the input;

High input impedance.

Figure 4.6a Error detection by an operational amplifier

The input current to the amplifier can be assumed to be negligible, and

f21 iii =+ (4.6)

f

0

2

2

1

1

R

v0

R

0v

R

0v =

+

and

+= 2

2

f

1

f0 v

R

R

R

Rv (4.7)

If Rf= R1 = R2, v1 is made equal to input ( i ), and v2 is made equal to output ( 0 ), we have

)(v 0i0 =

= (error) (4.8)

The negative sign can be removed by using an inverter (as shown in the following example). Operational amplifiers are used in electrical control systems and as comparison elements in many

hydraulic positioning systems.

Example

In Figure 4.6, Rf = 1M , R1 = R2 = 0.1 M , v1 is a voltage proportional to the input

displacement i , and v2 is a voltage proportional to the output displacement 0 and is arranged to

be fed back in a negative sense. Assuming the proportional constant is 1V/degree, determine theamplification through the op.amp and show how the sign of the error output can be inverted.

Figure 4.6b An inverter

Rf

vov1

v2

R1

R2

ifi1

i2

Rf

vev0

R ifi


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We have

= 0i0 M1.0

M1

M1.0

M1v = ( )0i10 (4.9)

The amplification is therefore 4.

The sign of the error can be inverted as shown in Figure 4.6.

We have

fii = (4.10)

f

e0

R

v0

R

0v =

(4.11)

0f

e vR

Rv = (4.12)

and, if Rf is made equal to R,

0e vv = (4.13)

3. Control Elements (Actuators)

Control elements are those elements in which the amplified and conditioned error signal is usedto regulate some energy source to the process.

3.1 Process-control Valves

In many process systems, the control element is the pneumatically actuated control valve,

illustrated in Figure 4.7, which is used to regulate the flow of some fluid.

A control valve is essentially a pressure-reducing valve and consists of two major parts: the

valve-body assembly and the valve actuator.

a) Valve actuators

The most common type of valve actuator is the pneumatically operated spring-and-diaphragm

actuator illustrated in Figure 4.7, which uses air pressure in the range 0.2bar to 1.0bar unless apositioner is used which employs higher pressure to give larger thrusts and quicker action. Theair can be applied to the top (air-to-close) or the bottom (air-to-open) of the diaphragm,

depending on the safety requirements in the event of an air-supply failure.


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b) Val ve-body design

Most control-valve bodies fall into two categories: single-seated and double-seated.

+ Single-seated valves have a single valve plug and seat and hence can be readily designed fortight shut-off with virtually zero flow in the closed position. Unless some balancing arrangementis included in the valve design, a substantial axial stem force can be produced by the flowing

fluid stream.

+ Double-seated valves have two valve plugs and seats, as illustrated in Figure 4.7. Due to the

fluid entering the centre and dividing in both upward and downward directions, the

hydrodynamic effects of fluid pressure tent to cancel out and the valves are said to be balanced.

Due to the two valve opening, flow capacities up to 30% greater than for the same nominal size

single-seat valve can be achieved. They are, however, more difficult to design to achieve tight

shut-off.

The valve plugs and seats known as the valve trim are usually sold as matched sets which

have been ground to a precise fit in the fully closed position.

Figure 4.7 A process-control valve


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The valve plugs are of two main types: the solid plug and the skirted V-port plug, as illustrated in

Figure 4.8. All valves have a throttling action which causes a reduction in pressure. If the

pressure increases again too rapidly, air bubbles entrained in the fluid implode, causing rapid

wear on the valve plugs. This process is known as cavitation. The skirted V-port plugs have lesstendency to cause this rapid pressure recovery and are therefore less prone to cavitation.

Figure 4.8 Control valve plugs


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c) Valve flow character istics

The flow characteristic of a valve is the relationship between the rate of flow change and the

valve lift. The characteristics quoted by the manufacturers are theoretical or inherent flowcharacteristics obtained for a constant pressure drop across the valve. The actual or installedcharacteristics are different from the inherent characteristics since they incorporate the effects ofline losses acting in series with the pressure drop across the valve. The larger the line losses due

to pipe friction etc., the greater the effect on the characteristic.

Figure 4.9 Types of valve flow characteristics

Three main types of characteristic illustrated in Figure 4.9 are:

i) Quick-opening the open port area increases rapidly with valve lift and the maximum flowrate is obtained after about 20% of the value lift. This is used for on-off applications.

ii) Linear the flow is directly proportional to valve lift. This is used example in bypass service

of pumps and compressors.

iii) Equal-percentage the change in flow is proportional to the rate of flow just before the flow

change occurred; that is, an equal percentage of flow change occurs per unit valve lift. This is


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used when major changes in pressure occur across the valve and where there is limited data

regarding flow conditions in the system.

3.2 Hydraulic Servo Valve

In hydraulic control systems, the hydraulic energy from the pump is converted to mechanical

energy by means of a hydraulic actuator. The flow of fluid from the pump to the actuator in most

systems is controlled by a servo-valve.

A servo-valve is a device using mechanical motion to control fluid flow. There are three main

modes of control:

i) sliding the spool valve

ii) seating the flapper valve;iii) flow-dividing the jet-pipe valve.

a) Spool Valves

Spool valves are the most widely used type of valve. They incorporate a sliding spool moving in

a ported sleeve as illustrated in Figure 4.4. The valves are designed so that the output flow fromthe valve, at a fixed pressure drop, is proportional to the spool displacement from the null

position.

Figure 4.10 A spool valve

Spool valves are classified according to the following criteria.

The number of ways flow can enter or leave the valve. A four-way valve is required for use

with double-acting cylinders.


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The number of lands on the sliding spool. Three and four lands are the most commonly used as

they give a balanced valve, i.e. the spool does not tend to move due to fluid motion through the

valve.

The valve-centre characteristic, i.e. the relationship between the land width and the port opening.

The flow-movement characteristics is directly related to the type of valve centre employed.Figure 4.11 illustrates the characteristics of the three possibilities discussed below.

Figure 4.11 Valve-centre characteristics

i) Critical-centre or line-on. The land width is exactly the same size as the port opening. This is

the ideal characteristics as it gives a linear flow-movement relationship at constant pressure drop.It is very difficult to achieve in practice, however, and slightly overlapped characteristics is

usually employed.

ii) Closed-centre or overlapped. The land width is larger than the port opening. If the overlap is

too large, a dead-band results, i.e. a range of spool movement in the null position which produces

no flow. This produces undesirable characteristics and can lead to steady-state errors and

instability problems.


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iii) Open-centre or underlapped. The land width is smaller than the port opening. This means that

there is continuous flow through the valve, even in the null position, resulting in large power

losses. Its main applications is in high-temperature environments, which require a continuous

flow of fluid to maintain reasonable fluid temperatures.

b) Flapper Valves

Flapper valves incorporate a flapper-nozzle arrangement. They are used in low-cost single-stage

valves for systems requiring accurate control of small flows. A typical arrangement is illustrated

in Figure 4.12.

Figure 4.12 A Dowty single-stage servo-valve

Control of flow and pressure in the service line is achieved by altering the position of the

diaphragm relative to the nozzle, by application of an electrical input current to the coil.

Increasing the nozzle gap causes a reduction in service-port pressure, since the flow to the return

line is increased.


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c) Jet-pipe Valves

Jet-pipe valves employ a swivelling-jet arrangement and are only used as the first stage of some

two-stage electrohydraulic spool valves.

d) Two-stage electrohydraul ic servo-valves

These are among the most commonly used valves. A typical arrangement is illustrated in Figure

4.13, which shows a Dowty series 4551 M range servo-valve. This incorporates a double

flapper-nozzle arrangement as the first stage, driving the second-stage pool.

Figure 4.13 A Dowty electrohydraulic servo-valve

The flapper of the first-stage hydraulic amplifier is rigidly attached to the mid-point of thearmature and is collected by current input to the coil. The flapper passes between two nozzles,

forming a double flapper-nozzle arrangement so that, as the flapper is moved, pressure increasesat one nozzle while reducing at the other. These two pressures are fed to opposite ends of the

main spool, causing it to move.

The second stage is a conventional four-way four-land sliding spool valve. A cantilever feedback

spring is fixed to the flapper and engages a slot at the centre of the spool. Spool displacement

causes a torque in the feedback wire which opposes the original input-signal torque on the

armature. Spool movement continues until these two torques are balanced, when the flapper, with

the forces acting on it in equilibriums, is restored to its null position between the nozzles.


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3.3 Hydraulic Actuators

The hydraulic servo-valve is used to control the flow of high-pressure fluid to hydraulic actuators.

The hydraulic actuator converts the fluid pressure into an output force or torque which is used tomove some load.

There are two main types of actuator: the rotary and the linear, the later being the most

commonly used.

Linear actuators are commonly known as rams, cylinders, or jacks, depending on their

application. For most applications a double-acting cylinder is required these have a port on each

side of the piston so that the piston rod can be powered in each stroke direction, enabling fine

control to be achieved. A typical cylinder design is shown in Figure 4.14.

Figure 4.14 A linear actuator

Example

Figure 4.15 shows a diagrammatic hydraulic servo-valve/cylinder arrangement. Assuming thatthe flow through the valve is directly proportional to the valve spool movement, and neglecting

leakage and compressibility effects in the cylinder, derive a simple transfer operator for this

system.

Figure 4.15 A servo-valve/cylinder arrangement

Supply

Exhaust

xv

0


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Referring to Figure 4.15:

For the servo-valve:

Volumetric flow rate through the valve v valve spool movement vx

vvxKv = (4.14)

where Kv = valve characteristic

volumetric flow rate to the cylinder v = effective cylinder area piston velocity

dt

dAv 0

= (4.15)

Using s operator (Laplace transform), we have

0Asv = (4.16)

Substituting for v , we get

0vv AsxK = (4.17)

Therefore the transfer operator is

As

K

x

v

v

0=

i.e. an integrator, since = dts

1. (4.18)

3.4 Electrical Elements: D.C. Servo Motors

D.C servo-motors have the same operating principle as conventional d.c. motors but have special

design features such as high torque and low inertia, achieved by using long small-diameter rotors.

Two methods of controlling the motor torque are used:

a) field control Figure 4.16(a)b) armature control Figure 4.16(b)


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Figure 4.16 Control of d.c. servo-motors

a) Field Control

With field control, the armature current is kept approximately constant and the field current is

varied by the control signal. Since only small currents are required, this means that the field canbe supplied direct from electronic amplifiers, hence the special servo-motors are wound with a

split field and are driven by push-pull amplifiers.

Most of these systems are damped artificially by means of velocity feedback, which requires a

voltage proportional to speed. This is achieved by means of a tachogenerator which is built with

the motor in a common unit.

Field-controlled d.c. motors are used for low-power systems up to about 1.5kW and have the

advantage that the control power is small and the torque produced is directly proportional to the

control signal; however, they have a relatively slow speed of response.

b) Armature Control

With armature control, the field current is varied by the control signal.

Considerable development has taken place in the design of this type of motor for use in robot

drive systems. A common form in use is the disc armature motor (sometimes called a pancakemotor). This consists of a permanent magnet field and a thin disk armature consisting of copper

tracks etched or laminated onto a non-metalic surface. These weigh less than conventional iron-

core motors giving very good power to weight ratios and hence a fast speed of response. Power

outputs in the range 0.1 to 10kW are typical.

(a) Field control (b) Armature control


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3.5 Electrical Elements: A.C. Servo-motors

A.C. servo-motors are usually two-phase induction motors with the two stator coils placed at

right angles to each others as shown schematically in Figure 4.17. The current in one coil is keptconstant, while the current in the other coil is regulated by an amplified control signal. Thisarrangement gives a linear torque/control-signal characteristic over a limited working range.

They are usually very small low-power motors, up to about 0.25kW.

Figure 4.17 A two-phase a.c. servo-motor

As with the d.c. motors in the previous section, servo-motor tachogenerator units are supplied to

facilitate the application of velocity feedback.

3.6 Hydraulic Control Element (Steering Gear)

Where a flowing liquid is used as the operation medium, this can be generally considered as

hydraulic control. Hydraulics is, however, usually concerned with the transmission of power,

rather than the transmission of signals.

Hydraulic systems enable the transfer of power over large distances with infinitely variable speed

control of linear and rotary motions. High static forces or torques can be applied and maintainedfor long periods by compact equipment. The equipment itself is safe and reliable, and overload or

supply failure situations can be safeguarded against. Hydraulic operation of a ships steering gear

is usual and use is often made of hydraulic equipment for both mooring and carriage handlingdeck machinery.

Hydraulic systems utilize pumps, valves, motors or actuators and various ancillary fittings. The

system components can be interconnected in a variety of different circuits. Using their low or

medium present oil.

Example of a hydraulic control system (Ship Steering Machine)

A.C.referencevoltage Fixed

referencewindings

Amplifiedcontrolsignal

Motorshaft

Controlwindings


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Figure 4.18 Simplified diagram of a two stage hydraulic steering machine

3.7 Pneumatic Control Elements

Where a control signal is transmitted by the use of a gas this is generally known as pneumatics.Air is the usual medium and the control signal may be carried by a varying pressure or flow. The

variable pressure or flow. The variable pressure signal is most common and will be considered in

relation to the devices used. There are principally position-balance or force-balance devices.Position balance relates to the balancing of linkages and lever movements and the nozzle-flapper

device is an example. Force balance relates to a balancing of forces and the only true example of

this is the stacked controller. Pivoted beams which are moved by bellows and nozzle-flappers are

sometimes considered as force-balance devices. Fluidics is the general term for device where theinteraction of flows of a medium result in a control signal.

Air as a control medium is usually safe to use in hazardous areas, unless oxygen increases the

hazard. No return path is required as the air simply leaks away after use. It is freely and readily

available although a certain amount of cleaning as well as compressing is required. The signaltransmission is slow by comparison with electronics, and the need for compressors and storage

vessels is something if a disadvantage. Pneumatic equipment has been extensive applied inmarine control systems and is still very popular.

Examples of Pneumatic Control Elements

Nozzle-flapper

The nozzle-flapper arrangement is used in many pneumatic devices and can be considered as a

transducer, a valve or an amplifier. It transduces a displacement into a pneumatic signal. The

flapper movement acts to close or open a restriction and thus vary air flow through the nozzle.

The very small linear movement of the flapper is then converted into a considerable control

port

poil

poilstarboard

Relay operatedvalves poil

(a)

(b)

(c)

rudder

telemoter

steering

cylinder floating lever


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pressure output from the nozzle. The arrangement is shown in Figure 4.19(a). A compressed air

supply is provided at a pressure of about 1 bar. The air must pass through an opening which is

larger than the orifice, e.g. about 0.40mm. The position of the flapper in relation to the nozzle

will determine the amount of air that escapes. If the flapper is close to the nozzle a highcontrolled pressure will exist; if some distance away, then a low pressure. The characteristic

curve relating controlled pressure and nozzle-flapper distance is shown in Figure 4.19(b). Thesteep, almost linear section of this characteristic is used in the actual operation of the device. The

maximum flapper movement is about 20 microns or micrometres in order to provide a fairly

linear characteristic. The nozzle-flapper arrangement is therefore a proportional transducer, valve

or amplifier. Since the flapper movement is very small it is not directly connected to a measuring

unit unless a feedback device is used.

Figure 4.19 Nozzle-flapper mechanism: (a) arrangement; (b) characteristic

Bellows

The bellows is used in some pneumatic devices to provide feedback and also as a transducer to

convert an input pressure signal into a displacement. A simple bellows arrangement is shown in

Figure 4.20. The bellows will elongate when the supply pressure increases and some

displacement, x, will occur. The displacement will be proportional to the force acting on the base,

Supply

air

To control valve,controller, etc

(closed system)

Orifice Nozzle

To measuring

unit

Flapper

Nozzle flapper separation

operating range

Supplypressure

Airpressure

(a)

(b)


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i.e. supply pressure area. The actual amount of displacement will be determined by the spring-

stiffness of the bellows. Thus

( )ntDisplacemebellowsof

stiffnessSpring

bellows

ofArea

pressure

Supply

=

The spring-stiffness and the bellows area are both constants and therefore the bellows is a

proportional transducer.

Figure 4.20 Bellows mechanism

In some feedback arrangements a restrictor is fitted to the air supply to the bellows. The effect ofthis will be to introduce a time delay into the operation of the bellows. This time delay will be

related to the size of the restriction and the capacitance of the bellows.

In practise it is usual for bellows to be made of brass with a low spring-stiffness and to insert aspring. The displacement may therefore be increased, and also the effects of any pressure

variations.

Bellows

Displacement, x

Fixed end

Supply air


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22

4. Examples of Control Systems

4.1 Thickness 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 4.21.

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 -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 4.21 Thickness control system

4.2 Level Control System

Propose a control system to maintain a fixed fluid level in a tank. The flow is to be regulated on

the input side, and the output from the tank is flowing into a process with a variable demand.

a) The input will be the desired fluid level and the output the actual level.

b) Since the output is a variable level, a capacitive transducer will be suitable.

Electro-hydraulic

servo valve

Power

piston

-gauge

Input

Rotary

potentiometerAmplifier


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23

c) Since the system is a process type system, a commercial controller will be suitable and the

desired level will therefore be a set-point position on the controller. If a pneumatic controller

is chosen, the electrical signal from the capacitive level transducer will have to be converted

into a pneumatic signal by means of an electro-pneumatic converter.d) The choice of a pneumatic controller means that the system will be electro-pneumatic.

e) A suitable control element will be an air-to-open pneumatically actuated control valve.

Figure 4.22 shows a simple arrangement for the level control system.

Figure 4.22 Level control system

SUMMARY OF MODULE 4

Module 4 is summarised as follows:

General structure of a control system: process, transducer (measurement), recorder,comparison element, controller, final control element blocks;

Control components including comparison elements and final control elements

Examples of control systems and their components: thickness control system and levelcontrol system.

Electro-pneumatic

converter

Capacitive

transducer

Set-point

level

Pneumaticrecorder &

controller

Inlet flow Outlet flow

Process

control

valve


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24

Exercises

1. Figure 10.23 shows a d.c. remote position control system:

Figure 10.23 A remote position control system

Figure 10.24 shows a block diagram for the remote position control system, where

Figure 10.24 Block diagram for the remote position control system

Kp = potentiometer sensitivity (V/rad)

G = amplifier gain (V/V)Km = motor constant (Nm/V)

J = equivalent inertial (kgm2)

Kf= equivalent viscous friction (Nms/rad)

n = gear ratio

Write the total feedback transfer function for the system.

2. Figure 10.25 shows an arrangement of an industrial heating and cooling system. Analyse the

system into its component parts and identify the function of each.

G

n

1

Input

potentiometerOutput )t(

Motor

system

Kp

Kp

sKJs

K

f

2

m

++++

Reduction

gearbox

Amplifier

Output

potentiometer

Inputi (t)

ErrorAmplifiers

Input

position

Potentiometer

Potentiometer

Output

position

D.C. motor

Load

Reduction

gearbox


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25

Figure 10.25 Air-conditioning system

3. Figure 10.26 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 lineardisplacement 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 pressure

oil to the actuator which moves the load.

Figure 10.26 An electro-hydraulic servo system

Recorder &

controller

Thermocouple

Cold water

Hot water

Fan

Three

way

valve

Drain

Potentiometer

Potentiometer

Required

motion

Differential

amplifierAmplifier

Electro-hydraulic

servo valve

Load

Output

motion

Feedback


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( )( ) sKKbsJRsLs

KK

3200aa

21

+++

4. Figure 10.27 shows a schematic diagram and a block diagram for a servo system. The

objective of this system is to control the position of the mechanical load in accordance with the

reference position.

Figure 10.27 Servo system: a) schematic diagram and b) block diagram

a) Reduce the block diagramb) Write a total feedback transfer function for the servo system.

K1ev

Ra La

K1ev ia

r

er ec

c

T

c

Input

device

Reference input Input potentiometer

Output potentiometer

Feedback signal

Error measuring device Amplifier Motor Gear train Load

K0+_

R(s) E(s)

n

Y(s)Ev(s) (s)

(a)

(b)

Documents

BCT-Module 04.pdf