Optimization-based nonlinear centralized controller tuning of liquid-liquid extraction processes

Farouq S. Mjalli*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


The control problem of an agitated contactor is considered in this work. A Scheibel extraction column is modeled using the non-equilibrium backflow mixing cell model. Model dynamic analysis shows that this process is highly nonlinear, thus the control problem solution of such a system needs to tackle the process nonlinearity efficiently. The control problem of this process is solved by developing a multivariable nonlinear control system implemented in MATLAB™. In this control methodology, a new controller tuning method is adopted, in which the time-domain control parameter-tuning problem is solved as a constrained optimization problem. A MIMO (multi-input multi-output) PI controller structure is used in this strategy. The centralized controller uses a 2 × 2 transfer function and accounts for loops interaction. The controller parameters are tuned using an optimization-based algorithm with constraints imposed on the process variables reference trajectories. Incremental tuning procedure is performed until the extractor output variables transient response satisfies a preset uncertainty which bounds around the reference trajectory. A decentralized model-based IMC (internal model control) control strategy is compared with the newly developed centralized MIMO PI control one. Stability and robustness tests are applied to the two algorithms. The performance of the MIMO PI controller is found to be superior to that of the conventional IMC controller in terms of stability, robustness, loops interaction handling, and step-change tracking characteristics.

Original languageEnglish
Pages (from-to)561-582
Number of pages22
JournalSolvent Extraction and Ion Exchange
Issue number4
Publication statusPublished - Jul 2005
Externally publishedYes


  • Centralized control
  • Internal model control
  • Liquid-liquid extraction
  • Multivariable control
  • NCD
  • Nonlinear control
  • Scheibel extractor

ASJC Scopus subject areas

  • Chemistry(all)
  • Chemical Engineering(all)


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