SRI LANKA INSTITUTE of ADVANCED TECHNOLOGICAL EDUCATION

Training Unit

Control Systems 2

Theory

No: EE 065

INDUSTRIETECHNIKINDUSTRIETECHNIK

ELECTRICAL and ELECTRONIC ENGINEERING

Instructor Manual

1

Training Unit

Control Systems 2

Theoretical Part

No.: EE 065

Edition: 2008 All Rights Reserved Editor: MCE Industrietechnik Linz GmbH & Co Education and Training Systems, DM-1 Lunzerstrasse 64 P.O.Box 36, A 4031 Linz / Austria Tel. (+ 43 / 732) 6987 – 3475 Fax (+ 43 / 732) 6980 – 4271 Website: www.mcelinz.com

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CONTROL SYSTEMS 2

CONTENTS Page

LEARNING OBJECTIVES...................................................................................................3

1 CONTROL UNIT...........................................................................................................4

2 DISCONTINUOUS CONTROL UNIT (TWO POSITION CONTROL UNIT) .................5

2.1 Bimetallic control unit ...........................................................................................5

2.2 Multiple position control unit.................................................................................6

3 CONTINUOUS CONTROL UNITS ...............................................................................7

3.1 Proportional action control unit (P control unit) ....................................................7

3.1.1 Transfer function ..............................................................................................9

3.2 Integral action control units (I control units) .......................................................11

3.3 Proportional-Integral control unit (PI control unit) ..............................................13

4 THE DERIVATIVE ACTION (D MEMBER)................................................................17

4.1 PD Control unit...................................................................................................18

4.2 PID control unit ..................................................................................................19

5 CONTROLLERS (EXAMPLES OF DESIGN) .............................................................21

5.1 Control units without auxiliary energy ................................................................21

5.2 Control unit with auxiliary energy .......................................................................21

5.3 Hydraulic controllers ..........................................................................................23

5.4 Pneumatic control unit .......................................................................................25

5.5 Electrical control systems ..................................................................................28

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CONTROL SYSTEMS 2

LEARNING OBJECTIVES

The trainee should ...

… state the function of the control unit.

… classify "discontinuous control units".

… explain the dependency of the output quantity an the input quantity for both P & PI

control units.

… become familiar with the circuit diagram of a PI control unit. ... state how the D part

functions with the help of the transfer function.

… classify amplifiers into 3 groups.

… describe the Operation of the feedback bellows of a pneumatic P control unit.

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CONTROL SYSTEMS 2

1 CONTROL UNIT

A control unit is a device which furnishes a correcting signal for final control unit to control

the process in order to bring the controlled variable value close or equal to the desired

value.

Control units may be divided into:

- discontinuous control units and

- continuous control units

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2 DISCONTINUOUS CONTROL UNIT (TWO POSITION CONTROL UNIT)

With this type only two values of the manipulated variable are possible.

2.1 Bimetallic control unit

The correcting element only recognises the position "ON" and "OFF",

example; bimetallic controller on an electric iron.

If the temperature rises, the bimetallic strip bends upwards. If the temperature falls below

the set value, the electric circuit closes and the heating element is warmed by the current.

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2.2 Multiple position control unit

Example: temperature regulating circuit with three position bimetallic control unit.

R1 … R2 heat resistors

During the heating process the upper contact is closed and heating resistor R1 is switched

on.

There is a heavy current flow, i. e. , the correcting variable is at its maximum value.

As the temperature rises the bimetallic strip bends further. Heating resistor R2 is switched

on, in series with R1

The current flow decreases. The correcting variable is adjusted to its medium value.

If the temperature continues to rise the bimetallic strip breaks the heating circuit.

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3 CONTINUOUS CONTROL UNITS

With a change in the controller input, a gradual change in the controller output is

produced.

3.1 Proportional action control unit (P control unit)

(Proportional means "staying at the same ratio").

The output quantity is proportional to the input quantity.

Example: gas pressure regulator

F ... spring counteracting the gas pressure

Every value of the controlled variable (X) has a corresponding valve of the correcting

variable (Y).

The movement of the graduated indicator is equal an both sides when the pivot (L) of the

lever is exactly in the middle of the arm a b.

If the pivot is the right of the centre of the arm, larger values of Y will be obtained for

smaller X values.

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This effect is called "amplification".

The amplification factor ( V) is determined by the choice of the fulcrum (L).

Displacing the fulcrum to the left means that large x values will yield small y values.

Strictly speaking, it is not a matter of amplification here but rather of attenuation.

Nevertheless, even here one speaks of an amplifier.

(Amplification factor less than 1)

•

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Example: Level control

If the lever arms a and b are equal in length, the valve will likewise open by 1 cm when the

water level sinks by 1 cm.

With every valve however, there is a maximum valve opening (4 cm for instance).

If the water level sinks by more than 4 cm, the inflow cannot increase. The regulator can

only operate within a certain range, the proportional range xp .

The P rangexp is that range in which the controlled variable must vary in order to vary the

correcting variable over its entire range, y.

3.1.1 Transfer function

The transfer function is a function describing the change of the output quantity after a step

change in the input quantity.

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Transfer function of the P control unit:

When there is a step change in the controlled variable x (a sudden lifting of the float for

example), the correcting variable also changes in a step fashion.

The change in the correcting variable is dependent an Kp

(proportional action factor).

Proportional action factor Kp

The ratio yn: xp (correcting range to proportional range) a : b

and is designated as proportional action factor Kp .

The proportional action factor Kp is the quotient of change in output quantity and change

in input quantity, of the P control unit.

Block diagram

The P control unit is represented symbolically by its transfer function.

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Disadvantages of the P control unit

In a control system using proportional control action only the controlled variable never

reaches the desired value. This effect is known as steady state errors (offset).

These errors are dependent on:

- magnitude of the disturbance variable

- the P range of adjustment.

3.2 Integral action control units (I control units)

(Integrating means adding together or combining).

Level control

If inflow and outflow are equal, the level will remain the same. If the inflow increases and

the outflow remains constant, the level (output quantity) will rise until the tank overflow.

With any input flow which is greater than the outflow, the level will rise to the overflow

point.

In this case a definite output flow can no longer be assigned to every Input flow.

The difference between the liquid Input, and the liquid output accumulates in the tank.

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This behaviour is called integral behaviour.

The time in which the tank fills up is now dependent on the difference between liquid Input

and liquid output.

In other words:

The speed at which the correcting variable changes is proportional to the change in the

controlled variable.

The greater the variation, the faster the change in the correcting element.

The more the float is lowered, the greater the applied voltage at the servomotor.

The regulating speed of the valve is therefore dependent on the altered position of the

float.

Transfer function of the 1 control unit

The integral control unit does not come to rest before the deviation has become zero.

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The transfer function shows that the 1 control unit works more slowly than the P control

unit.

Advantage: no steady state error (offset)

Disadvantage: relatively slow

3.3 Proportional-Integral control unit (PI control unit)

The correcting variable is the sum of the output quantity of a proportional action control

unit and of an integral action control unit. This is achieved by connecting a P and an I

controller in parallel.

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In the example of the level regulation, this means superposition of the motor and float

movement.

P - part

The rise in the water level causes the sliding valve to close.

I - part

The motor shifts the sliding valve via a stem until the required set valve is readjusted.

•

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Transfer function

For a step change in the controlled variable.

The correcting variable changes at first in a similar manner to the P control unit.

Because of the I part of the control unit, an additional change in the correcting variable

takes place.

Reset time Tn

Reset time is the time required by the correcting unit (calculated from the moment a step

deviation occurs) to reset the path, an account of the integral action, it has already

covered in consequence of the P part.

Step responses for various Tn adjustments

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The shorter Tn is, the more rapidly the output quantity rises.

With PI controllers

Block diagram

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4 THE DERIVATIVE ACTION (D MEMBER)

The magnitude of the output quantity is dependant an the rate of change the input quantity

and the time constant, T .

Transfer function

With an input step change xw , the correcting variable y is temporarily and abruptiy

changed, and returns thereafter to its original value. With a constant rate of change of the

deviation, the D control unit makes a constant adjustment to the correcting unit.

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4.1 PD Control unit

Transfer function

The correcting variable y jumps temporarily towards infinity.

The correcting pulse is very powerful and appears as a unit impulse function.

The correcting variable returns immediately to the valueYp .

Transfer function with constant time variation of the controlled variable

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At the onset of the controlled variable, a jump occurs at point t1 due to the D effect; this

jump is proportional to the rate of change of the controlled variable.

This sudden variation is called derivative action. Subsequently there occurs a continuous

change in the correcting variable which is proportional to the change in the controlled

variable.

Derivative action time TV

The derivative action time corresponds to that time which would be necessary with a P

control to bring the change in the correcting variable to the value reached in one jump as

a result of the D influence.

4.2 PID control unit

Transfer function

The D influence causes a rapid, temporary change in the correcting variable. However,

the correcting variable does not return to its original value, because now the P influence of

the control brings about an adjustment of the correcting variable which corresponds to the

proportional action factor Kp.

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The D part of the correcting variable change is proportional to the speed of change of the

controlled variable.

True transfer function for control units

Since all control units exhibit a certain delay, the transfer functions illustrated previously

are practically impossible.

Control units with delay exhibit the following transfer functions.

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5 CONTROLLERS (EXAMPLES OF DESIGN)

There are two main types of control unit

- Control units without auxiliary energy

- Control units with auxiliary energy

5.1 Control units without auxiliary energy

When there is a deviation of the controlled variable from the set value, the correcting unit

is varied without supplementary energy.

Example: temperature regulating circuit with bimetallic

control unit.

5.2 Control unit with auxiliary energy

A power amplifier provides the required correcting unit energy.

Amplifier

Function

The amplifier has the function of making available the energy necessary for the correcting

unit.

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There are three main types of amplifier:

- Pneumatic amplifiers

- Hydraulic amplifiers

- Electric amplifiers

Pneumatic and Hydraulic amplifiers

Air or liquids serve as auxiliary energy.

Types:

- Jet pipe amplifiers (see hydraulic control units)

- Nozzle-baffie amplifiers (see pneumatic control units)

Electrical amplifiers

Operational amplifiers are used as electrical amplifiers.

Design:

Several transistors are incorporated in an integrated circuit chip. Small Input quantities

(currents and voitages) produce output quantities which have been greatly amplified.

Block diagram

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5.3 Hydraulic controllers

On-off controller

These types of controllers are used where a rapid movement of the piston to either

extreme position is required. The jet pipe is positioned at neutral when the measured

value and set point value are equal.

Proportional controller

The proportional action is obtained when a feedback linkage from piston to jet pipe is

provided. When the jet pipe moves from neutral position to the right because of a change

in measured variable, the piston will move to the right so far that the jet pipe is brought

back to neutral position.

The effect of feedback is controlled by changing the position of the pivot as shown an the

figure.

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Proportional plus integral controller

Proportional plus integral control actions are obtained by adding an auxiliary piston and a

valve to a proportional controller as shown in the figure. Suppose the jet pipe is moved to

the right, both cylinders move to the right because of the proportional control action. As

there is a spring in the auxiliary cylinder, the pressure on the left side of the piston in the

auxiliary cylinder must be higher than the pressure on the right side in order to overcome

the opposing force of the spring.

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This differential pressure causes a flow through the by-pass valve from left to right side of

the auxiliary cylinder. Through this flow, the pressure in the right side of the auxiliary

cylinder begins to

increase until the pressures an both sides of the auxiliary cylinder are in equilibrium.

During the time the fiow passes through the by-pass valve, the spring in the cylinder will

move the piston from right to the left. Moving the piston to the left reduces the negative

feedback effect and causes the main piston to move to further in the original direction.

5.4 Pneumatic control unit

Function

Maintain the pressure in a pressure pipe constant.

P-control unit

A metal bellows B1 determines the controlled variable. The force generated by the

pressure in the pipe is transmitted to the balance arm.

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The unit is fed with a constant air supply pressure Ps.

This pressure acts on the balance arm, and on the diaphragm (correcting unit).

If the pressure in the output pipe, P varies this change is transmitted to the balance arm

by the bellows 1.

The gap between the jet and the flap at the end of the balance arm is changed.

If the distance is reduced to zero (increase in pressure), the nozzle back pressure closes

the valve.

If the controlled pressure in P decreases, bellows 1 contracts. As a result the jet is freed

by the balance arm flap, the pressure over the diaphragm is reduced, and the valve is

opened. This process repeats itseif in rapid succession, because even small variations in

pressure change the distance between the jet and the flap.

The amplification (lever deflection) of the control unit is reduced by installing a feedback

bellows.

PI-control unit

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Bellows 2, similarly, is controlled by the inlet pressure. The pressure in bellows 2,

therefore, attains the same value as that in the feedback bellows. When they are at equal

distances from the fulcrum the forces cancel each other out. The adjustable reset

restriction installed in front of bellows 2 ensures that the pressure in it rises slowly.

PID-control unit

An adjustable restriction in front of the feedback bellows delays the feedback action.

When there is a change in the controlled variable, the amplification is high at first (strong

control of the correcting unit).

As the pressure in the feedback bellows increases, the amplification reduces. When the

pressure in bellows 2 also reaches the pressure in the feedback bellows, it neutralises the

force of the feedback bellows.

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5.5 Electrical control systems

These are composed of an operational amplifier with input and feedback resistors.

The command variable (voltage of the set point adjuster) and the controlled variable

(measured voltage) are connected to the input resistors Rinl and Rin2 .

P-control unit

When there is a deviation, a voltage difference between the command variable Vw and

the controlled variable Vx is created.

A corresponding current Ifb flows through the feedback resistor.

Output voltage

Wiring diagram

Transfer function

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I-control unit

A deviation causes a current hb to flow.

The capacitor Cfb in the feedback path charges up and causes a voltage Vy .

Wiring diagram

Transfer function

PI-control unit

An additional resistor is wired into the circuit in the feedback path.

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Wiring diagram

Transfer function

PID-control unit

Wiring diagram

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Transfer function

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EE065

Control Systems 2

Theoretical Test

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EE 065

CONTROL SYSTEMS 2

TEST

1. Explain the function of the control unit.

2. Give an example for the use of the two position control unit.

3. Name 3 types of amplifier.

4. On which quantities is the control deviation of a P control unit dependent?

5. State one function of a pneumatic control unit.

6. Explain the function of an amplifier in a control system.

7. Describe the construction of an electric amplifier.

8. Explain the difference between a discontinuous and a continuous control unit.

9. Name the advantage and disadvantage of an I control unit.

10. Explain the term "Proportional action factor".

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EE 065

CONTROL SYSTEMS 2

TEST

(Solution)

1. To eliminate any deviation of the controlled variable from its command variable (set

value).

2. Bimetallic control unit in an eiectric iron.

3. Electrical amplifier, pneumatic amplifier, hydraulic amplifier.

4. The magnitude of the disturbance variable and the proportional action factor.

5. Maintain the pressure in a pressure pipe constant.

6. The amplifier has the function of making availabie the energy necessary for

controlling the correcting unit.

7. Several transistors are incorporated in an integrated circuit chip. Small input

quantities (currents and voltages) produce greatly amplified output quantities.

8. With a discontinuous control unit only two values of the correcting variable are

possibie. With a continuous control unit a gradual change of the correcting variable

is produced.

9. Advantage: no steady state deviation (offset). Disadvantage: reiatively slow.

10. The proportional action factor Kp is the quotient of the output quantity and the input

quantity.

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KEY TO EVALUATION

PER CENT

MARK

88 – 100

1

75 – 87

2

62 – 74

3

50 – 61

4

0 – 49

5