A closer look at the figures used so far to describe the effect of proportional control shows that the output is assumed to be reverse acting. In other words, a rise in process temperature causes the control signal to fall and the valve to close. This is usually the situation on heating controls. This configuration would not work on a cooling control; here the 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.
The 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 2°C.
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 2°C. The same valve opening of 66.7% now coincides with the room temperature at 18°C.
The effects of manual reset are demonstrated in Figure 5.2.15.
Integral control - automatic reset action
‘Manual reset’ is usually unsatisfactory in process plant where each load change will require a reset action. It is also quite 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.
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 ‘integral action’. Automatic reset uses an electronic or pneumatic integration routine to perform the reset function. The most commonly 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 time taken for the controller output to change due to the integral action to equal the output change due to the proportional action. Integral action gives a steadily increasing corrective action as long as an error continues to exist. Such corrective action will increase with time and must therefore, at some time, be sufficient to eliminate the steady state error altogether, providing sufficient time elapses before another change occurs. The controller allows the integral time 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 shown in Figure 5.2.16, for 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 the proportional 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 heat exchanger is designed to maintain water at a fixed temperature.
The set point is 80°C, the P-band is set at 5°C (±2.5°C), and the load suddenly changes such that the returning water temperature falls almost instantaneously to 60°C.
Figure 5.2.16 shows the effect of this sudden (step change) in load on the actual water temperature. The measured value changes almost instantaneously from a steady 80°C to a value of 60°C.
By the nature of the integration process, the generation of integral control action must lag behind the proportional control action, introducing a delay and more dead time to the response. This could have serious consequences in practice, because it means that the initial control response, which in a proportional system would be instantaneous and fast acting, is now subjected to a delay and responds slowly. This may cause the actual value to run out of control and the system to oscillate. These oscillations may increase or decrease depending on the relative values of the controller gain and the integral action. If applying integral action it is important to make sure, that it is necessary and 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 large step change or the system being shut down, the value of the integral can become excessively large and cause overshoot 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 other words, 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 action
A Derivative action (referred to by the letter D) measures and responds to the rate of change of process signal, and adjusts 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 when there is a change in the process condition. It is interesting to note that derivative action will only apply itself when there 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 applying too much can cause more problems than it solves.
D action is again adjustable within the controller, and referred to as TD in time units:
TD = 0 – Means no D action.
TD = Infinity – Means infinite D action.
P + D controllers can be obtained, but proportional offset will probably be experienced. It is worth remembering that the main disadvantage with a P control is the presence of offset. To overcome and remove offset, ‘I’ action is introduced. The frequent existence of time lags in the control loop explains the need for the third action D. The result is a P + I + D controller which, if properly tuned, can in most processes give a rapid and stable response, with no offset and without overshoot.
P 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.
Summary of modes of control
A 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.
The various characteristics can be summarised, as shown in Figure 5.2.17.
Finally, the controls engineer must try to avoid the danger of using unnecessarily complicated controls for a specific application. The least complicated control action, which will provide the degree of control required, should always be selected.
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 to achieve its final value from its initial value, had the original rate of increase been maintained. This concept is depicted in Figure 5.12.18.
Example 5.2.2 A practical appreciation of the time constant
Consider two tanks of water, tank A at a temperature of 25°C, and tank B at 75°C. A sensor is placed in tank A and allowed to reach equilibrium temperature. It is then quickly transferred to tank B. The temperature difference between the two tanks is 50°C, and 63.2% of this temperature span can be calculated as shown below:
63.2% of 50°C = 31.6°C
The initial datum temperature was 25°C, consequently the time constant for this simple example is the time required for the sensor to reach 56.6°C, as shown below:
25°C + 31.6°C = 56.6°C
Often referred to as instability, cycling or oscillation. Hunting produces a continuously changing deviation from the normal operating point. This can be caused by:
• 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 to achieve and may result in a large proportional band in an attempt to achieve stability.
If the system load suddenly increases, the two-port valve will open wider, filling the heat exchanger with high temperature steam. The heat transfer rate increases extremely quickly causing the water system temperature to overshoot. The rapid increase in water temperature is picked up by the sensor and directs the two-port valve to close quickly. This causes the water temperature to fall, and the two-port valve to open again. This cycle is repeated, the cycling only ceasing when the PID terms are adjusted. The following example (Example 5.2.3) gives an idea of the effects of a hunting steam system.
Example 5.2.3 The effect of hunting on the system in Figure 5.2.19
Consider the steam to water heat exchanger system in Figure 5.2.19. Under minimum load conditions, the size of the heat exchanger is such that it heats the constant flowrate secondary water from 60°C to 65°C with a steam temperature of 70°C. The controller has a set point of 65°C and a P-band of 10°C.
Consider a sudden increase in the secondary load, such that the returning water temperature almost immediately drops by 40°C. The temperature of the water flowing out of the heat exchanger will also drop by 40°C to 25°C. The sensor detects this and, as this temperature is below the P-band, it directs the pneumatically actuated steam valve to open fully.
The steam temperature is observed to increase from 70°C to 140°C almost instantaneously. What is the effect on the secondary water temperature and the stability of the control system?
As demonstrated in Module 13.2 (The heat load, heat exchanger and steam load relationship), the heat exchanger temperature design constant, TDC, can be calculated from the observed operating conditions and Equation 13.2.2:
In this example, the observed conditions (at minimum load) are as follows:
When the steam temperature rises to 140°C, it is possible to predict the outlet temperature from Equation 13.2.5:
The heat exchanger outlet temperature is 80°C, which is now above the P-band, and the sensor now signals the controller to shut down the steam valve.
The steam temperature falls rapidly, causing the outlet water temperature to fall; and the steam valve opens yet again. The system cycles around these temperatures until the control parameters are changed. These symptoms are referred to as ‘hunting’. The control valve and its controller are hunting to find a stable condition. In practice, other factors will add to the uncertainty of the situation, such as the system size and reaction to temperature change and the 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 and steam heated heat exchanger would not be a problem.
Lag 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 is opened admitting large amounts of cold air. The room temperature will fall but there will be a delay while the mass of the sensor cools down to the new temperature - this is known as control lag. The delay time is also referred to as dead time.
Having then asked for more heat from the room heater, it will be some time before this takes effect and warms up the room to the point where the thermostat is satisfied. This is known as system lag or thermal lag.
This relates to the control valve and is the ratio between the maximum controllable flow and the minimum controllable flow, between which the characteristics of the valve (linear, equal percentage, quick opening) will be maintained. With most control valves, at some point before the fully closed position is reached, there is no longer a defined control over flow in accordance with the valve characteristics. Reputable manufacturers will provide rangeability figures for their valves.
Turndown ratio is the ratio between the maximum flow and the minimum controllable flow. It will be substantially less than 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.