Robust Control of a Distillation Column

  • Da-Wei Gu
  • Petko H. Petkov
  • Mihail M. Konstantinov
Part of the Advanced Textbooks in Control and Signal Processing book series (C&SP)


In this chapter we present the design of a robust control system for a high-purity distillation column. The original nonlinear model of the column is of high order and it includes parametric gain and time-delay uncertainty. A low-order linearized distillation column model is used in the design of a 1-degree-of-freedom \(\mathcal{H}_{\infty}\) loop-shaping controller and a 2-degree-of-freedom (2DOF) μ-controller. Both controllers ensure robust stability of the closed-loop system and fulfillment of a mixture of time-domain and frequency-domain specifications. A reduced order μ-controller is then found that preserves the robust stability and robust performance of the closed-loop system. The simulation of the closed-loop system with the nonlinear distillation column model shows very good performance for different reference and disturbance signals as well as for different values of the uncertain parameters.


Robust Stability Distillation Column Liquid Holdup Transfer Function Matrix Complementary Sensitivity Function 
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  1. 62.
    Green, M., Limebeer, D.J.N.: Linear Robust Control. Prentice Hall, Englewood Cliffs (1995) MATHGoogle Scholar
  2. 97.
    Limebeer, D.J.N.: The specification and purpose of a controller design study. In: Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, UK, December 1991, pp. 1579–1580 (1991) Google Scholar
  3. 106.
    Lundström, P., Skogestad, S., Doyle, J.C.: Two-degree-of-freedom controller design for an ill-conditioned distillation process using μ-synthesis. IEEE Trans. Control Syst. Technol. 7, 12–21 (1999) CrossRefGoogle Scholar
  4. 126.
    Murad, G., Gu, D.-W., Postlethwaite, I.: Robust internal model control of a binary distillation column. In: IEEE International Conference on Industrial Technology, Shanghai, China, December 1996, pp. 194–198 (1996) Google Scholar
  5. 139.
    Postlethwaite, I., Lin, J.L., Gu, D.W.: Robust control of a high purity distillation column using μ–K iteration. In: Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, UK, December 1991 Google Scholar
  6. 154.
    Skogestad, S.: Dynamics and control of distillation columns: a tutorial introduction. Chem. Eng. Res. Des. 75, 539–562 (1997) CrossRefGoogle Scholar
  7. 155.
    Skogestad, S., Postlethwaite, I.: Multivariable Feedback Control, 2nd edn. Wiley, Chichester (2005) Google Scholar
  8. 156.
    Skogestad, S., Morari, M., Doyle, J.C.: Robust control of ill-conditioned plants: high purity distillation. IEEE Trans. Autom. Control 33, 1092–1105 (1988) MathSciNetMATHCrossRefGoogle Scholar
  9. 160.
    Tang, K.S., Man, K.F., Gu, D.-W.: Structured genetic algorithm for robust \(\mathcal{H}_{\infty}\) control systems design. IEEE Trans. Ind. Electron. 43(5), 575–582 (1996) CrossRefGoogle Scholar
  10. 178.
    Whidborne, J.F., Postlethwaite, I., Gu, D.-W.: Robust controller design using \(\mathcal{H}^{\infty}\) loop-shaping and the method of inequalities. IEEE Trans. Control Syst. Technol. 2, 455–461 (1994) CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Da-Wei Gu
    • 1
  • Petko H. Petkov
    • 2
  • Mihail M. Konstantinov
    • 3
  1. 1.Department of EngineeringUniversity of LeicesterLeicesterUK
  2. 2.Department of AutomaticsTechnical University of SofiaSofiaBulgaria
  3. 3.Civil Engineering and GeodesyUniversity of ArchitectureSofiaBulgaria

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