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1. Introduction
The correction element or final control element is the element in a control system which is responsible for transforming the output of a controller into a change in the process which aims to correct the change in the controlled variable. Thus, for example, it might be a valve which is operated by the output from the controller and used to change the rate at which liquid passes along a pipe and so change the controlled level of the liquid in a cistern. It might be a motor which takes the electrical output from the controller and transforms it a rotatory motion in order to move a load and so control its position. It might be a switch which is operated by the controller and so used to switch on a heater to control temperature.
The term actuator is used for the part of a correction/final control element that provides the power, i.e. the bit which moves, grips or applies forces to an object, to carry out the control action. Thus a valve might have an input from the controller and be used to vary the flow of a fluid along a pipe and so make a piston move in a cylinder and result in linear motion. The piston-cylinder system is termed an actuator.
In this section pneumatic/hydraulic and electric correction control elements, along with actuators, are discussed.
2. Pneumatic and hydraulic systems
Process control systems frequently require control of the flow of a fluid.
The valves used as the correction elements in such situations are frequently pneumatically operated, even when the control system is otherwise electrical. This is because such pneumatic devices tend to be cheaper and more easily capable of controlling large rates of flow. The main drawback with pneumatic systems is, however, the compressibility of air. This makes it necessary to have a storage reservoir to avoid changes in pressure occurring as a result of loads being applied.
Hydraulic signals do not have this problem and can be used for even higher power control devices. They are, however, expensive and there are hazards associated with oil leaks which do not occur with air leaks.
2.1 Current to pressure converter
Generally the signals required by a pneumatic correction element are in the region of 20 to 100 kPa gauge pressure, i.e. pressure above the atmospheric pressure. FIG. 1 shows the principle of one form of a current to pressure converter that can be used to convert a current output from a controller, typically in the range 4 to 20 mA, to a pneumatic pressure signal of 20 to 100 kPa to operate a final control element. The current from the controller passes through coils mounted on a pivoted beam. As a consequence, the coils are then attracted towards a magnet, the extent of the attraction depending on the size of the current. The movement of the coils cause the lever to rotate about its pivot and so change the separation of a flapper from a nozzle. The position of the flapper in relation to the nozzle determines the size of the output pressure in the system.
FIG. 1 Current to pressure converter
2.2 Pressure sources
With a pneumatic system a source of pressurized air is required. This can be provided by an electric motor driving an air compressor (FIG. 2). The air is drawn from the atmosphere via a filter. Since the air compressor increases the temperature of the air, a cooling system is likely to follow and, since air also contains a significant amount of moisture, a moisture separator to remove the moisture from the air. A storage reservoir is used to smooth out any pressure fluctuations due to the compressibility of air. A pressure relief valve provides protection against the pressure in the system rising above a safe level.
FIG. 2 A pressurized air source
With a hydraulic system a source of pressurized oil is required. This can be provided by a pump driven by an electric motor. The pump pumps oil from a sump through a non-return valve and an accumulator and back to the sump (FIG. 3). The non-return valve is to prevent the oil being back-driven to the pump. A pressure relief valve is included so that the pressure is released if it rises above a safe level. The accumulator is essentially just a container in which the oil is held under pressure against an external force and is there to smooth out any short-term fluctuations in the output oil pressure. If the oil pressure rises then the piston moves to increase the volume the oil can occupy and so reduces the pressure. If the oil pressure falls then the piston moves in to reduce the volume occupied by the oil and so increase its pressure.
Figure 3: A source of pressurized oil
2.3 Control valves
Pneumatic and hydraulic systems use control valves to give direction to the flow of fluid through a system, control its pressure and control the rate of flow. These types of valve can be termed directional control valves, pressure control valves and flow control valves. Directional control valves, sometimes termed finite position valves because they are either completely open or completely closed, i.e. they are on/off devices, are used to direct fluid along one path or another. They are equivalent to electric switches which are either on or off . Pressure control valves, often termed pressure regulator valves, react to changes in pressure in switching a flow on or off, or varying it. Flow control valves, sometimes termed infinite position valves, vary the rate at which a fluid passes through a pipe and are used to regulate the flow of material in process control systems. Valves are discussed in more detail later in this section.
2.4 Actuators
Fluid power actuators can be classified in two groups: linear actuators which are used to move an object or apply a force in a straight line and rotary actuators which are used to move an object in a circular path.
The hydraulic or pneumatic cylinder is a linear actuator, the principles and form being the same for both versions with the differences being purely a matter of size as a consequence of the higher pressures used with hydraulics. The hydraulic/pneumatic cylinder consists of a hollow cylindrical tube along which a piston can slide. FIG. 4(a) shows the single acting form and FIG. 4(b) the double acting form.
The single acting form has the control pressure applied to just one side of the piston, a spring often being used to provide the opposition to the movement of the piston. The piston can only be moved in one direction along the cylinder by the signal from the controller. The double acting form has control pressures that can be applied to each side of the piston.
When there is a difference in pressure between the two sides the piston moves, the piston being able to move in either direction along the cylinder.
The choice of cylinder is determined by the force required to move the load and the speed required. Hydraulic cylinders are capable of much larger forces than pneumatic cylinders. However, pneumatic cylinders are capable of greater speeds.
Since pressure is force per unit area, the force produced by a piston in a cylinder is equal to the cross-sectional area of the piston, this being effectively the same as the internal cross-sectional area of the cylinder, multiplied by the difference in pressure between the two sides of the piston. Thus for a pneumatic cylinder with a pressure difference of 500 kPa and having an internal diameter of 50 mm,
force = pressure x area = 500 x 10^3 x 0.25 pi x 0.050^2 = 982 N
A hydraulic cylinder with the same diameter and a pressure difference of 15 000 kPa, hydraulic cylinders being able to operate with higher pressures than pneumatic cylinders, will give a force of 29.5 kN. Note that the maximum force available is not related to the flow rate of hydraulic fluid or air into a cylinder but is determined solely by the pressure and piston area.
FIG. 4 (a) Single acting, (b) double acting cylinder
FIG. 5 Movement of a piston in a cylinder
The speed with which the piston moves in a cylinder is determined by the rate at which fluid enters the cylinder. If the flow rate of hydraulic liquid into a cylinder is a volume of Q per second, then the piston must sweep out a volume of Q. If a piston moves with a velocity v then, in one second, it moves a distance of v (FIG. 5). But for a piston of cross-sectional area A this must mean that the volume swept out by the piston in 1 s is Av. Thus we must have:
Q = Av
Thus the speed v of a hydraulic cylinder is equal to the flow rate of liquid Q through the cylinder divided by the cross-sectional area A of the cylinder. The speed is determined by just the piston area and the flow rate. For example, for a hydraulic cylinder of diameter 50 mm and a hydraulic fluid flow of 7.5 x 10^-3 m^3/s:
speed v = Q/A = [7.5 x 10^-3] / [0.25 pi x 0.050^2] = 3.8 m/s
Rotary actuators give rotary motion as a result of the applied fluid pressure. FIG. 6 shows a rotary actuator which gives partial rotary movement. Continuous rotation is possible with some forms and then they are the equivalent of electric motors. FIG. 7 shows one form, known as a vane motor. The vanes are held out against the walls of the motor by springs or hydraulic pressure. Thus, when there is a pressure difference between the inlet and outlets of the motor, rotation occurs.
FIG. 6 Rotary actuator
FIG. 7 Vane motor
Example:
A hydraulic cylinder is to be used in a manufacturing operation to move a workpiece through a distance of 250 mm in 20 s. If a force of 50 k-Ohm is required to move the workpiece, what is the required pressure difference and hydraulic liquid flow rate if a cylinder with a piston diameter of 150 mm is to be used? As derived above, the force produced by the cylinder is equal to the product of the cross-sectional area of the cylinder and the working pressure. Thus the required pressure is:
pressure=F/A = 2.8MPa
The average speed required is 250/20 = 12.5 mm/s. As derived above, the speed of a hydraulic cylinder is equal to the flow rate of liquid through the cylinder divided by the cross-sectional area of the cylinder. Thus the required flow rate is:
flow rate = speed x area
= 0.0125 X 0.25 pi x 0.150^2 = 2.2 x 10^-4 m/s
3 Directional control valves
Directional control valves are widely used in control systems as elements for switching on or off hydraulic or pneumatic pressures which can then, via some actuator, control the movement of some item. A directional control valve on the receipt of some external signal, which might be mechanical, electrical or a pressure signal, changes the direction of, or stops, or starts the flow of fluid in some part of a pneumatic/hydraulic circuit.
The basic symbol for a control valve is a square. With a directional control valve two or more squares are used, with each square representing the positions to which the valve can be switched. Thus, FIG. 8(a) represents a valve with two switching positions. FIG. 8(b) a valve with three switching positions. Lines in the boxes are used to show the flow paths with arrows indicating the direction of flow (FIG. 9(a)) and shut-off positions indicated by terminated lines (FIG. 9(b)). The pipe connections, i.e. the inlet and outlet ports of the valve, are indicated by lines drawn on the outside of the box and are drawn for just the 'rest/initial/neutral position', i.e. when the valve is not actuated (FIG. 9(c)). You can imagine each of the position boxes to be moved by the action of some actuator so that it connects up with the pipe positions to give the different connections between the ports.
Directional control valves are described by the number of ports and the number of positions. Thus, a 2/2 valve has 2 ports and 2 positions, a 3/2 valve 3 ports and 2 positions, a 4/2 valve 4 ports and 2 positions, a 5/3 valve 5 ports and 3 positions. FIG. 10 shows some commonly used examples and their switching options and FIG. 11 the means by which valves can be switched between positions.
FIG. 8 (a) Two position, (b) three position valves
FIG. 9 (a) Flow path, (b) shut-off, (c) input connections
FIG. 10 Commonly used direction valves: P or 1 indicates the pressure
supply ports, R and S or 3 and 5 the exhaust ports, A and B or 2 and 4 the
signal output ports
FIG. 11 Examples of valve actuation methods
FIG. 12 Symbol for a solenoid-activated valve with return spring
Application ---- In section 4.4.5 an antilock brake system (ABS) for a car is discussed and Figure 4.17 shows how valves are used.
FIG. 13 Control of a single-acting cylinder: (a) before solenoid activated,
(b) when solenoid activated
FIG. 14 Control of a double-acting cylinder
As an illustration, FIG. 12 shows the symbol for a 3/2 valve with solenoid activation and return by means of a spring. Thus, when the solenoid is not activated by a current though it, the signal port 2 is connected to the exhaust 3 and so is at atmospheric pressure. When the solenoid is activated, the pressure supply P is connected to the signal port 2 and thus the output is pressurized.
FIG. 13 shows how such a valve might be used to cause the piston in a single-acting cylinder to move; the term single-acting is used when a pressure signal is applied to only one side of the piston. When the switch is closed and a current passes through the solenoid, the valve switches position and pressure is applied to extend the piston in the cylinder.
FIG. 14 shows how a double-solenoid activated valve can be used to control a double-acting cylinder. Momentary closing switch SI causes a current to flow through the solenoid at the left-hand end of the valve and so result in the piston extending. On opening SI the valve remains in this extended position until a signal is received by the closure of switch S2 to activate the right-hand solenoid and return the piston.
3.1 Sequencing
Situations often occur where it is necessary to activate a number of cylinders in some sequence. Thus event 2 might have to start when 1 is completed, event 3 when event 2 has been completed. For example, we might have: only when cylinder A is fully extended (event 1 cylinder B start extending (event 2), and cylinder A can only retracting (event 3) when cylinder B has fully extended (event discussions of sequential control it is common practice to give cylinder a reference letter A, B, C, D, etc., and to indicate the state each cylinder by using a + sign if it's extended or a - sign if retracted. Thus a sequence of operations might be shown as A+ , B+, A-, B- indicates that the sequence of events is cylinder A extend, follow cylinder B being extended, followed by cylinder A retracting, follow cylinder B retracting. FIG. 15 illustrates this with a displace step diagram. FIG. 16 shows a circuit that could be used to generate this displacement-event diagram for two cylinders A and B.
FIG. 15 Displacement-event diagram
FIG. 16 Two-actuator sequential operation
In order to generate the displacement-event diagram of FIG. 15 the sequence of operations with FIG. 16 is:
Event 1
1. Start push-button pressed.
2. Cylinder A extends, releasing limit switch a-.
Event 2
3. Cylinder A fully extended, limit switch a+ operated to start B extending.
4. Cylinder B extends, limit switch b- released.
Event 3
5 Cylinder B fully extended, limit switch b+ operated to start cylinder A retracting.
6. Cylinder A retracts, limit switch a+ released.
Event 4
7. Cylinder A fully retracted, limit switch a- operated to start cylinder B retracting.
8. Cylinder B retracts, limit switch b+ released.
Event 5
9. Cylinder B fully retracted, limit switch b- operated to complete the cycle.
The cycle can be started again by pushing the start button. If we wanted the system to run continuously then the last movement in the sequence would have to trigger the first movement.
As an illustration of the types of problems that sequential control can be used for, consider the control required with an automatic machine to perform a number of sequential actions such as positioning objects, operating clamps and then operating some machine tool (FIG. 17). This requires the switching in sequence of a number of cylinders, the movements of the cylinder pistons being the mechanisms by which the actions are initiated.
3.2 Shuttle valve
The most common form of directional control valve is the shuttle or spool valve. Shuttle valves have a spool moving horizontally within the valve body. Raised areas, termed lands, block or open ports to give the required valve operation. FIG. 18 illustrates these features with a 3/2 valve. In the first position, the shuttle is located so that its lands block off the 3 port and leave open, and connected, the 1 and 2 ports. In the second position, the shuttle is located so that it blocks of the 1 port and leaves open, and connected, the 2 and 3 ports. The shuttle can be made to move between these two positions by manual, mechanical, electrical or pressure signals applied to the two ends of the shuttle.
FIG. 18 3/2 shuttle valve
FIG. 19 shows an example of a 4/3 shuttle valve. It has the rest position with all ports closed. When the shuttle is moved from left to right, the pressure is applied to output port 2 and port 4 is connected to the exhaust port. When the shuttle moves from right to left, pressure is applied to output port 4 and port 2 is connected to the exhaust port.
FIG. 19 4/3 shuttle valve
FIG. 20 Example
Example:
State what happens for the pneumatic circuit shown in FIG. 20 when the push-button is pressed and then released.
The right-hand box shows the initial position with the pressure source, i.e. the circle with the dot in the middle, connected to a closed port and the output from the right-hand end of the cylinder connected to the exhaust port, i.e. the open triangle. When the push-button is pressed the connections between the ports become those indicated in the left-hand box. The pressure source is then connected to the output port and hence to the right-hand end of the cylinder and forces the piston back against its spring and so from left to right. When the push-button is released, the connections between the ports become those in the right-hand box and the right-hand end of the cylinder is exhausted. The piston then moves back from left to right.
4. Flow control valves
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 (FIG. 21). The term single seated is used where just one plus is involved and double seated where there 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.
FIG. 21 Body globe valve: (a) single, (b) double seated
FIG. 22 Direct action: (a) air pressure increase to close, (b) air
pressure increase to open
FIG. 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 (FIG. 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 pressure and those 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, direct and reverse action forms (FIG. 23) with the difference being the position of the spring. The valve body is joined to the diaphragm element by the yoke.
FIG. 23 (a) Direct action (b) reverse action.
FIG. 24 Effect of plug shape on flow.
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, FIG. 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 FIG. 24 shows how the shape of the plug determines how the rate of flow is related to the displacement of the valve stem:
1. Linear 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 i t is a constant. If Q is the flow rate at a valve stem displacement S and ^ma x is the maximum flow rate at the maximum stem displacement Qmax , then we have:
Q/ Qmax=S/ Smax
or the percentage change in the flow rate equals the percentage change in the stem displacement. Such valves are widely used for the control of liquids entering cisterns when the liquid level is being 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-off control systems where the valve has to move quickly from open to closed and vice versa.
3. Equal percentage plug
The 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.:
Hence we can write 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 = Qmin. If we write this expression for small changes and then integrate it we obtain:
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 m^3/s. 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 the percentage flow rate is the same as the percentage stem displacement, then a percentage stem displacement of 50% gives a percentage flow rate of 50%, i.e. 10 m^3/s.
Example:
A valve has a stem movement at full travel of 30mm and an equal percentage plug. This gives a flow rate of 2 m^3/s when the stem position is 0. When the stem is at full travel there is a maximum flow rate of 20 m^3/s. What will be the flow rate when the stem movement is 15 mm?
Using the equation:
4.2 Rangeability and turndown
The term rangeability R is used for the ratio Qmax/Qmin, i.e. the ratio of the maximum to minimum rates of controlled flow. Thus, if the minimum 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 term turndown is used for the ratio:
turndown = normal max flow /min. controllable flow
For example, a valve might be required to handle a maximum flow which is 70% of that possible. With a minimum flow rate of 2.0% of the maximum flow possible, then the turndown is 70/2.0 = 35.
4.3 Control valve sizing
The term control valve sizing is 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:
rate of flow Q = K __/[pressure drop]
where A T is a constant which depends on the size of the constriction produced by the presence of the valve. The equations used for determining valve sizes are based on this equation. For a liquid, this equation is written as:
Q = Av√[Δ p /ρ m^3/s
where Av is the valve flow coefficient, delta p the pressure drop in Pa across the valve and p the density in kg/m^3 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:
G is the specific gravity (relative density) and Ap is the pressure difference. Other equations are available for gases and steam. For gases:
where T is the temperature on the Kelvin scale and p the inlet pressure.
For steam:
where V is the specific volume of the steam in m^3/kg, the specific volume being the volume occupied by 1 kg. Table 1 shows some typical values of ^v, Cv and the related valve sizes.
Table 1 Flow coefficients and valve size
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 m^3/s and the permissible pressure drop across the valve at this flow rate is 300 kPa.
Taking the density of water as 1000 kg/m^3 we have:
Thus, using Table 1, this value of coefficient indicates that the required valve size is 960 mm.
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 to operate the valve and so increase the speed of valve movement. FIG. 25 shows the basic elements of a positioner.
FIG. 25 Valve 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 the nozzle and so cuts down the air escaping from it. As a consequence, the 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.
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