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Final Control Elements Characteristics

In many control systems the rate of flow of a fluid along a pipe is

controlled by a valve which uses pneumatic action to move a valve stem

and hence a plug or plugs into the flow path, so altering the size of the

gap through which the fluid can flow (Figure 6.21). The term single

seatedis used where just one plus is involved and double seatedwherethere are two. A single-seated valve has the advantage compared with

the double-seated valve of being able to close more tightly but the

disadvantages that the force on the plug is greater from the fluid and so a

larger area diaphragm may be needed.

Figure 6.22 shows the basic elements of a common form of such a

control valve. The movement of the stem, and hence the position of the

plug or plugs in the fluid flow, results from the use of a diaphragm

moving against a spring and controlled by air pressure (Figure 6.22).

The air pressure from the controller exerts a force on one side of the

diaphragm, the other side of the diaphragm being at atmospheric

pressure, which is opposed by the force due to the spring on the other

side. When the air pressure changes then the diaphragm moves until

there is equilibrium between the forces resulting from the pressiu^e andthose from the spring. Thus the pressure signals from the controller

result in the movement of the stem of the valve. There are two alternative

forms, directand reverse action forms (Figure 6.23) with the difference

being the position of the spring. The valve body is joined to the

diaphragm element by the yoke.

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6.4.1 Forms of plug

There are many forms of valve body and plug. The selection of the form

of body and plug determine the characteristic of the control valve, i.e. the

relationship between the valve stem position and the flow rate through it.

For example. Figure 6.24 shows how the selection of plug can be used to

determine whether the valve closes when the controller air pressure

increases or opens when it increases and Figure 6.24 shows how the

shape of the plug determines how the rate of flow is related to the

displacement of the valve stem:

1Linear plug

The change in flow rate is proportional to the change in valve stem

displacement, i.e.:change in flow rate = k(change in stem displacement)

where it is a constant. IfQ is the flow rate at a valve stem

displacement Sand ^max is the maximum flow rate at the maximum

stem displacement S'max, then we have:

or the percentage change in the flow rate equals the percentage

change in the stem displacement. Such valves are widely used forthe control of liquids entering cisterns when the liquid level is being

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controlled.

2 Quick-opening plug

A large change in flow rate occurs for a small movement of the

valve stem. This characteristic is used for on-oflf control systems

where the valve has to move quickly from open to closed and vice

versa.

3Equal percentage plugThe amount by which the flow rate changes is proportional to the

value of the flow rate when the change occurs. Thus, if the amount

by which the flow rate changes is Ag for a change in valve stem

position A5, then it is proportional to the value of the flow Q when

the change occurs, i.e.

where k is a constant. Generally this type of valve does not cut off

completely when at the limit of its stem travel, thus when S = 0 we

have Q = gmin. If we write this expression for small changes and

then integrate it we obtain:

And so

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Example

A valve has a stem movement at full travel of 30 mm and has a

linear plug which has a minimum flow rate of 0 and a maximum

flow rate of 20 mVs. What will be the flow rate when the stem

movement is 15 mm?

The percentage change in the stem position from the zero setting is

(15/30) X 100 = 50%. Since tlie percentage flow rate is the same asthe percentage stem displacement, then a percentage stem

displacement of 50% gives a percentage flow rate of 50%, i.e.

10 mVs.

ExampleA valve has a stem movement at full travel of 30 nun and an equal

percentage plug. This gives a flow rate of 2 mVs when the stem

position is 0. When the stem is at fiill travel there is a maximum

flow rate of 20 mVs. What will be the flow rate when the stem

movement is 15 mm?

6.4.2 Rangeability and turndown

The term rangeability R is used for tlie ratio Qnax/Qmn, i.e. the ratio of

the maximum to minimum rates of controlled flow. Thus, if theminimum controllable flow is 2.0% of the maximum controllable flow,

then the rangeability is 100/2.0 = 50. Valves are often not required to

handle the maximum possible flow and the tenn turndown is used for the

For example, a valve might be required to handle a maximum flow

which is 70% of tliat possible. With a minimum flow rate of 2.0% of the

maximum flow possible, tlien the turndown is 70/2.0 = 35.

6.4.3 Control valve sizing

The term control valve sizingis used for the procedure of determining

the correct size, i.e. diameter, of the valve body. A control valve changes

the flow rate by introducing a constriction in the flow path. But

introducing such a constriction introduces a pressure difference between

the two sides of the constriction. The basic equation (from an application

of Bernoulli's equation) relating the rate of flow and pressure drop is:

where AT is a constant which depends on the size of the constrictionproduced by the presence of the valve. The equations used for

determining valve sizes are based on this equation. For a liquid, this

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equation is written as:

where >4v is the valve flow coefficient, Ap the pressure drop in Pa across

the valve and p the density in kg/m^ of the fluid. Because the equation

was originally specified with pressure in pounds per square inch and

flow rate in American gallons per minute, another coefficient Cv based

on these units is widely quoted. With such a coefficient and the

quantities in SI units, we have:

where Vis the specific volume of tlie steam in m^/kg, the specific volume

being the volume occupied by 1 kg. Table 6.1 shows some typical values

of ^v, Cv and the related valve sizes.

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Example

Determine the valve size for a valve that is required to control the

flow of water when the maximum flow rate required is 0.012 mVs

and the permissible pressure drop across the valve at this flow rate is

300 kPa.

Taking the density of water as 1000 kg/m^ we have

Thus, using Table 6.1, this value of coefficient indicates that the

required valve size is 960 mm.

6.4.4 Valve positioners

Frictional forces and unbalanced forces on the plug may prevent the

diaphragm from positioning the plug accurately. In order to overcome

this, valve positioners may be fitted to the control valve stem. They

position the valve stem more accurately and also provide extra power tooperate the valve and so increase the speed of valve movement. Figure

6.25 shows the basic elements of a positioner.

The output from the controller is applied to a spring-loaded bellows. A

flapper is attached to the bellows and is moved by pressure applied to the

bellows. An increase in this pressure brings the flapper closer to thenozzle and so cuts down the air escaping from it. As a consequence, the

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pressure applied to the diaphragm is increased. The resulting valve stem

displacement takes the flapper away from the nozzle until the air leakage

from the nozzle is just sufficient to maintain the correct pressure on the

diaphragm.Air

6.4.5 Other forms of flow control valves

The type of control valve described in the earlier parts of this section isbasically thesplit-body globe valve body with a plug or plugs. This is the

most commonly used form. There are, however, other forms. Figure

6.26(a) shows a 3-way globe. Other valve types are thegate (Figure

6.26(b)), the ball(Figure 6.26(c)), the butterfly (Figure 6.26(d)) and the

louvre (Figure 6.26(e)). All excise control by restricting the fluid flow.

Ball valves use a ball with a through-hole which is rotated; they have

excellent shut-oflf capability. Butterfly valves rotate a vane to restrict the

air flow and, as a consequence, suffer from the problem of requiring

significant force to move from the full-open position and so can 'stick' in

that position.

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6.4.6 Fail-safe design

Fail-safe design means that the design of a plant has to take account of

what will happen if the power or air supply fails so that a safe shut-down

occurs. Thus, in the case of a fuel valve, the valve should close if failure

occurs, while for a cooling water valve the failure should leave the valve

open. Figure 6.27 shows a direct acting valve which shuts down the fluid

flow if the air supply to the diaphragm fails.

6.5 Motors

Electric motors are frequently used as the final control element in

position or speed-control systems. The basic principle on which motors

are based is that a force is exerted on a conductor in a magnetic field

when a current passes through it. For a conductor of lengthL carrying a

current / in a magnetic field of flux densityB at right angles to the

conductor, the forceFequalsBIL.

There are many different types of motor. In the following, discussion

is restricted to those types of motor that are commonly used in control

systems, this including d.c. motors and the stepper motor. Astepper

motoris a form of motor that is used to give a fixed and consistentangular movement by rotating an object through a specified number of

revolutions or fraction of a revolution.

6.5.1 D.c. motors

In the d.c. motor, coils of wire are mounted in slots on a cylinder of

magnetic material called the armature. The armature is mounted on

bearings and is free to rotate. It is mounted in the magnetic field

produced byfield poles. This magnetic field might be produced by

permanent magnets or an electromagnet with its magnetism produced by

a current passing through the, so-termed, ^/eW coils. Whether permanent

magnet or electromagnet, these generally form the outer casing of the

motor and are termed thestator. Figure 6.28 shows the basic elements of

d.c. motor with the magnetic field of the stator being produced by acurrent through coils of wire. In practice there will be more than one

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armature coil and more than one set of stator poles. The ends of the

armature coil are connected to adjacent segments of a segmented ring

called the commutatorwhich rotates witli the armature. Brushes in fixed

positions make contact with the rotating commutator contacts. They

carry direct current to the armature coil. As the armature rotates, the

commutator reverses the current in each coil as it moves between the

field poles. This is necessary if the forces acting on the coil are to remain

acting in the same direction and so continue the rotation.

For a d.c. motor with the field provided by a permanent magnet, thespeed of rotation can be changed by changing the size of the current to

the armature coil, the direction of rotation of the motor being changed by

reversing the current in the armature coil. Figure 6.29 shows how, for a

permanent magnet motor, the torque developed varies with the rotational

speed for different applied voltages. The starting torque is proportional

to the applied voltage and the developed torque decreases with increasing

speed.

D.c. motors with field coils are classified as series, shunt, compound

and separately excited according to how the field windings and armature

windings are connected.