Ziegler-Nichols Tuning
Some engineers have reportedly used a Ziegler-Nichols approach for tuning liquid-level loops. If the response of an open-loop process test shows an identifiable amount of dead time, then the parameter determination method depicted by Figure 6-7 and Equations 6-8 and 6-9 can be used. Table 6-1 can then be used to determine tuning parameters. The disadvantage of this technique is that it does not take into consideration either the worst-case disturbance nor the allowable maximum deviation of level.
Proportional-Only Control
If there is no reason to maintain the level at a fixed set point, but the aim is rather to prevent deviations beyond a particular limit, then you can use a proportional-only controller. Assum- ing that the allowable excursions above and below set point are equal, then the controller gain should be set according to this equation:
(6-31)
or the proportional band to 2 × ∆Lmax. The bias (manual reset) should be set to 50 percent. With this arrangement, if the disturbance is such that a controller output of 50 percent is required, the level will be at set point. Otherwise, there will be a steady-state offset between set point and level measurement. On a step change in inflow, the level will respond as a first- order lag with a time constant equal to the holdup time divided by the controller gain.
For a given value of ∆Lmax, this technique provides the lowest rate of change of the outflow, hence the minimum amount of disturbance to a downstream process unit. This can be a real advantage because when the inflow is very low and a large increase can be expected, there is more room to absorb the inflow. When the inflow is very high the level is high, so there is a large volume to allow a slow decrease in the outflow. The disadvantage of this method is that the level is rarely at set point. This is more of a disadvantage from the standpoint of the opera- tor’s acceptance of the technique than a technological limitation, however.
If closer control about the set point is desired, the controller gain can be increased. Although there is no theoretical upper limit for the gain on a proportional-only controller for an integrat- ing process, in practice, this will be limited by resonance that may occur within the loop. If the level sensor is an external cage type, there may be manometer effect between the liquid in the vessel and the liquid within the level-sensor cage. This will appear as an oscillation within the control loop, even though the total mass holdup may be unchanging. If the liquid has a large surface area, a resonant sloshing may occur, with a period that is proportional to the cross-sec- tional dimension. For a probe or other type of point-source measurement, this will also show up as an oscillation within the loop. Furthermore, splashing, such as from upper trays in a dis- tillation tower, may cause noise to appear on the level measurement. Thus, there will be a practical limit to the controller gain. Even so, many level loops are successfully controlled
∆ C max 100 K 2 L =
any measurement noise present will cause excessive valve action. Therefore, the gain may be reduced, in favor of utilizing some integral action within the controller.
Averaging Liquid-level Control
We mentioned earlier that many liquid-level loops are not critical. It is possible to tolerate fluctuation, even offset, if it smooths out the flow to a downstream process unit. This can be accomplished by lowering the controller gain and using a small amount of integral action. Such a technique is called “averaging liquid-level control” since it maintains the long-term average of the level at the set point.
Nonlinear Control
Some manufacturers provide a nonlinear control algorithm that has the effect of increasing the controller gain as the measurement gets further away from set point. The “error-squared algo- rithm” was introduced in chapter 5. This algorithm has a very low gain at set point, with increasing gain as the measurement gets further away from set point. Some manufacturers accomplish a similar function by using linear characterization of the error signal. Sometimes the nonlinearization is applied only to one controller mode, such as proportional mode or inte- gral mode, with the other controller modes seeing the normal error signal. This approach pro- vides a form of averaging level control.
An interesting approach for surge tank and averaging level control is presented in reference [6- 6]. Here the following form of error-squared algorithm for PI control is recommended:
. (6-32)
When written in the form:
(6-33)
it is obvious that this is a form of scheduled tuning in which both the effective controller gain, KC, and the effective integral time, TI, are made proportional to the absolute value of error. The result is that the product, effective controller gain times effective integral time, is con- stant, at all values of error.
, 2 C I
e e
e
1
m
K
*
e dt
100
100
T
=
+
∫
C Ie
e
m
K
e
e dt
100
100* T
=
+
∫
C C e ˆK K 100 =.
Therefore .
According to reference [6-6], other forms of implementation of error-squared PI control (including that depicted by Figure 5-8) may go unstable, since the product, effective gain times the effective integral time, varies with error.
There are certain analogies between this concept and the analytically developed technique for tuning liquid level loops presented earlier. From Equation 6-21 it is seen that:
(6-34)
Thus, for a selected decay ratio, which determines ζ through Equation 6-26, and a fixed holdup time, TL, the product of gain and integral time is constant. While the analogy probably cannot be stretched too far, there are additional analogies related to controller tuning which can be made:
• A larger value for the product, KCTI, will cause a more stable control loop.
• For a fixed value of KCTI, a larger value of KC, consequentlysmaller value for TI, will reduce both the maximum deviation due to a step load change and the period of oscil- lation.
As far as is known, no manufacturer provides an error-squared algorithm which is the equiva- lent of Equation 6-32 or 6-33. This form could be custom implemented by the special pro- gramming capabilities of many manufacturers’ systems, however.
OTHER TUNING SITUATIONS: RUNAWAY PROCESSES
Runaway processes are unstable in the open loop. That is, if the controller is left on manual, the measurement will continue to climb or fall until some physical (possibly disastrous) limit is reached. An example is an exothermic reactor. As the temperature rises, the reaction rate increases, causing a greater rate of heat evolution, and consequently a more rapid rise in tem- perature. Such processes are often controlled by modulating the flow of cooling water to the jacket of the reactor.
An interesting phenomenon occurs with runaway processes. As with most processes, an exces- sive controller gain will cause the loop to oscillate. But, in contrast with most processes, a gain that is too low will also cause loss of process control by allowing the measurement to continue to climb or fall. Thus, there is both an upper limit and a lower limit for the controller gain. The difference between these limits is the permissible window for the gain. If there is a wide win-
I I
100
ˆT
T
e
=
C I C Iˆ ˆ
K T
=
K T
2 C I LK T
=
4ζ
T
may ensue if the window is narrow.
Exothermic chemical reactors are often developed by first constructing a laboratory or pilot- sized unit. Suppose such a reactor has been built and, because of the wide window of permissi- ble controller gain, is relatively easy to control. Then, the reactor is scaled up to a production- sized unit. As the size is increased, the volume, which determines the rate of heat evolution, increases as the cube of the dimensions, whereas the jacket surface area, which determines the rate of heat removal, increases as the square of the dimensions. These two factors cause the acceptable window for controller gain to decrease as the size of the reactor is increased. In other words, a small, easy-to-control reactor may scale up to a large, very difficult-to-control reactor.
Often an exothermic reactor is controlled by measuring the reactor (or reactor effluent) tem- perature and cascading this temperature controller to a jacket water-temperature controller. Whether the cascade is present or not, a significant amount of derivative action is usually required in the reactor temperature controller to improve the stability of the loop. If a cascade is present, it can also have derivative action. This is one example of where derivative on error, rather than derivative on measurement, is preferred. The secondary controller may or may not have integral action.
Admittedly, we have not given any tuning rules for the runaway process, since each process will be decidedly different. However, we have discussed some of the factors influencing the choice of controller modes as well as some of the tuning problems involved.
TYPICAL TUNING VALUES FOR PARTICULAR TYPES OF
LOOPS
If the valve and sensor are properly sized and ranged, then most loops of a particular type will have similar tuning parameters. Thus, by using a table of typical values, one can start with tun- ing values that are at least “in the ballpark.” Table 6-10 presents typical values for the four most common types of control loops: flow, temperature, pressure, and level.
PRACTICAL CONSIDERATIONS FOR LOOP TUNING
Suppose you’re called into the control room to correct an alleged loop tuning problem. Proba- bly the worst thing you could do is to immediately begin changing a tuning parameter. There are several things you should do first.
(1) Find out as much as you can about the loop. If this is not a new loop, then has this tuning problem just started? If so, what has changed? Is the process operating at a different condition? Is the set point different? Does this happen some of the time but not others?
(2) Put the loop on manual. If the oscillations persist, there is certainly not a tuning problem with this loop; rather, some other loop is oscillating and that is being reflected by the oscillations of this loop.
(3) Consider other equipment in the loop. Give particular consideration to the valve. Is it sticking? Is it operating very close to either end of its calibrated travel? (4) Understand the process phenomena. Is there something unusual about the process
or its behavior?
(5) If there is a controller tuning log available (it is a “must” for every control room!), then examine it. What has been the tuning history of the loop?
(6) Finally, if you are convinced that this truly is a tuning problem, then make note of the existing tuning parameters. Try to improve the loop performance by the tech- nique “improving as-found tuning parameters” described earlier, rather than by making either open-loop or closed-loop process tests.
Once you have found new parameters, test the process by making a small set point change, and if possible, a small load upset. Before leaving, note these in the tuning log, along with any pro- cess data (throughput rate, feed composition, product specifications, etc.) that are pertinent to this particular situation.
Table 6-10. Rules of Thumb for Tuning Common Control Loop
Loop Type Gain (Prop Band) Reset, Mins/Repeat
(Repeats/Min) Derivative, Minutes
Flow 0.4 – 0.65 (150% - 250%) – 0.25 (4 – 10) None Temperature 2-10 (10% - 50%) 2 – 10 (0.1 – 0.5) to 2.0 (always less than reset)
Pressure, Gas
20 – 50
(2% - 5%) May not be needed None
Pressure, Liquid 0.5 – 2.0 (50% - 200%) – 0.25 (4 – 10) None Pressure, Vapor 2 – 10 (10% - 50%) 2 – 10 (0.1 – 1.0) 0.1 to 2.0 (always less than reset)
Level See text See text None
Composition – 1.0
(100% - 1000%)
10 – 30
6-1. J. G. Ziegler and N. B. Nichols. “Optimum Settings for Automatic Controllers,” Transactions of the ASME, vol. 64, 1942, pp. 759-68.
6-2. G. H. Cohen and G. A.Coon. “Theoretical Considerations of Retarded Control,” Taylor Instrument Companies Bulletin #TDS-10A102.
6-3. A. M. Lopez, J. A.Miller, C. L. Smith, and P. W. Murrill. “Controller Tuning Relationships Based on Integral Performance Criteria,” Instrumentation Technol- ogy, November 1967, pp. 57-62.
6-4. B. G. Lipták, ed. Instrument Engineers’ Handbook – Process Control, 3d ed., Chilton Book Co., 1995.
6-5. E. B. Dahlin. “Designing and Tuning Digital Controllers,” Instruments and Con- trol Systems, June 1968, p. 77.
6-6. Product Application Manual, Techmation, Inc., Tempe, AZ. Also available from http://www.protuner.com/app6.pdf.