Model-reference robust tuning of 2DoF PI controllers for first- and second-order plus dead-time controlled processes

Víctor M. Alfaro, Ramon Vilanova

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63 Citations (Scopus)


The aim of this paper is to present a robust tuning method for two-degree-of-freedom (2DoF) proportional integral (PI) controllers. This is based on the use of a model reference optimization procedure with servo and regulatory target closed-loop transfer functions for first- and second-order plus dead-time (FOPDT, SOPDT) controlled process models. The designer is allowed to deal with the performance/robustness trade-off of the closed-loop control system by specifying the desired robustness level by selecting a maximum sensitivity in the range from 1.4 to 2.0. In addition, a smooth servo/regulatory performance combination is obtained by forcing both closed-loop transfer functions to perform as closely as possible to non-oscillatory dynamic targets. A unified set of controller tuning equations is provided for FOPDT and SOPDT models with normalized dead-times from 0.1 to 2.0 that guarantees the achievement of the design robustness level. The robustness of the control system is analyzed as well as the robustness-fragility and performance-fragility of the optimized controllers. Comparative examples show the effectiveness of the proposed tuning method. The exact achievement of the control system robustness target for all the controlled process models considered (first- and second-order) is one of the distinctive characteristics of the proposed model reference robust tuning (MoReRT) method. © 2011 Elsevier Ltd. All rights reserved.
Original languageEnglish
Pages (from-to)359-374
JournalJournal of Process Control
Publication statusPublished - 1 Feb 2012


  • Fragility
  • Model reference
  • PI control
  • Robust control
  • Two-degree-of-freedom


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