# Should You be Using Lambda Tuning?

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

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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.