I'm looking for a control method for a production process with the following characteristics:

  • 1 control variable
  • many process parameters (+-50)
  • 1 resulting variable
  • continuous measurement of resulting variable with 30-90 second delay
  • complex physics that govern the process and numerous factors that determine the (non-linear) relation between control variable and resulting variable

With constant process/input parameters, the distribution of the resulting variable is normal.

The control method should ensure that the resulting variable should be above a set minimum and that the average of the resulting value should be as close to the limit as possible. Being above the lower limit makes the product more expensive, being below the lower limit however is more expensive: the product is scrapped.

Now I want to try the following: I have want to make a statistical model using some process parameters as input predicting the control variable that leads to the desired value for the resulting variable. Next to the value of the control variable, I also want to determine the 'confidence' or distribution of that value. Then I want to state a portion of the time the control variable must be above the lower limit (i.e. 3 sigma). Consecutively I'd like to set the setpoint for the control variable at the such a value that I achieve the given portion above the lower limit. To illustrate what I envision I made the illustration below.

Feed forward Control Optimization based on prediction confidence

Do you think this setup makes any sense? Am I missing any obvious alternative solution that is much simpler? Is this a known approach?

  • 2
    $\begingroup$ I think you can start with MPC (Model Predictive Control). $\endgroup$ Oct 20, 2016 at 22:26
  • $\begingroup$ I'm not sure what you are asking. Are you looking to estimate the current state of the system using a delayed output variable + several known parameters? Or are you trying to get the controller to maintain the most efficient input while keeping the state within an acceptable range? $\endgroup$ Dec 5, 2016 at 18:56

2 Answers 2


This is more a comment than an answer but I don't have enough reputation to comment yet:

  • I understand that deriving a first-principles model may be too complex, but be aware that a good statistical model for your case will surely need a lot of good data. It is not enough with having a lot of data, the input variables must be excited in order to cover the input space. Normally this is not the case with industrial real data, where most of the online measurements are close to the same region in the input space

  • Why not feedback control? You don't need a model for feedback control (although it helps) and 30-90 seconds is not such a big delay for most chemical processes (it depends on the process and it may not be a chemical process at all)

  • Otherwise, if you have a lot of data and you manage to set up a good data driven model, your approach can work but you will need to recalibrate your model often

  • $\begingroup$ A bit late, but let me cover your remarks: - Deriving a first principles model is too complex (its a complex interaction between multiple fluids). The input space is fairly well covered, but obviously not completely. That would pose a challenge. - Its a mechanical process (not chemical) where the timescale of disturbances needing response is in the order of seconds. - Fair point - the modelled machinery continuously drifts and hence the model would need continuous recalibration. $\endgroup$
    – marqram
    May 19, 2020 at 9:38

In a totally different field, I've approached this by building a model that predicts a distribution rather than a single value. Some examples I've used:

  • Quantile regression (Neural Network, using a different (pinball) loss function for each quantile)
  • Predicting both Mean and Standard deviation

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