Proportional Gain

7/31/2019 Proportional Gain

1/36

Top

Modes of control

An automatic temperature control might consist of a valve, actuator, controller and sensor detecting the spacetemperature in a room. The control system is said to be 'in balance' when the space temperature sensor does notregister more or less temperature than that required by the control system. What happens to the control valve when

the space sensor registers a change in temperature (a temperature deviation) depends on the type of control systemused. The relationship between the movement of the valve and the change of temperature in the controlled mediumis known as the mode of control or control action.

There are two basic modes of control:

On/Off - The valve is either fully open or fully closed, with no intermediate state.

Continuous - The valve can move between fully open or fully closed, or be held at any intermediate position.

Variations of both these modes exist, which will now be examined in greater detail.

Top

On/off controlOccasionally known as two-step or two-position control, this is the most basic control mode. Considering the tank ofwater shown in Figure 5.2.1, the objective is to heat the water in the tank using the energy given off a simple steamcoil. In the flow pipe to the coil, a two port valve and actuator is fitted, complete with a thermostat, placed in the waterin the tank.

Fig. 5.2.1 On/offtemperature control of water in a tank

The thermostat is set to 60C, which is the required temperature of the water in the tank. Logic dictates that if theswitching point were actually at 60C the system would never operate properly, because the valve would not know

whether to be open or closed at 60C. From then on it could open and shut rapidly, causing wear.

For this reason, the thermostat would have an upper and lower switching point. This is essential to prevent over-rapidcycling. In this case the upper switching point might be 61C (the point at which the thermostat tells the valve to shut)and the lower switching point might be 59C (the point when the valve is told to open). Thus there is an in-builtswitching difference in the thermostat of 1C about the 60C set point.

This 2C (1C) is known as the switching differential. (This will vary between thermostats). A diagram of theswitching action of the thermostat would look like the graph shown in Figure 5.2.2. The temperature of the tankcontents will fall to 59C before the valve is asked to open and will rise to 61C before the valve is instructed to close.
http://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#tophttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#tophttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#tophttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#tophttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#tophttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#top


2/36

Fig. 5.2.2 On/off switching action of thethermostat

Figure 5.2.2 shows straight switching lines but the effect on heat transfer from coil to water will not be immediate. Itwill take time for the steam in the coil to affect the temperature of the water in the tank. Not only that, but the water inthe tank will rise above the 61C upper limit and fall below the 59C lower limit. This can be explained by crossreferencing Figures 5.2.2 and 5.2.3. First however it is necessary to describe what is happening.

At point A (59C, Figure 5.2.3) the thermostat switches on, directing the valve wide open. It takes time for the transferof heat from the coil to affect the water temperature, as shown by the graph of the water temperature in Figure 5.2.3.

At point B (61C) the thermostat switches off and allows the valve to shut. However the coil is still full of steam, whichcontinues to condense and give up its heat. Hence the water temperature continues to rise above the upper switchingtemperature, and 'overshoots' at C, before eventually falling.

Fig. 5.2.3 Tank temperatureversus time

From this point onwards, the water temperature in the tank continues to fall until, at point D (59C), the thermostattells the valve to open. Steam is admitted through the coil but again, it takes time to have an effect and the watertemperature continues to fall for a while, reaching its trough of undershoot at point E.

The difference between the peak and the trough is known as the operating differential. The switching differential ofthe thermostat depends on the type of thermostat used. The operating differential depends on the characteristics of

the application such as the tank, its contents, the heat transfer characteristics of the coil, the rate at which heat istransferred to the thermostat, and so on.

Essentially, with on/off control, there are upper and lower switching limits, and the valve is either fully open or fullyclosed - there is no intermediate state.

However, controllers are available that provide a proportioning time control, in which it is possible to alter the ratio ofthe 'on' time to the 'off' time to control the controlled condition. This proportioning action occurs within a selectedbandwidth around the set point; the set point being the bandwidth mid point.


3/36

If the controlled condition is outside the bandwidth, the output signal from the controller is either fully on or fully off,acting as an on/off device. If the controlled condition is within the bandwidth, the controller output is turned on and offrelative to the deviation between the value of the controlled condition and the set point.

With the controlled condition being at set point, the ratio of 'on' time to 'off' time is 1:1, that is, the 'on' time equals the'off' time. If the controlled condition is below the set point, the 'on' time will be longer than the 'off' time, whilst if abovethe set point, the 'off' time will be longer, relative to the deviation within the bandwidth.

The main advantages of on/off control are that it is simple and very low cost. This is why it is frequently found ondomestic type applications such as central heating boilers and heater fans.

Its major disadvantage is that the operating differential might fall outside the control tolerance required by theprocess. For example, on a food production line, where the taste and repeatability of taste is determined by precisetemperature control, on/off control could well be unsuitable.

By contrast, in the case of space heating there are often large storage capacities (a large area to heat or cool that willrespond to temperature change slowly) and slight variation in the desired value is acceptable. In many cases on/offcontrol is quite appropriate for this type of application.

If on/off control is unsuitable because more accurate temperature control is required, the next option is continuouscontrol.

Top

Continuous control

Continuous control is often called modulating control. It means that the valve is capable of moving continually tochange the degree of valve opening or closing. It does not just move to either fully open or fully closed, as with on-offcontrol.

There are three basic control actions that are often applied to continuous control:

Proportional (P)

Integral (I)

Derivative (D)

It is also necessary to consider these in combination such as P + I, P + D, P + I + D. Although it is possible tocombine the different actions, and all help to produce the required response, it is important to remember that both theintegral and derivative actions are usually corrective functions of a basic proportional control action.

The three control actions are considered below.

Proportional controlThis is the most basic of the continuous control modes and is usually referred to by use of the letter 'P'. The principleaim of proportional control is to control the process as the conditions change.

This section shows that:

The larger the proportional band, the more stable the control, but the greater the offset.

The narrower the proportional band, the less stable the process, but the smaller the offset.

The aim, therefore, should be to introduce the smallest acceptable proportional band that will always keep theprocess stable with the minimum offset.

In explaining proportional control, several new terms must be introduced.

To define these, a simple analogy can be considered - a cold water tank is supplied with water via a float operatedcontrol valve and with a globe valve on the outlet pipe valve 'V', as shown in Figure 5.2.4. Both valves are the samesize and have the same flow capacity and flow characteristic. The desired water level in the tank is at point B(equivalent to the set point of a level controller).
http://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#tophttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#tophttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#top


4/36

It can be assumed that, with valve 'V' half open, (50% load) there is just the right flowrate of water entering via thefloat operated valve to provide the desired flow out through the discharge pipe, and to maintain the water level in thetank at point at B.

The questions these people ask about steam are markedly different.

Fig. 5.2.4 Valve 50%open

The system can be said to be in balance (the flowrate of water entering and leaving the tank is the same); undercontrol, in a stable condition (the level is not varying) and at precisely the desired water level (B ); giving the requiredoutflow.

With the valve 'V' closed, the level of water in the tank rises to point A and the float operated valve cuts off the watersupply (see Figure 5.2.5 below).

The system is still under control and stable but control is above level B. The difference between level B and the actualcontrolled level, A, is related to the proportional band of the control system.

Once again, if valve 'V' is half opened to give 50% load, the water level in the tank will return to the desired level,point B.

Fig. 5.2.5 Valve closedThis means the system is simpler and less expensive than, for example, a high temperature hot water system. The

high efficiency of steam plant means it is compact and makes maximum use of space, something which is often at apremium within plant.

Furthermore, upgrading an existing steam system with the latest boilers and controls typically represents 50% of thecost of removing it and replacing it with a decentralised gas fired system.

Q. How will the operating and maintenance costs of a steam system affect overheadcosts ?


5/36

Centralised boiler plant is highly efficient and can use low interruptible tariff fuel rates. The boiler can even be fuelledby waste, or form part of a state-of-the-art Combined Heat and Power plant.

Steam equipment typically enjoys a long life - figures of thirty years or more of low maintenance life are quite usual.

Modern steam plant, from the boiler house to the steam using plant and back again, can be fully automated. Thisdramatically cuts the cost of manning the plant.

Sophisticated energy monitoring equipment will ensure that the plant remains energy efficient and has a low manningrequirement.

All these factors in combination mean that a steam system enjoys a low lifetime cost.

Q. If a steam system is installed, how can the most use be made of it ?

Steam has a range of uses. It can be used for space heating of large areas, for complex processes and forsterilisation purposes.

Using a hospital as an example, steam is ideal because it can be generated centrally at high pressure, distributedover long distances and then reduced in pressure at the point of use. This means that a single high pressure boilercan suit the needs of all applications around the hospital, for example, heating of wards, air humidification, cooking of

food in large quantities and sterilisation of equipment.

It is not as easy to cater for all these needs with a water system.

Q. What if needs change in the future ?

Steam systems are flexible and easy to add to. They can grow with the company and be altered to meet changingbusiness objectives.

Q. What does using steam say about the company ?

The use of steam is environmentally responsible. Companies continue to choose steam because it is generated with

high levels of fuel efficiency. Environmental controls are increasingly stringent, even to the extent that organisationshave to consider the costs and methods of disposing of plant before it is installed. All these issues are consideredduring the design and manufacture of steam plant.

Fig. 5.2.6 Valve openThe system is under control and stable, but there is an offset; the deviation in level between points B and C. Figure5.2.7 combines the three conditions used in this example.

The difference in levels between points A and C is known as the Proportional Band or P-band, since this is thechange in level (or temperature in the case of a temperature control) for the control valve to move from fully open tofully closed.


6/36

One recognised symbol for Proportional Band is Xp.

The analogy illustrates several basic and important points relating to proportional control:

The control valve is moved in proportion to the error in the water level (or the temperature deviation, in thecase of a temperature control) from the set point.

The set point can only be maintained for one specific load condition.

Whilst stable control will be achieved between points A and C, any load causing a difference in level to thatof B will always provide an offset.

Fig. 5.2.7 Proportional bandNote: By altering the fulcrum position, the system Proportional Band changes. Nearer the float gives a narrower P-band, whilst nearer the valve gives a wider P-band. Figure 5.2.8 illustrates why this is so. Different fulcrum positionsrequire different changes in water level to move the valve from fully open to fully closed. In both cases, It can be seenthat level B represents the 50% load level, A represents the 0% load level, and C represents the 100% load level. Itcan also be seen how the offset is greater at any same load with the wider proportional band.

Fig.5.2.8 Demonstrating the relationship between P-band and offset

The examples depicted in Figures 5.2.4 through to 5.2.8 describe proportional band as the level (or perhapstemperature or pressure etc.) change required to move the valve from fully open to fully closed. This is convenient formechanical systems, but a more general (and more correct) definition of proportional band is the percentage changein measured value required to give a 100% change in output. It is therefore usually expressed in percentage termsrather than in engineering units such as degrees centigrade.

For electrical and pneumatic controllers, the set value is at the middle of the proportional band. The effect of changingthe P-band for an electrical or pneumatic system can be described with a slightly different example, by using atemperature control.

The space temperature of a building is controlled by a water (radiator type) heating system using a proportionalaction control by a valve driven with an electrical actuator, and an electronic controller and room temperature sensor.The control selected has a proportional band (P-band or Xp) of 6% of the controller input span of 0 - 100C, and thedesired internal space temperature is 18C. Under certain load conditions, the valve is 50% open and the required


7/36

internal temperature is correct at 18C.

A fall in outside temperature occurs, resulting in an increase in the rate of heat loss from the building. Consequently,the internal temperature will decrease. This will be detected by the room temperature sensor, which will signal thevalve to move to a more open position allowing hotter water to pass through the room radiators.

The valve is instructed to open by an amount proportional to the drop in room temperature. In simplistic terms, if the

room temperature falls by 1C, the valve may open by 10%; if the room temperature falls by 2C, the valve will openby 20%.

In due course, the outside temperature stabilises and the inside temperature stops falling. In order to provide theadditional heat required for the lower outside temperature, the valve will stabilise in a more open position; but theactual inside temperature will be slightly lower than 18C.

Example 5.2.1 and Figure 5.2.9 explain this further, using a P-band of 6C.

Example 5.2.1 Consider a space heating application with the following characteristics:

1. The required temperature in the building is 18C.2. The room temperature is currently 18C, and the valve is 50% open.3. The proportional band is set at 6% of 100C = 6C, which gives 3C either side of the 18C set point.

Figure 5.2.9 shows the room temperature and valve relationship:

Fig. 5.2.9 Room temperatureand valve relationship - 6C proportional band

As an example, consider the room temperature falling to 16C. From the chart it can be seen that the new valveopening will be approximately 83%.

With proportional control, if the load changes, so too will the offset:

A load of less than 50% will cause the room temperature to be above the set value.

A load of more than 50% will cause the room temperature to be below the set value.

The deviation between the set temperature on the controller (the set point) and the actual room temperature is calledthe 'proportional offset'.


8/36


9/36

Example 5.2.2Let the input span of a controller be 100C.

If the controller is set so that full change in output occurs over a proportional band of 20% the controller gain is:

Equally it could be said that the proportional band is 20% of 100C = 20C and the gain is:

Therefore the relationship between P-band and Gain is:

As a reminder:

A wide proportional band (small gain) will provide a less sensitive response, but a greater stability.

A narrow proportional band (large gain) will provide a more sensitive response, but there is a practical limitto how narrow the Xp can be set.

Too narrow a proportional band (too much gain) will result in oscillation and unstable control.

For any controller for various P-bands, gain lines can be determined as shown in Figure 5.2.11, where the controllerinput span is 100C.


10/36

Fig.5.2.11 Proportional band and gain

Reverse or direct acting control signalA closer look at the figures used so far to describe the effect of proportional control shows that the output is assumedto be reverse acting. In other words, a rise in process temperature causes the control signal to fall and the valve toclose. This is usually the situation on heating controls. This configuration would not work on a cooling control; herethe valve must open with a rise in temperature. This is termed a direct acting control signal. Figures 5.2.12 and 5.2.13

depict the difference between reverse and direct acting control signals for the same valve action.

Fig. 5.2.12 Reverse acting signal


11/36

Fig. 5.2.13 Direct acting signalOn mechanical controllers (such as a pneumatic controller) it is usual to be able to invert the output signal of thecontroller by rotating the proportional control dial. Thus, the magnitude of the proportional band and the direction ofthe control action can be determined from the same dial.

On electronic controllers, reverse acting (RA) or direct acting (DA) is selected through the keypad.

Gain line offset or proportional effectFrom the explanation of proportional control, it should be clear that there is a control offset or a deviation of the actualvalue from the set value whenever the load varies from 50%.

To further illustrate this, consider Example 5.2.1 with a 12C P-band, where an offset of 2C was expected. If theoffset cannot be tolerated by the application, then it must be eliminated.

This could be achieved by relocating (or resetting) the set point to a higher value. This provides the same valveopening after manual reset but at a room temperature of 18C not 16C.

Fig. 5.2.14 Gain line offset

Manual resetThe offset can be removed either manually or automatically. The effect of manual reset can be seen in Figure 5.2.14,and the value is adjusted manually by applying an offset to the set point of 2C.

It should be clear from Figure 5.2.14 and the above text that the effect is the same as increasing the set value by 2C.The same valve opening of 66.7% now coincides with the room temperature at 18C.


12/36

The effects of manual reset are demonstrated in Figure 5.2.15.

Fig.5.2.15 Effect of manual reset

Integral control - automatic reset action'Manual reset' is usually unsatisfactory in process plant where each load change will require a reset action. It is alsoquite common for an operator to be confused by the differences between:

Set value - What is on the dial.

Actual value - What the process value is.

Required value - The perfect process condition.


13/36

Such problems are overcome by the reset action being contained within the mechanism of an automatic controller.

Such a controller is primarily a proportional controller. It then has a reset function added, which is called 'integralaction'. Automatic reset uses an electronic or pneumatic integration routine to perform the reset function. The mostcommonly used term for automatic reset is integral action, which is given the letter I.

The function of integral action is to eliminate offset by continuously and automatically modifying the controller output

in accordance with the control deviation integrated over time. The Integral Action Time (IAT) is defined as the timetaken for the controller output to change due to the integral action to equal the output change due to the proportionalaction. Integral action gives a steadily increasing corrective action as long as an error continues to exist. Suchcorrective action will increase with time and must therefore, at some time, be sufficient to eliminate the steady stateerror altogether, providing sufficient time elapses before another change occurs. The controller allows the integraltime to be adjusted to suit the plant dynamic behaviour.

Proportional plus integral (P + I) becomes the terminology for a controller incorporating these features.

The integral action on a controller is often restricted to within the proportional band. A typical P + I response is shownin Figure 5.2.16, for a step change in load.

Fig. 5.2.16 P+IFunction after a step change in load

The IAT is adjustable within the controller:

If it is too short, over-reaction and instability will result.

If it is too long, reset action will be very slow to take effect.

IAT is represented in time units. On some controllers the adjustable parameter for the integral action is termed'repeats per minute', which is the number of times per minute that the integral action output changes by theproportional output change.

Repeats per minute = 1/(IAT in minutes)

IAT = Infinity - Means no integral action IAT = 0 - Means infinite integral action

It is important to check the controller manual to see how integral action is designated.

Overshoot and 'wind up'With P+ I controllers (and with P controllers), overshoot is likely to occur when there are time lags on the system.

A typical example of this is after a sudden change in load. Consider a process application where a process heatexchanger is designed to maintain water at a fixed temperature.


14/36

The set point is 80C, the P-band is set at 5C (2.5C), and the load suddenly changes such that the returning watertemperature falls almost instantaneously to 60C.

Figure 5.2.16 shows the effect of this sudden (step change) in load on the actual water temperature. The measuredvalue changes almost instantaneously from a steady 80C to a value of 60C.

By the nature of the integration process, the generation of integral control action must lag behind the proportionalcontrol action, introducing a delay and more dead time to the response. This could have serious consequences inpractice, because it means that the initial control response, which in a proportional system would be instantaneousand fast acting, is now subjected to a delay and responds slowly. This may cause the actual value to run out ofcontrol and the system to oscillate. These oscillations may increase or decrease depending on the relative values ofthe controller gain and the integral action. If applying integral action it is important to make sure, that it is necessaryand if so, that the correct amount of integral action is applied.

Integral control can also aggravate other situations. If the error is large for a long period, for example after a largestep change or the system being shut down, the value of the integral can become excessively large and causeovershoot or undershoot that takes a long time to recover. To avoid this problem, which is often called 'integral wind-up', sophisticated controllers will inhibit integral action until the system gets fairly close to equilibrium.

To remedy these situations it is useful to measure the rate at which the actual temperature is changing; in otherwords, to measure the rate of change of the signal. Another type of control mode is used to measure how fast the

measured value changes, and this is termed Rate Action or Derivative Action.

Derivative control - rate actionA Derivative action (referred to by the letter D) measures and responds to the rate of change of process signal, andadjusts the output of the controller to minimise overshoot.

If applied properly on systems with time lags, derivative action will minimise the deviation from the set point whenthere is a change in the process condition. It is interesting to note that derivative action will only apply itself whenthere is a change in process signal. If the value is steady, whatever the offset, then derivative action does not occur.

One useful function of the derivative function is that overshoot can be minimised especially on fast changes in load.However, derivative action is not easy to apply properly; if not enough is used, little benefit is achieved, and applyingtoo much can cause more problems than it solves.

D action is again adjustable within the controller, and referred to as TD in time units:

T D = 0 - Means no D action.

T D = Infinity - Means infinite D action.

P + D controllers can be obtained, but proportional offset will probably be experienced. It is worth remembering thatthe main disadvantage with a P control is the presence of offset. To overcome and remove offset, 'I' action isintroduced. The frequent existence of time lags in the control loop explains the need for the third action D. The resultis a P + I + D controller which, if properly tuned, can in most processes give a rapid and stable response, with nooffset and without overshoot.

PID controllersP and I and D are referred to as 'terms' and thus a P + I + D controller is often referred to as a three term controller.

Top

Summary of modes of controlA three-term controller contains three modes of control:

Proportional (P) action with adjustable gain to obtain stability.

Reset (Integral) (I) action to compensate for offset due to load changes.

Rate (Derivative) (D) action to speed up valve movement when rapid load changes take place.
http://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#tophttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#tophttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#top


15/36

The various characteristics can be summarised, as shown in Figure 5.2.17.

Fig.5.2.17 Summary of control modes and responsesFinally, the controls engineer must try to avoid the danger of using unnecessarily complicated controls for a specificapplication. The least complicated control action, which will provide the degree of control required, should always beselected.

Top

Further terminology

Time constant
http://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#tophttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#tophttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#top


16/36

This is defined as: 'The time taken for a controller output to change by 63.2% of its total due to a step (or sudden)change in process load'.

In reality, the explanation is more involved because the time constant is really the time taken for a signal or output toachieve its final value from its initial value, had the original rate of increase been maintained. This concept is depictedin Figure 5.12.18.

Fig. 5.2.18 Time constant

Example 5.2.2 A practical appreciation of the time constantConsider two tanks of water, tank A at a temperature of 25C, and tank B at 75C. A sensor is placed in tank A andallowed to reach equilibrium temperature. It is then quickly transferred to tank B. The temperature difference betweenthe two tanks is 50C, and 63.2% of this temperature span can be calculated as shown below:

63.2% of 50C = 31.6C

The initial datum temperature was 25C, consequently the time constant for this simple example is the time requiredfor the sensor to reach 56.6C, as shown below:

25C + 31.6C = 56.6C

HuntingOften referred to as instability, cycling or oscillation. Hunting produces a continuously changing deviation from thenormal operating point. This can be caused by:

Hunting

The proportional band being too narrow. The integral time being too short.

The derivative time being too long.

A combination of these.

Long time constants or dead times in the control system or the process itself.

In Figure 5.2.19 the heat exchanger is oversized for the application. Accurate temperature control will be difficult toachieve and may result in a large proportional band in an attempt to achieve stability.


17/36

If the system load suddenly increases, the two port valve will open wider, filling the heat exchanger with hightemperature steam. The heat transfer rate increases extremely quickly causing the water system temperature toovershoot. The rapid increase in water temperature is picked up by the sensor and directs the two port valve to closequickly. This causes the water temperature to fall, and the two port valve to open again. This cycle is repeated, thecycling only ceasing when the PID terms are adjusted. The following example (Example 5.2.3) gives an idea of theeffects of a hunting steam system.

Fig.5.2.19 Hunting

Example 5.2.3 The effect of hunting on the system in Figure 5.2.19Consider the steam to water heat exchanger system in Figure 5.2.19. Under minimum load conditions, the size of theheat exchanger is such that it heats the constant flowrate secondary water from 60C to 65C with a steamtemperature of 70C. The controller has a set point of 65C and a P-band of 10C.

Consider a sudden increase in the secondary load, such that the returning water temperature almost immediatelydrops by 40C. The temperature of the water flowing out of the heat exchanger will also drop by 40C to 25C. Thesensor detects this and, as this temperature is below the P-band, it directs the pneumatically actuated steam valve toopen fully.

The steam temperature is observed to increase from 70C to 140C almost instantaneously. What is the effect on thesecondary water temperature and the stability of the control system?

As demonstrated in Tutorial 13.2 (The heat load, heat exchanger and steam load relationship), the heat exchangertemperature design constant, TDC, can be calculated from the observed operating conditions and Equation 13.2.2:

Equation 13.2.2Where:

TDC = Temperature Design Constant

T s = Steam temperature

T 1 = Secondary fluid inlet temperature

T 2 = Secondary fluid outlet temperature

In this example, the observed conditions (at minimum load) are as follows:


18/36

When the steam temperature rises to 140C, it is possible to predict the outlet temperature from Equation 13.2.5:

Equation 13.2.5Where:

T s = 140C

T 1 = 60C - 40C = 20C temperature

TDC = 2

The heat exchanger outlet temperature is 80C, which is now above the P-band, and the sensor now signals thecontroller to shut down the steam valve.

The steam temperature falls rapidly, causing the outlet water temperature to fall; and the steam valve opens yetagain. The system cycles around these temperatures until the control parameters are changed. These symptoms arereferred to as 'hunting'. The control valve and its controller are hunting to find a stable condition. In practice, otherfactors will add to the uncertainty of the situation, such as the system size and reaction to temperature change andthe position of the sensor.

Hunting of this type can cause premature wear of system components, in particular valves and actuators, and gives

poor control.

Example 5.2.3 is not typical of a practical application. In reality, correct design and sizing of the control system andsteam heated heat exchanger would not be a problem.

LagLag is a delay in response and will exist in both the control system and in the process or system under control.

Consider a small room warmed by a heater, which is controlled by a room space thermostat. A large window isopened admitting large amounts of cold air. The room temperature will fall but there will be a delay while the mass of


19/36

the sensor cools down to the new temperature - this is known as control lag. The delay time is also referred to asdead time.

Having then asked for more heat from the room heater, it will be some time before this takes effect and warms up theroom to the point where the thermostat is satisfied. This is known as system lag or thermal lag.

Rangeability

This relates to the control valve and is the ratio between the maximum controllable flow and the minimum controllableflow, between which the characteristics of the valve (linear, equal percentage, quick opening) will be maintained. Withmost control valves, at some point before the fully closed position is reached, there is no longer a defined control overflow in accordance with the valve characteristics. Reputable manufacturers will provide rangeability figures for theirvalves.

Turndown ratioTurndown ratio is the ratio between the maximum flow and the minimum controllable flow. It will be substantially lessthan the valve's rangeability if the valve is oversized.

Although the definition relates only to the valve, it is a function of the complete control system.

Top

What do I do now?

The printable version of this page has now been replaced byThe Steam and Condensate Loop Book

View the complete collection ofSteam Engineering Tutorials

Control loops

An open loop control systemOpen loop control simply means there is no direct feedback from the controlled condition; in other words, noinformation is sent back from the process or system under control to advise the controller that corrective action isrequired. The heating system shown in Figure 5.3.1 demonstrates this by using a sensor outside of the room beingheated. The system shown in Figure 5.3.1 is not an example of a practical heating control system; it is simply beingused to depict the principle of open loop control.

Fig. 5.3.1 Openloop control

The system consists of a proportional controller with an outside sensor sensing ambient air temperature. Thecontroller might be set with a fairly large proportional band, such that at an ambient temperature of -1C the valve isfull open, and at an ambient of 19C the valve is fully closed. As the ambient temperature will have an effect on theheat loss from the building, it is hoped that the room temperature will be controlled.

However, there is no feedback regarding the room temperature and heating due to other factors. In mild weather,although the flow of water is being controlled, other factors, such as high solar gain, might cause the room tooverheat. In other words, open control tends only to provide a coarse control of the application.
http://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#tophttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#tophttp://www.spiraxsarco.com/resources/steam-book.asphttp://www.spiraxsarco.com/resources/steam-book.asphttp://www.spiraxsarco.com/resources/steam-book.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials.asphttp://www.spiraxsarco.com/resources/steam-book.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/basic-control-theory.asp#top


20/36

Figure 5.3.2 depicts a slightly more sophisticated control system with two sensors.

Fig. 5.3.2 Openloop control system with outside temperature sensor and water temperature sensor

The system uses a three port mixing valve with an actuator, controller and outside air sensor, plus a temperaturesensor in the water line.

The outside temperature sensor provides a remote set point input to the controller, which is used to offset the watertemperature set point. In this way, closed loop control applies to the water temperature flowing through the radiators.

When it is cold outside, water flows through the radiator at its maximum temperature. As the outside temperaturerises, the controller automatically reduces the temperature of the water flowing through the radiators.

However, this is still open loop control as far as the room temperature is concerned, as there is no feedback from thebuilding or space being heated. If radiators are oversized or design errors have occurred, overheating will still occur.

Closed loop controlQuite simply, a closed loop control requires feedback; information sent back direct from the process or system. Usingthe simple heating system shown in Figure 5.3.3, the addition of an internal space temperature sensor will detect the

room temperature and provide closed loop control with respect to the room.

In Figure 5.3.3, the valve and actuator are controlled via a space temperature sensor in the room, providing feedbackfrom the actual room temperature.


21/36

Fig. 5.3.3 Closed loopcontrol system with sensor for internal space temperature

DisturbancesDisturbances are factors, which enter the process or system to upset the value of the controlled medium. Thesedisturbances can be caused by changes in load or by outside influences.

For example; if in a simple heating system, a room was suddenly filled with people, this would constitute adisturbance, since it would affect the temperature of the room and the amount of heat required to maintain thedesired space temperature.

Feedback controlThis is another type of closed loop control. Feedback control takes account of disturbances and feeds this information

back to the controller, to allow corrective action to be taken. For example, if a large number of people enter a room,the space temperature will increase, which will then cause the control system to reduce the heat input to the room.

Feed-forward controlWith feed-forward control, the effects of any disturbances are anticipated and allowed for before the event actuallytakes place.

An example of this is bringing the boiler up to high fire before bringing a large steam-using process plant on line. Thesequence of events might be that the process plant is switched on. This action, rather than opening the steam valveto the process, instructs the boiler burner to high fire. Only when the high fire position is reached is the process steamvalve allowed to open, and then in a slow, controlled way.

Single loop controlThis is the simplest control loop involving just one controlled variable, for instance, temperature. To explain this, asteam-to-water heat exchanger is considered as shown in Figure 5.3.4.


22/36

Fig.5.3.4 Single loop control on a heating calorifier

The only one variable controlled in Figure 5.3.4 is the temperature of the water leaving the heat exchanger. This isachieved by controlling the 2-port steam valve supplying steam to the heat exchanger. The primary sensor may be athermocouple or PT100 platinum resistance thermometer sensing the water temperature.

The controller compares the signal from the sensor to the set point on the controller. If there is a difference, thecontroller sends a signal to the actuator of the valve, which in turn moves the valve to a new position. The controllermay also include an output indicator, which shows the percentage of valve opening.

Single control loops provide the vast majority of control for heating systems and industrial processes.

Other terms used for single control loops include:

Set value control.

Single closed loop control.

Feedback control.

Multi-loop control

The following example considers an application for a slow moving timber-based product, which must be controlled toa specific humidity level (see Figures 5.3.5 and 5.3.6).


23/36


24/36

Cascade controlWhere two independent variables need to be controlled with one valve, a cascade control system may be used.

Figure 5.3.7 shows a steam jacketed vessel full of liquid product. The essential aspects of the process are quiterigorous:

The product in the vessel must be heated to a certain temperature.

The steam must not exceed a certain temperature or the product may be spoiled.

The product temperature must not increase faster than a certain rate or the product may be spoiled.

If a normal, single loop control was used with the sensor in the liquid, at the start of the process the sensor woulddetect a low temperature, and the controller would signal the valve to move to the fully open position. This wouldresult in a problem caused by an excessive steam temperature in the jacket.

Fig. 5.3.7 Jacketed vesselThe solution is to use a cascade control using two controllers and two sensors:

A slave controller (Controller 2) and sensor monitoring the steam temperature in the jacket, and outputting asignal to the control valve.

A master controller (Controller 1) and sensor monitoring the product temperature with the controller outputdirected to the slave controller.

The output signal from the master controller is used to vary the set point in the slave controller, ensuring thatthe steam temperature is not exceeded.

Example 5.3.1 An example of cascade control applied to a process vesselThe liquid temperature is to be heated from 15C to 80C and maintained at 80C for two hours.

The steam temperature cannot exceed 120C under any circumstances.

The product temperature must not increase faster than 1C/minute.

The master controller can be ramped so that the rate of increase in water temperature is not higher than thatspecified.

The master controller is set in reverse acting mode, so that its output signal to the slave controller is 20 mA at lowtemperature and 4 mA at high temperature.

The remote set point on the slave controller is set so that its output signal to the valve is 4 mA when the steamtemperature is 80C, and 20 mA when the steam temperature is 120C.In this way, the temperature of the steam cannot be higher than that tolerated by the system, and the steam pressurein the jacket cannot be higher than the, 1 bar g, saturation pressure at 120C.


25/36

Top

Dynamics of the process

This is a very complex subject but this part of the text will cover the most basic considerations.

The term 'time constant', which deals with the definition of the time taken for actuator movement, has already been

outlined in Tutorial 5.1; but to reiterate, it is the time taken for a control system to reach approximately two-thirds of itstotal movement as a result of a given step change in temperature, or other variable.

Other parts of the control system will have similar time based responses - the controller and its components and thesensor itself. All instruments have a time lag between the input to the instrument and its subsequent output. Even thetransmission system will have a time lag - not a problem with electric/electronic systems but a factor that may need tobe taken into account with pneumatic transmission systems.

Figures 5.3.8 and 5.3.9 show some typical response lags for a thermocouple that has been installed into a pocket forsensing water temperature.

Fig. 5.3.8 Step change 5C

Fig. 5.3.9 Ramp change 5C

Apart from the delays in sensor response, other parts of the control system also affect the response time. Withpneumatic and self-acting systems, the valve/actuator movement tends to be smooth and, in a proportional controller,directly proportional to the temperature deviation at the sensor.

With an electric actuator there is a delay due to the time it takes for the motor to move the control linkage. Becausethe control signal is a series of pulses, the motor provides bursts of movement followed by periods where the actuatoris stationary. The response diagram (Figure 5.3.10) depicts this. However, because of delays in the processresponse, the final controlled temperature can still be smooth.
http://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/control-loops-and-dynamics.asp#tophttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/control-loops-and-dynamics.asp#tophttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/control-loops-and-dynamics.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/control-loops-and-dynamics.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/control-loops-and-dynamics.asphttp://www.spiraxsarco.com/resources/steam-engineering-tutorials/basic-control-theory/control-loops-and-dynamics.asp#top


26/36

Fig. 5.3.10 Comparison of responseby different actuators

The control systems covered in this Tutorial have only considered steady state conditions. However the process orplant under control may be subject to variations following a certain behaviour pattern. The control system is requiredto make the process behave in a predictable manner. If the process is one which changes rapidly, then the controlsystem must be able to react quickly. If the process undergoes slow change, the demands on the operating speed ofthe control system are not so stringent.

Much is documented about the static and dynamic behaviour of controllers and control systems - sensitivity, responsetime and so on. Possibly the most important factor of consideration is the time lag of the complete control loop.

The dynamics of the process need consideration to select the right type of controller, sensor and actuator.

Process reactionsThese dynamic characteristics are defined by the reaction of the process to a sudden change in the control settings,known as a step input. This might include an immediate change in set temperature, as shown in Figure 5.3.11.

The response of the system is depicted in Figure 5.3.12, which shows a certain amount of dead time before theprocess temperature starts to increase. This dead time is due to the control lag caused by such things as an electricalactuator moving to its new position. The time constant will differ according to the dynamic response of the system,affected by such things as whether or not the sensor is housed in a pocket.

Fig. 5.3.11 Step input


27/36

Fig. 5.3.12 Components of processresponse to step changes

The response of any two processes can have different characteristics because of the system. The effects of deadtime and the time constant on the system response to a sudden input change are shown graphically in Figure 5.3.12.

Systems that have a quick initial rate of response to input changes are generally referred to as possessing a firstorder response.

Systems that have a slow initial rate of response to input changes are generally referred to as possessing a secondorder response.

An overview of the basic types of process response (effects of dead time, first order response, and second orderresponse) is shown in Figure 5.3.13.


28/36

Fig. 5.3.13Response curves

This Tutorial will concentrate on available automatic control choices and the decisions which must be made beforeselection. Guidance is offered here rather than a set of rules, because actual decisions will depend upon varyingfactors; some of which, such as cost, personal preferences and current fashions, cannot be included here.

ApplicationIt is important to reflect on the three basic parameters discussed at the beginning of Tutorial 5.1: Safety, Stability and

Accuracy.

In order to select the correct control valve, details of the application and the process itself are required. For example:

Are any safety features involved? For instance, should the valve fail-open or fail-closed in the event of power

failure? Is separate control required for high and low limit? What property is to be controlled? For instance, temperature, pressure, level, flow?

lWhat is the medium and its physical properties. What is the flowrate?

What is the differential pressure across a control valve across the load range?

What are the valve materials and end connections?

What type of process is being controlled? For instance, a heat exchanger used for heating or processpurposes?

For temperature control, is the set point temperature fixed or variable?

Is the load steady or variable and, if it is variable, what is the time scale for change, fast or slow?

How critical is the temperature to be maintained?

Is a single loop or multi-loop control required?

What other functions (if any) are to be carried out by the control? For instance, normal temperature controlof a heating system, but with added frost protection during 'off' periods?

Is the plant or process in a hazardous area? Is the atmosphere or environment corrosive by nature or is the valve to be fitted externally or in a 'dirty'

area?

What motive power is available, such as electricity or compressed air, and at what voltage and pressure?

Motive powerThis is the power source to operate the control and drive the valve or other controlled device. This will usually beelectricity, or compressed air for a pneumatic system, or a mixture of both for an electropneumatic system. Self-actingcontrol systems require no external form of power to operate; they generate their own power from an enclosedhydraulic or vapour pressure system.


29/36

To some extent, the details of the application itself may determine the choice of control power. For example, if thecontrol is in a hazardous area, pneumatic or self-acting controls may be preferable to expensive intrinsically safe orexplosion-proof electric/electronic controls.

The following features are listed as a general comment on the various power source options:

Self-acting controlsAdvantages:

Robust, simple, tolerant of 'unfriendly' environments.

Easy to install and commission.

Provide proportional control with very high rangeability.

Controls can be obtained which fail-open or fail-closed in the event of an unacceptable overrun intemperature.

They are safe in hazardous areas.

Relatively maintenance free.

Disadvantages:

Self-acting temperature controls can be relatively slow to react, and Integral and Derivative control functionscannot be provided.

Data cannot be re-transmitted.

Pneumatic controlsAdvantages:

Robust.

They operate very quickly, making them suitable for processes where the process variables change rapidly.

The actuators can provide a high closing or opening force to operate valves against high differentialpressures.

The use of valve positioners will ensure accurate, repeatable control.

Pure pneumatic controls are inherently safe and actuators provide smooth operation.

Can be arranged to provide fail-open or fail-closed operation without additional cost or difficulty.

Disadvantages:

The necessary compressed air system can be expensive to install, if no supply already exists.

Regular maintenance of the compressed air system may be required.

Basic control mode is on/off or proportional although combinations of P+I and P+ I +D are available, butusually at greater cost than an equivalent electronic control system.

Installation and commissioning is straightforward and of a mechanical nature.

Electric controlsAdvantages:

Highly accurate positioning.

Controllers are available to provide high versatility with on-off or P+I+D combinations of control mode, andmulti-function outputs.

Disadvantages:

Electric valves operate relatively slowly, meaning they are not always suitable for rapidly changing processparameters such as pressure control on loads that change quickly.


30/36

Installation and commissioning involves both electrical and mechanical trades and the cost of wiring andinstallation of a separate power supply must be taken into account.

Electric actuators tend to be less smooth than their pneumatic counterparts. Spring return actuators arerequired for fail open or fail closed functions: This can substantially reduce the closing force available andthey usually cost more.

Intrinsically safe or explosion-proof electric controls are needed for use in hazardous areas; they are anexpensive proposition and, as such, a pneumatic or electropneumatic solution may be required, as

described below. Special installation techniques are required for these types of hazardous areas.

Electropneumatic controlsAdvantages:

Electropneumatic controls can combine the best features of electronic and pneumatic controls. Suchsystems can consist of pneumatically actuated valves, electric/electronic controllers, sensors and controlsystems, plus electropneumatic positioners or converters.

The combination provides the force and smooth operation of a pneumatic actuator/valve with the speed andaccuracy of an electronic control system. Fail-open or fail-closed operation can be provided without costpenalty and, by using suitable barriers and/or confining the electric/electronic part of the control system to'safe' (non-hazardous) areas, they can be used where intrinsic safety is required.

Disadvantages:

Electrical and compressed air supplies are required, although this is not normally a problem in industrialprocessing environments.

There are three important factors to take into account when considering the application and the required powersource:

Changes in load.

Whether the set value is critical or non-critical.

Whether the set value has to be varied.

The diagrams in Figure 5.4.1 and 5.4.2 help to explain


31/36

Fig.5.4.1 Changes in load and time


32/36

Fig.5.4.2 Critical nature of the set value

What type of controls should be installed?Different applications may require different types of control systems. Self-acting and pneumatic controls can be usedif load variations are fairly slow and if offset can be accepted, otherwise electropneumatic or electric controls shouldbe used. Figure 5.4.3 shows some different applications and suggestions on which method of control may beacceptable.


33/36

Fig.5.4.3 Variable set value and its critical nature


34/36

Types of valves and actuatorsThe actuator type is determined by the motive power which has been selected: self-acting, electrical, pneumatic orelectropneumatic, together with the accuracy of control and actuator speed required.

As far as valve selection is concerned, with steam as the flowing medium, choice is restricted to a two port valve.However, if the medium is water or another liquid, there is a choice of two port or three port valves. Their basic effectson the dynamics of the piping system have already been discussed.

A water application will usually determine whether a three port valve is used to mix or divert liquid flow. If changes insystem pressure with two port valves are acceptable, their advantages compared with three port valves include lowercost, simplicity and a less expensive installation. The choice of two port valves may also allow the inherent systempressure change to be used to switch on sequential pumps, or to reduce or increase the pumping rate of a variablespeed pump according to the load demand.

When selecting the actual valve, all the factors considered earlier must be taken into account which include; bodymaterial, body pressure/temperature limits, connections required and the use of the correct sizing method. It is alsonecessary to ensure that the selection of valve/actuator combination can operate against the differential pressureexperienced at all load states. (Differential pressure in steam systems is generally considered to be the maximumupstream steam absolute pressure. This allows for the possibility of steam at sub-atmospheric pressure on thedownstream side of the valve).

Controllers

Safety is always of great importance. In the event of a power failure, should the valve fail-safe in the open or closedposition?

Is the control to be direct-acting (controller output signal rises with increase in measured variable) or reverse-acting(controller output signal falls with increase in measured variable)?

If the application only requires on/off control, a controller may not be needed at all. A two-position actuator may beoperated from a switching device such as a relay or a thermostat. Where an application requires versatility, the multi-function ability of an electronic controller is required; perhaps with temperature and time control, multi-loop, multi-input/output.

Having determined that a controller is required, it is necessary to determine which control action is necessary, forinstance on/off, P, P I, or P I D.

The choice made depends on the dynamics of the process and the types of response considered earlier, plus the

accuracy of control required.

Before going any further, it is useful to define what is meant by 'good control'. There is no simple answer to thisquestion. Consider the different responses to changes in load as shown in Figure 5.4.4.


35/36

Fig.5.4.4 Examples of different responses to changes in load

Self-acting control is normally suitable for applications where there is a very large 'secondary-side' thermal capacitycompared to the 'primary-side' capacity.

Consider a hot water storage calorifier as shown in Figure 5.4.5 where the large volume of stored water is heated bya steam coil.


36/36

Fig.5.4.5 Hot water storage calorifier

When the water in the vessel is cold, the valve will be wide open, allowing steam to enter the coil, until the storedwater is heated to the desired temperature. When hot water is drawn from the vessel, the cold water which enters thevessel to take its place will reduce the water temperature in the vessel. Self-acting controls will have a relatively largeproportional band and as soon as the temperature drops, the valve will start to open. The colder the water, the moreopen the steam valve.

Figure 5.4.6 shows a non-storage plate type heat exchanger with little thermal storage capacity on either the primaryor the secondary side, and with a fast reaction time. If the load changes rapidly, it may not be possible for a self-acting control system to operate successfully. A better solution would be to use a control system that will react quickly

to load changes, and provide accuracy at the same time.

Fig. 5.4.6 Heatexchanger with little storage capacity

Proportional Gain

Documents

Transcript of Proportional Gain