A
tuning method based on achieving smooth set point response is becoming more
popular. The method guarantees stability, robustness and no overshoot. Shouldn't
you be using it?
The
goal of lambda tuning is to match the setpoint response to a first order time
constant called lambda. The response is first delayed by the process dead time.
Lambda tuning is a model based method. From a model of the process, you derive
the tuning parameters. Given a model, the tuning method for an ideal type PID
controller is simple once you convert the units properly. Parallel and series
type controllers require different tuning. (For PI controllers, series and ideal
tuning is the same.)
The
design concept behind lambda is to cancel the process with the controller and
then use a first order filter to get the response you want. It is similar to
Model Predictive tuning and hence has some of the same disadvantages (see "How
to Control Dead Time Processes", Control Engineering, March 1998). A
standard recommended lambda time for good robustness is 3 times the process time
constant. For fast lambda tuning it is recommended to set the lambda time equal
the time constant.
Lambda
Tuning Example
A
process with a gain of 1, dead time of .2 minutes and time constant of 10
minutes. The fast lambda tuning (lambda=10 min) for this process yields:
Proportional
Band = 100
Integral = 10 min/rep
The
resulting set point and load responses are shown as green lines in the figure.
The setpoint response is smooth and does not overshoot. Neither does the
response to a load upset. And the output to the controller is also smooth with
no overshoot, ensuring long valve life.
Tuning
for Load Rejection Has Huge Cost Savings
During
a load upset the time and amount that the process variable is away from setpoint
is what is significant. This is quantified by calculating the Integrated
Absolute Error. This simply means adding up the error each sample time. Another
way of looking at it is the IAE is the area in the graph between the setpoint
and the process variable.
With
poor tuning for load rejection, an upset in the direction towards expensive
results causes you to give away product. Or, a load causes off-spec product.
With better tuning you can give away less of the expensive ingredients while
staying on spec.
For
example, MTBE added to gasoline increases octane. MTBE is expensive so you want
to add just enough to reach the pump octane level. Add more MTBE and you are
giving it away at the gas pump. You cannot add less MTBE than regulations
permit. You want to control the addition of MTBE as close as possible to spec.
Lowest IAE tuning does this for you.
Lambda
Compared to Tuning for Good Load Response
We've
also tuned this same loop using tuning for good load rejection. The resulting PI
settings are:
Proportional
Band = 8.2
Integral = 3 min/rep
The
resulting set point and load responses are shown as red lines in the figure. The
response is very fast with little overshoot. With tuning for load
rejection the Integrated Absolute Error is a factor of 40 times faster than
lambda tuning. This is 4,000% faster. This difference is very
significant since the improvement in Integrated Absolute Error or IAE is
directly proportional to the money saved from faster response.
The
minimum IAE tuning guarantees the minimum amount of product give away while
staying close to specifications. Thus, an improvement in IAE is directly
proportional to the dollars saved. In our example, the load tuning will save us
4,000% more over the lambda tuning.
Conclusion
The
above example demonstrates the difference between tuning methods. If the process
dead time in the example were 1, the difference is less. With a dead time of 10,
the two methods are almost the same. Careful consideration should be given to
any tuning method before it is applied throughout the plant. ExperTune's tuning,
analysis, and simulation let you compare different tuning methods and decide
which is best for each process.
This
article was written and provided by John Gerry P.E., president of Expertune.
Expertune designs pre-packaged industrial software which maximizes productivity
and efficiency and reduces waste in the process industries: chemical, pulp and
paper, utilities, refining, and food processing. For more information on
Expertune, please visit their website at: www.expertune.com.
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copyright 1999-2003 ExperTune Inc.
