1 May 2005
Trial and error: An organized procedure
By Harold Wade
Seek the fewest number of parameter changes and experimental upsets to the process.
Ziegler-Nichols, Cohen-Coon, and related techniques for controller tuning have been around for over 50 years.
More recently, a number of commercial software tuning aids have become available. In spite of this, it is still commonplace to tune control loops manually using a trial-and-error technique.
An inexperienced tuner normally does not follow any organized procedure and consequently, spends too much time, causes unnecessary upsets to the process, or gives up with only satisfactory results.
With an organized procedure, it should be possible to obtain acceptable performance as rapidly as possible; that is, with the fewest number of parameter changes and with minimal experimental upsets to the process.
Here is an organized procedure for tuning that will achieve that goal. This procedure is only applicable to a certain class of control loops, specifically loops for self-regulating processes using a proportional-plus-integral (PI) controller.
Although control loops for non self-regulating processes (such as liquid level) are not in this domain, nor are loops using derivative control, the applicability still covers a significant proportion of all loops.
Many consider trial-and-error controller tuning an art-a skill requiring the exercise of intuitive facilities, which one cannot learn through study.
A science, on the other hand, is methodological activity. To convert an art into a science, one must conceive of methods, which cover normal circumstances plus most anomalous circumstances that may arise.
Investigate several angles
A typical tuning session begins when a plant operator requests help from an instrumentation technician or control systems engineer. Usually, the request results because the loop is oscillating unacceptably or it is sluggish in returning to the set point after a load upset.
The cause for the unsatisfactory performance may not lie with the controller tuning. Therefore, before starting to tune, it is important to investigate several process, equipment, and operating conditions. For instance, is it a sticky valve? Are there external disturbances affecting the loop?
For the purpose of this discussion, however, let us suppose we've ruled out other causes and it is truly a controller-tuning problem. Here is where an organized procedure for tuning the loop will be helpful.
In the absence of other disturbances, the existing tuning parameters give rise to the present control loop behavior. Collectively, the tuning parameters and the characteristics of the loop behavior are the as-found data.
Two parameters, controller gain, and integral time, represent the as-found tuning. If the loop is oscillating, two parameters will characterize the process behavior, the decay ratio, and the period of oscillation.
There exists an alternative definition of decay ratio. This alternative definition only works in an anomalous situation-such as if one of the first two peaks does not cross the set point. The period of oscillation and integral time must be in the same units, as in minutes for period and minutes (per repeat) for integral time.
The set of as-found data represents a particle of knowledge about the control loop, which can be a starting point for improving the loop performance.
If a Ziegler-Nichols type test were to run on the loop, either in the open or closed loop, we would in essence be starting anew and ignoring the knowledge we now have about the loop behavior.
Desirable set point response
The basic premise for this procedure is when we have a well-tuned loop, there's a predictable relation between the period, P, of oscillation and the integral time, TI. A reasonable relationship is:
1½ < P/T1 < 2 (1)
Equivalent expressions, which will be useful later, are:
1½ T1 < P < 2 (2)
1/2 P < T1 < 2/3 (3)
Setting the period-to-integral time ratio between 11/2 and 2 is equivalent to setting the phase shift through the PI controller to lie in the range of approximately 13°-18°.
Experienced tuners have often qualitatively estimated the phase lag through a PI controller, and if excessive, have increased the integral time. The criterion stated here merely makes this a quantitative procedure. The target range, 11/2 to 2, is an empirical ratio, rather than one that has come about through analysis. Experience shows this is valid for most loops where the dead time is a relatively small fraction of the process time constant. For longer dead time-to-time constant ratios, the target range can move upward.
Another premise is a decay ratio of approximately 1/4-quarter-amplitude decay-represents acceptable tuning. This well-known and accepted criterion is a compromise between the most desirable set point response (no overshoot) and good response to a load upset (return to set point as rapidly as possible).
For some applications, it is preferable to favor the set point response at the expense of less favorable response to a disturbance. This procedure will provide a couple of fire escapes to accommodate this preference.
The intelligent trial-and-error tuning procedure is as follows:
If the loop is not oscillating, increase the controller gain enough to cause a damped oscillation to occur. This will allow observance of the period of oscillation.
If the loop is oscillating but the period of oscillation is not within the range of 11/2 to 2, readjust the integral time to lie within the range of 1/2 to 2/3 of the present period.
If the period of oscillation does meet the criterion-it lies between 11/2 to 2 times the integral time-adjust the controller gain until a 1/4 decay or other desired damping characteristic happens.
Each time a single tuning parameter is changed, the effect of this new parameter should be determined by making a small set point change. Only one tuning parameter should change at a time.
A convenient method of logging the progress of a tuning session uses this form. The first line is for recording the as-found data, and each successive line is for recording the parameter changes plus resulting behavior of new trials. Acceptable performance is usually realizable in three-to-four trials.
One should only manipulate one tuning parameter per trial. Also, if the units of reset action repeats per minute rather than minutes per repeat, invert the actual tuning parameter, reset rate, to get integral time, TI. When a new value for TI is determined, invert this to obtain the actual entry parameter.
Behind the byline
Harold Wade (HLWade@aol.com) has degrees, including a doctorate, in mechanical and systems engineering. He's a senior member of ISA and a member of IEEE and AIChE. Wade is president of Wade Associates and has worked at Honeywell, Foxboro, and Biles. He also teaches courses in process control systems design for ISA. Wade's latest tome is Basic and Advanced Regulatory Control: System Design and Application, ISA Press, 2004.
How to improve the as-found state
Here is how a typical tuning session will play out.
With the as-found behavior, the period is greater than 2 times TI, so exit the right end of decision box 3 to a box that instructs us to set TI to somewhere between 1/2 and 2/3 of the present period, or between 7.5 and 10 minutes.
Suppose we choose 8.0 minutes per repeat. Enter this, and make a small set point change. Now the response appears as in the second figure. Record the results on trial line 1 of the log.
In an actual plant situation, we would probably stop at this point. However, for instructional purposes, suppose we try to get closer to 1/4 decay. The benefit would be a slightly improved response to a disturbance.
The period-reset time criterion is met, so exit the bottom of decision block three, the left end of block five, then exit the bottom of decision block six (If we really did not want quarter-amplitude decay, we would exit the right end of block six and be finished).
The instructions are to increase the gain. At a decay ratio of 0.13, the figure below instructs us to multiply the gain by a factor of about 1.15. Multiply this by the current gain, and get a new value of 2.3. Enter this, and make another small set point change.
This yields the behavior shown by the figure below-behavior after second tuning. Record the results on trial line two of the log.
Again, we are tempted to say, "Good enough." But suppose we make one more attempt.
Following the same path as before, and again using the flowchart, we get a gain adjustment factor of 1.1, which results in a new gain of 2.53 (a gain entry of 2.5 would be sufficiently precise). This produces the behavior shown in the "loop responses" figure-behavior after third tuning. We log our results on trial line three.
This time, we are sufficiently close to quarter-amplitude decay. (Don't be a slave to numbers!) We accept this as our final tuning. Thus, we have improved the as-found tuning with at most three tuning changes.