Industrial controllers , basic theory
The first and most basic characteristic of the controller response has been shown to be either direct or reverse action. Once this distinction has been made, several types of responses are used to control a process. These are:
On/off control is illustrated in figure 5
for a reverse acting controller and an air-to-close valve. An on/off controller only has two outputs, either full maximum or full minimum. For this system it has been determined that when the measurement falls below the set point, the valve must be closed to cause it to increase. Thus, whenever the signal to the automatic controller is below the set point, the controller output will be 100%. As the measurement crosses the set point the controller output goes to 0%. This eventually causes the measurement to decrease and as the measurement crosses the set point again, the output goes to maximum. This cycle will continue indefinitely, because the controller cannot balance the supply against the load. This continuous oscillation may, or may not, be acceptable depending upon the amplitude and length of the cycle. Rapid cycling causes frequent upsets to the plant supply system and excessive valve wear. The time of each cycle depends on the dead time in the process because the dead time determines how long it takes for the measurement signal to reverse its direction once it crosses the set point and the output of the controller changes. The amplitude of the signal depends on how rapidly the measurement signal changes during each cycle. On large capacity process, such as temperature vats, the large capacity causes a very long time constant. Therefore, the measurement can change only very slowly.
The result is that the cycle occurs within a very narrow band around the set point, and this control may be quite acceptable, if the cycle is not too rapid. By far the most common type of control used in industry is on/off control. However if the process measurement is more responsive to changes in the supply , the amplitude and frequency of the cycle begins to increase. At some point, this cycle will become unacceptable and some form of proportional control must be applied.
In order to study the remaining three modes of automatic control open loop responses will be used. Open loop means that only the response of the controller will be considered.
Figure 6 shows an automatic controller with an artificial signal from a manual regulator introduced as the measurement. The set point is introduced normally and the output is recorded. With this arrangement, the specific controller responses to any desired change in measurement can be observed.
Proportional action - Proportional controllers
Fig. 6-A . The effects of adding P, I, and D actions to a controller
Home heating systems, air conditioners, and refrigerators ordinarily have their temperature regulating done by "on-off" (sometimes called by engineers "bangbang") switches of some kind. For example, in Fig. 6-A in the left, if a temperature is too low, and a heater is therefore turned on, there is a time delay until the heat begins to spread throughout the system and it reaches the temperature sensor ("thermostat"). When this sensor finally does turn off the heat source, it will be too late to prevent some excessive heat from continuing to spread through the system, so the temperature will overswing and temporarily become too high. This is shown in the top diagram of the figure ("not damped").
It is an oscillation, like electronic oscillations in LC circuits where the inductor causes overswing of voltage in the capacitor, even after the transistor has turned off the input . In general, it is partly caused by a time lag (or "phase difference") between the power source and the sensor.
There are two convenient ways to decrease the overswing effect in heating systems. The one used in most home systems is called an "anticipator." A very small heater is placed right next to the sensor, so when the heat is turned on, the sensor responds sooner than it would otherwise, thus decreasing the time lag. It has also been used in laboratory and factory equipment. While this makes the problem less bad, it does not completely eliminate overswing.
|A better way to attack the problem, used in most modern engineering temperature controllers, is called "proportional control." In this system, the amount of heat (or cooling effect in a refrigerator) is decreased as the temperature gets closer and closer to the desired value. In other words, the power applied is proportional to the "error signal" that the sensor is indicating. This proportionality is the "P" in modern systems which are referred to as "PID controllers."|
The Effect of P
The proportionality (which usually requires fairly complex electronics) has the overall effect of "damping" the controller system, and this decreases the overswing. Sometimes the knob on a controller that adds this function is labeled "damping," but most often it is called "proportional band (PB)." If the "band" is made narrower, there is a steeper gradient of power increase as the temperature goes down; if the band is set by the operator to be wider, there is a more gradual application of power (but over a wider temperature range).
The Effect of I
The damping can be used too much, and in fact it is difficult to avoid this and still stop the oscillations. When it is "overdamped" (see Fig. 6-A ), it will "settle" at the wrong temperature, somewhat "offset" from the true desired value. (The dashed line in the figure shows the true desired temperature. As usual in scientific diagrams, capital T is temperature, and small t is time.) The cure for this problem is to use "integration." This makes use of a simple computer, usually analog instead of digital, which adds up (integrates) the error signals (desired temperature minus the sensor temperature), repeated at various times, and it slowly changes the amount of heat output to cut this integrated error down to zero. Sometimes it is expressed in units of time (usually from 30 seconds to 2 minutes) over which the integration is carried out before it is then repeated. The integration knob on a PID controller sometimes is labeled "reset," because it changes the "setting" temperature to an artificially modified value, in order to slowly drift the temperature to what is really desired. It should be noted that this knob only has an effect on errors that exist for a long time, not on short-term "upsets."
The Effect of D
Sometimes the overall effect of a controller, in spite of the various correction factors, still overswings when a short blast of cold air occasionally occurs, etc.
To minimize this, a "derivative" computer can be used. This is sensitive to the slope of the measured temperature versus time, and if it is fast, it allows more corrective effect to be applied. The knob is sometimes labeled "D" and sometimes "rate." It does not affect long-term "offset" errors.
PID controllers are used for much more than temperature settings. More and more automation machinery is controlled by such equipment, which prevents the motion of robot arms from oscillating, and minimizes cumulative error, etc.
Some factory workers fail to understand the principles outlined above and simply "twiddle the knobs" almost randomly, hoping to get good control by luck.
Usually the best sequence of setting these controllers is to adjust P first, then I, and then D, taking considerable time to let things reach a constant value before making the next change.
Proportional response is the basis for the three mode controller. If the other two, integral (reset) and derivative, are present, they are added to the proportional response. "Proportional" means the that the present change in the output of the controller is some multiple of the percent change in the measurement
This multiple is called the "gain" of the controller. For some controllers, proportional action is adjusted by such a "gain" adjustment, while for others a "proportional band" adjustment is used. Both have the same purposes and effect.
Figure 7 illustrates the response of a proportional controller by an input/output pointer pivoting on one oil these positions. With the pivot in the center between the input and the output graph, 100% change in measurement is required to obtain 100% change in output, or full valve travel .A controller adjusted to respond in this way is said to have a 100% proportional band. When the pivot is moved to the right hand position, the measurement input would have to change by 200% in order to obtain full output change from 0% to 100%, this is called a 200% proportional band. Finally, if the pivot were in the left hand position and if the measurement moved only over 50% of the scale the output would change over 100% of the scale. This is called a 50% proportional band. Thus, the smaller the proportional band, the smaller amount the measurement must change to cause full valve travel. Or, in other words the smaller the proportional band, the greater the output change for the same size measurement change. This same relationship is represented by figure 8.
This graph shows how the controller output will respond as a measurement
deviates from set point. Each line on the graph represents a particular
adjustment of the proportional band. Two basic properties of proportional
control can be observed from this graph:
1. For every value of proportional band whenever the measurement
equals the set point, the output is 50%.
2. Each value of the proportional band defines a unique relationship between measurement and output. For every measurement value there is a specific output value. For example; using the 100% proportional band line , whenever the measurement is 25% above the set point, the output from the controller must be 25%. The output from the controller can be 25% only if the measurement is 25% above setpoint. In the same way, whenever the output from the controller is 25%, the measurement will be 25% above set point. In other words there is one specific output value for every measurement value.
For any process control loop only one value of the proportional band is the best. As the proportional band is reduced, the controller response to any change in measurement becomes greater and greater. At some point depending upon the characteristic of each particular process, the response in the controller will be large enough to drive the measurement back in the opposite direction so far as to cause constant cycling the measurement. This proportional band value, known as the ultimate proportional band, is a limit on the adjustment of the controller in that loop. On the other hand, if too wide a proportional band is used, the controller response to any change in measurement is too small and the measurement is not controlled as tightly as possible. The determination of the proper proportional band for any application is part of the tuning procedure for that loop. Proper adjustment of the proportional band can be observed by the response of the measurement to an upset.
Figure 9 shows several examples of varying proportional band for the heat exchanger.
Ideally, the proper proportional band will produce quarter amplitude damping in which each half cycle is 1/2 the amplitude of the previous half cycle. The proportional band which will cause one quarter wave damping will be smaller, thereby yielding tighter control over the measured variable, as the dead time in the process decreases and the capacity increases.
One consequence of the application of proportional control to the basic control loop is offset. Offset means that the controller will maintain the measurement at a value different from the set point. This is most easily seen by referring to figure 3. Note that if the load valve is opened, flow will increase through the valve and the level will begin to fall. In order to maintain the level, the supply valve would have to open. But note that because of the proportional action of the linkage the increased open position can only be achieved at a lowered level. In other words, in order to restore the balance between the flow in and the flow out, the level must stabilize at a value below the set point. This difference, which will be maintained by the control loop, is called offset, and is characteristic of the application of proportional-only control feedback loops. The acceptability of proportional-only control depends on whether or not this offset can be tolerated. Since the error necessary to produce any output decreases with proportional band, the narrower the proportional band, the less the offset will be. For large capacity, small dead time applications accepting a very narrow proportional band, proportional-only control will probably be satisfactory since the measurement will remain within a small percentage band around the set point.
If it is essential that there be no steady state difference between measurement and set point under all load conditions, an additional function must be added to the controller.