Skip to main content
SpringerLink
Log in

Robust Control of a Distillation Column

  • Chapter
Mathematical Methods for Robust and Nonlinear Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 367))

  • 3066 Accesses

Abstract

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 design of a two-degree-of freedom (2DOF) \(\mathcal{H}_\infty\) loop shaping controller and a 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 which 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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abramovitch, D., Franklin, G.: A brief history of disk drive control. IEEE Control Systems Magazine 22, 28–42 (2002)

    Article  Google Scholar 

  2. Abramovitch, D., Franklin, G.: Disk drive control: The early years. In: Proceedings of the 15th IFAC Congress, Session T-Th-M12, Barcelona, Spain, July 2002, pp. 1–12 (2002) CD-ROM

    Google Scholar 

  3. Abramovitch, D., Hurst, T., Henze, D.: An overview of the PES Pareto method for decomposing baseline noise sources in hard disk postion error signals. IEEE Transactions on Magnetics 34, 17–23 (1998)

    Article  Google Scholar 

  4. Abramovitch, D., Wang, F., Hurst, T., Franklin, G.: Disk drive pivot nonlinearity modelling Part I: Frequency domain. In: Proceedings of the 1994 American Control Conference, Baltimore, MD, June 1994, pp. 2600–2603 (1994)

    Google Scholar 

  5. Abramovitch, D.Y.: Magnetic and optical disk control: Parallels and contrasts. In: Proceedings of the 2001 American Control Conference, Arlington, VA, June 2001, pp. 421–428 (2001)

    Google Scholar 

  6. Adamjan, V.M., Arov, D.Z., Krein, M.G.: Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem. Mat. USSR Sbornik 15, 31–73 (1971)

    Article  Google Scholar 

  7. Adams, R.J., Buffington, J.M., Sparks, A.G., Banda, S.S.: Robust Multivariable Flight Control. Springer, New York (1994)

    Google Scholar 

  8. Al-Saggaf, U.M., Franklin, G.F.: An error bound for a discrete reduced order model of a linear multivariable system. IEEE Transactions on Automatic Control 32, 815–819 (1987)

    Article  MATH  Google Scholar 

  9. Balas, G.J., Doyle, J.C., Glover, K., Packard, A., Smith, R.: μ-Analysis and Synthesis Toolbox: User’s Guide. MUSYN Inc. and The Mathworks, Inc (1995)

    Google Scholar 

  10. Bernstein, D.S., Haddad, W.M.: LQG control with an \(\mathcal{H}_\infty\) performance bound: A Riccati equation approach. IEEE Transactions on Automatic Control 34, 293–305 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  11. Blakelock, J.H.: Automatic Control of Aircraft and Missiles. Wiley, New York (1991)

    Google Scholar 

  12. Bryson, A.E.: Control of Spacecraft and Aircraft. Princeton University Press, Princeton (1994)

    Google Scholar 

  13. Buschek, H.: Design and flight test of a robust autopilot for the IRIS-T air-to-air missile. Control Engineering Practice 11, 551–558 (2003)

    Article  Google Scholar 

  14. Callier, F.M., Desoer, C.A.: Linear System Theory. Springer, New York (1991)

    MATH  Google Scholar 

  15. Chen, B.M., Lee, T.H., Venkataramanan, V.: Hard Disk Drive Servo Systems. Springer, Berlin (2002)

    Google Scholar 

  16. Chew, K.K., Tomizuka, M.: Digital control of repetetive errors in disk drive systems. IEEE Control Systems Magazine 10, 16–20 (1990)

    Article  Google Scholar 

  17. Choi, B.W., Gu, D.W., Postlethwaite, I.: Low-order \(\mathcal{H}_\infty\) Sub-Optimal Controllers. IEEE Proceedings – Part D 141, 243–248 (1994)

    MATH  Google Scholar 

  18. de Gaston, R.R.E., Safonov, M.G.: Exact calculation of the multiloop stability margin. IEEE Transactions on Automatic Control 33, 156–171 (1988)

    Article  MATH  Google Scholar 

  19. Desai, U.B., Pal, D.: A transformation approach to stochastic model reduction. IEEE Transactions on Automatic Control 29, 1097–1100 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  20. Desoer, C.A., Chan, W.S.: The feedback interconnection of lumped linear timeinvariant systems. Journal of the Franklin Institute 300, 335–351 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  21. Desoer, C.A., Vidyasagar, M.: Feedback Systems: Input-Output Properties. Academic Press, New York (1975)

    MATH  Google Scholar 

  22. Ding, J., Tomizuka, M., Numasato, H.: Design and robustness analysis of dual stage servo system. In: Proceedings of the 2000 American Control Conference, Chicago, IL, June 2000, pp. 2605–2609 (2000)

    Google Scholar 

  23. Doyle, J.C.: Analysis of feedback systems with structured uncertainties. IEEE Proceedings – Part D 129, 242–250 (1982)

    MathSciNet  Google Scholar 

  24. Doyle, J.C.: Structured uncertainty in control system design. In: Proceedings of the 24 IEEE Conference on Decision and Control, December 1985, pp. 260–265. IEEE Computer Society Press, Los Alamitos (1985)

    Google Scholar 

  25. Doyle, J.C.: A review of?: For case studies in robust control. In: Proceedings of 10th IFAC World Congress, Munich, Germany, July 1987, pp. 395–402 (1987)

    Google Scholar 

  26. Doyle, J.C., Francis, B.A., Tannenbaum, A.R.: Feedback Control Theory. Macmillan Publishing Co., New York (1992)

    Google Scholar 

  27. Du, C., Zhang, J., Guo, G.: Vibration analysis and control design comparison of HDDs using fluid bearing and ball bearing spindles. In: Proceedings of the 2002 American Control Conference, Anchorage, AK, May 2002, pp. 1378–1383 (2002)

    Google Scholar 

  28. Eltohamy, K.G.: Nonlinear optimal control of a triple inverted pendulum with single control input. International Journal of Control 69, 239–256 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  29. Enns, D.: Model Reduction for Control Systems Design. PhD thesis, Department of Aeronautics and Astronautics, Stanford University, Stanford, CA (1984)

    Google Scholar 

  30. Enns, D.: Model reduction with balanced realizations: An error bound and a frequency weighted generalization. In: Proceedings of the 23rd IEEE Conference on Decision and Control, Las Vegas, NV, pp. 127–132. IEEE Computer Society Press, Los Alamitos (1984)

    Google Scholar 

  31. Evans, R.B., Griesbach, J.S., Messner, W.C.: Piezoelectric microactuator for dual stage control. IEEE Transactions on Magnetics 35, 977–982 (1999)

    Article  Google Scholar 

  32. Fan, M.K.H., Tits, A.L.: Characterization and efficient computation of the structured singular value. IEEE Transactions on Automatic Control 31, 734–743 (1986)

    Article  MATH  Google Scholar 

  33. Fan, M.K.H., Tits, A.L., Doyle, J.C.: Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics. IEEE Transactions on Automatic Control 36, 25–38 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  34. Fernando, K.V., Nicholson, H.: Singular perturbational model reduction of balanced systems. IEEE Transactions on Automatic Control 27, 466–468 (1982)

    Article  MATH  Google Scholar 

  35. Fernando, K.V., Nicholson, H.: Singular perturbational approximation for discretetime systems. IEEE Transactions on Automatic Control 28, 240–242 (1983)

    Article  MATH  Google Scholar 

  36. Ferreres, G.: A Practical Approach to Robustness Analysis with Aeronautical Applications. Kluwer Academic Publishers/Plenum Publishers, New York (1999)

    MATH  Google Scholar 

  37. Fialho, I., Balas, G.J., Packard, A.K., Renfrow, J., Mullaney, C.: Gain-scheduled lateral control of the F-14 aircrfat during powered approach landing. Journal of Guidance, Control, and Dynamics 23, 450–458 (2000)

    Google Scholar 

  38. Francis, B.A.: A Course in \(\mathcal{H}_\infty\) Control Theory. Lecture Notes in Control and Information Sciences, vol. 88. Springer, Heidelberg (1987)

    MATH  Google Scholar 

  39. Franklin, G.F., Powell, J.D., Workman, M.L.: Digital Control of Dynamic Systems, 3rd edn. Addison-Wesley, Menlo Park (1998)

    Google Scholar 

  40. Furuta, K., Kajiwara, K., Kosuge, K.: Digital control of a double inverted pendulum on an inclined rail. International Journal of Control 32, 907–924 (1980)

    Article  MATH  Google Scholar 

  41. Furuta, K., Ochia, T., Ono, N.: Attitude control of a triple inverted pendulum. International Journal of Control 39, 1351–1365 (1984)

    Article  MATH  Google Scholar 

  42. Garcia-Benitez, E., Walkins, J., Yurkovich, S.: Nonlinear control with acceleration feedback for a two-link flexible robot. Control Engineering Practice 1, 989–997 (1993)

    Article  Google Scholar 

  43. Ge, S., Lee, T., Zhu, G.: Improving regulation of a single-link flexible manipulator with strain feedback. IEEE Transactions on Robotics and Automation 14, 179–185 (1998)

    Article  Google Scholar 

  44. Geniele, H., Patel, R., Khorasani, K.: End-point control of a flexible-link manipulator: Theory and experiment. IEEE Transactions on Control Systems Technology 5, 559–570 (1997)

    Article  Google Scholar 

  45. Ghanekar, M., Wang, D., Heppler, G.: Scaling laws for linear controllers of flexible link manipulators characterized by nondimensional groups. IEEE Transactions on Robotics and Automation 13, 117–127 (1997)

    Article  Google Scholar 

  46. Glover, K.: All optimal Hankel-norm approximations of linear multivariable systems and their l  ∞ -error bounds. International Journal of Control 39, 1115–1193 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  47. Glover, K.: Multiplicative approximation of linear multivariable systems with \(\mathcal{L}_\infty\) error bounds. In: Proceedings of the 1986 American Control Conference, Minneapolis, MN, pp. 1705–1709 (1986)

    Google Scholar 

  48. Glover, K., Doyle, J.C.: State-space formulae for all stabilizing controllers that satisfy an \(\mathcal{H}^\infty\) norm bound and relations to risk sensitivity. Systems & Control Letters 11, 167–172 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  49. Glover, K., Jonckheere, E.A.: A comparison of two Hankel norm methods for approximating spectra. In: Byrnes, C.I., Lindquist, A. (eds.) Modelling, Identification and Robust Control, North-Holland, Amsterdam (1986)

    Google Scholar 

  50. Goh, T.B., Li, Z., Chen, B.M., Lee, T.H., Huang, T.: Design and implementation of a hard disk drive servo system using robust and perfect tracking approach. In: Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, Arizona, December 1999, pp. 5247–5252. IEEE, Los Alamitos (1999)

    Google Scholar 

  51. Green, M.: Balanced stochastic realizations. Linear Algebra & its Applications 98, 211–247 (1988)

    Article  MATH  Google Scholar 

  52. Green, M.: A relative error bound for balanced stochastic truncation. IEEE Transactions on Automatic Control 33, 961–965 (1988)

    Article  MATH  Google Scholar 

  53. Green, M., Limebeer, D.J.N.: Linear Robust Control. Prentice-Hall, Englewood Cliffs (1995)

    MATH  Google Scholar 

  54. Greensite, A.L.: Analysis and Design of Space Vehicle Flight Control Systems. Spartan, New York (1970)

    Google Scholar 

  55. Gu, D.W., Choi, B.W., Postlethwaite, I.: Low-order stabilizing controllers. IEEE Transactions on Automatic Control 38, 1713–1717 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  56. Gu, D.W., Goh, S.J., Fitzpatrick, T., Postlethwaite, I., Measor, N.: Application of an expert system for robust controller design. In: Control’96, vol. 2, pp. 1004–1009 (1996)

    Google Scholar 

  57. Gu, D.W., Petkov, P.H., Konstantinov, M.M.: Direct Formulae for the \(\mathcal{H}_\infty\) Sub-Optimal Central Controller. Technical Report 1998-7, Niconet Report (1998), Available at http://www.win.tue.nl/niconet

  58. Gu, D.W., Petkov, P.H., Konstantinov, M.M.: Formulae for discrete \(\mathcal{H}_\infty\) loop shaping design procedure controllers. In: Proceedings of the 15th IFAC World Congress, paper 276, Session T-Mo-M15, Barcelona, Spain (July 2002), CD-ROM

    Google Scholar 

  59. Gu, D.W., Postlethwaite, I., Tsai, M.C.: \(\mathcal{H}_\infty\) super-optimal solutions. In: Leondes, C.T. (ed.) Advances in Control and Dynamic Systems, vol. 51, pp. 183–246. Academic Press, San Diego (1992)

    Google Scholar 

  60. Gu, D.W., Tsai, M.C., Postlethwaite, I.: State-space formulae for discrete-time optimization. International Journal of Control 49, 1683–1723 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  61. Guo, L., Lee, H.S., Hudson, A., Chen, S.-H.: A comprehensive time domain simulation tool for hard disk drive TPI prediction and mechanical/servo enhancement. IEEE Transactions on Magnetics 35, 879–884 (1999)

    Article  Google Scholar 

  62. Hammarling, S.: Numerical solution of the stable non-negative definite Lyapunov equation. IMA Journal of Numerical Analysis 2, 303–323 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  63. Hara, S., Hara, T., Yi, L., Tomizuka, M.: Two degree-of-freedom controllers for hard disk drives with novel reference signal generation. In: Proceedings of the 1999 American Control Conference, San Diego, CA, June 1999, pp. 4116–4121 (1999)

    Google Scholar 

  64. Helton, J.W.: Worst case analysis in the frequency domain: The \(\mathcal{H}_\infty\) approach to control. IEEE Transactions on Automatic Control 30, 1154–1170 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  65. Helton, J.W., Merino, O.: Classical Control Using \(\mathcal{H}_\infty\) Methods. Society for Industrial and Applied Mathematics, Philadelphia, PA (1998)

    Google Scholar 

  66. Hernandez, D., Park, S.-S., Horowitz, R., Packard, A.K.: Dual stage track-following servo design for hard disk drives. In: Proceedings of the 1999 American Control Conference, San Diego, CA, June 1999, pp. 4116–4121 (1999)

    Google Scholar 

  67. Hoyle, D., Hyde, R., Limebeer, D.J.N.: An \(\mathcal{H}_\infty\) approach to two-degree-of-freedom design. In: Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, UK, December 1991, pp. 1581–1585. IEEE Computer Society Press, Los Alamitos (1991)

    Chapter  Google Scholar 

  68. Hsu, C.S., Yu, X., Yeh, H.H., Banda, S.S.: \(\mathcal{H}_\infty\) compensator design with minimal order observer. In: Proceedings of the 1993 American Control Conference, San Francisco, CA (June 1993)

    Google Scholar 

  69. Huang, Y., Mathur, P., Messner, W.C.: Robustness analysis on a high bandwidth disk drive servo system with an instrumented suspension. In: Proceedings of the 1999 American Control Conference, San Diego, CA, June 1999, pp. 3620–3624 (1999)

    Google Scholar 

  70. Ishikawa, J., Yanagita, Y., Hattori, T., Hashimoto, M.: Head positioning control for low sampling rate systems based on two degree-of-freedom control. IEEE Transactions on Magnetics 32, 1787–1792 (1996)

    Article  Google Scholar 

  71. Iwasaki, T., Skelton, R.E.: All low order \(\mathcal{H}_\infty\) controllers with covariance upper bound. In: Proceedings of the 1993 American Control Conference, San Francisco, CA (June 1993)

    Google Scholar 

  72. Kajiwara, H., Apkarian, P., Gahinet, P.: LPV techniques for control of an inverted pendulum. IEEE Control Systems Magazine 19, 44–54 (1999)

    Article  Google Scholar 

  73. Karkoub, M., Balas, G., Tamma, K., Donath, M.: Robust control of flexible manipulators via μ-synthesis. Control Engineering Practice 8, 725–734 (2000)

    Article  Google Scholar 

  74. Kempf, C., Messner, W., Tomizuka, M., Horovitz, R.: Comparison of four discretetime repetetive control algorithms. IEEE Control Systems Magazine 13, 48–54 (1993)

    Article  Google Scholar 

  75. Kim, S.W., Anderson, B.D.O., Madievski, A.G.: Error bound for transfer function order reduction using frequency weighted balanced truncation. Systems & Control Letters 24, 183–192 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  76. Kobayashi, M., Yamaguchi, T., Horowitz, R.: Track-seeking controller design for dual-stage actuator in magnetic disk drives. In: Proceedings of the 2000 American Control Conference, Chicago, Illinois, June 2000, pp. 2610–2614 (2000)

    Google Scholar 

  77. Kozierok, C.M.: The PC Guide. The Reference Section on Hard Disk Drives (January 2003), Available at http://www.PCGuide.com

  78. Kung, S.: A new low-order approximation algorithm via singular value decomposition. In: Proceedings of the 18th IEEE Conference on Decision and Control, Ft. Lauderdale, Florida, December 1979, IEEE, Los Alamitos (1979)

    Google Scholar 

  79. Kung, S., Lin, D.W.: Optimal Hankel norm model reduction: Multivariable systems. IEEE Transactions on Automatic Control 26, 832–852 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  80. Larcombe, P.J.: On the generation and solution of the symbolic, open-loop charactersitic equation for a double inverted pendulum. International Journal of Systems Science 24, 2379–2390 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  81. Laub, A.J.: On computing balancing transformations. In: Proceedings of the Joint 1980 American Control Conference, San Francisco, CA, pp. FA8–E (August 1980)

    Google Scholar 

  82. Laub, A.J., Heath, M.T., Paige, C.C., Ward, R.C.: Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms. IEEE Transactions on Automatic Control 32, 115–121 (1987)

    Article  MATH  Google Scholar 

  83. Lee, H.S.: Controller optimization for minimum position error signals of hard disk drives. In: Proceedings of the 2000 American Control Conference, Chicago, Illinois, June 2000, pp. 3081–3085 (2000)

    Google Scholar 

  84. Leith, D.J., Leithead, W.E.: Survey of gain-scheduling analysis and design. International Journal of Control Control 73, 1001–1025 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  85. Li, Y., Thang, B., Shi, Z., Lu, Y.: Experimental study for trajectory tracking of a two-link flexible manipulators. International Journal of Systems Science 31, 3–9 (2000)

    Article  MATH  Google Scholar 

  86. 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. IEEE Computer Society Press, Los Alamitos (1991)

    Chapter  Google Scholar 

  87. Limebeer, D.J.N., Kasenally, E.M., Perkins, J.D.: On the design of robust two degree of freedom controllers. Automatica 29, 157–168 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  88. Lin, C.-A., Chiu, T.-Y.: Model reduction via frequency weighted balanced realization. CONTROL – Theory and Advanced Technology 8, 341–351 (1992)

    MathSciNet  Google Scholar 

  89. Lin, J.L.: Control System Design for Robust Stability and Robust Performance. PhD thesis, Department of Engineering, University of Leicester, Leicester, UK (May 1992)

    Google Scholar 

  90. Lin, J.L., Postlethwaite, I., Gu, D.W.:-K iteration: a new algorithm for μ-synthesis. Automatica 29, 219–244 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  91. Lind, R., Brenner, M.: Robust Aeroservoelastic Stability Analysis. Flight Test Applications. Springer, London (1999)

    Google Scholar 

  92. Lindquist, A., Picci, G.: On the stochastic realization problem. SIAM Journal of Control and Optimization 17, 365–389 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  93. Liu, Y., Anderson, B.D.O.: Singular perturbation of balanced systems. International Journal of Control 50(4), 1379–1405 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  94. De Luca, A., Siciliano, B.: Trajectory control of a non-linear one-link flexible arm. International Journal of Control 50, 1699–1715 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  95. Lundström, P., Skogestad, S., Doyle, J.C.: Two-degree-of-freedom controller design for an ill-conditioned distillation process using μ-synthesis. IEEE Transactions on Control Systems Technology 7, 12–21 (1999)

    Article  Google Scholar 

  96. Lunz, J.: Robust Multivariable Feedback Control. Prentice Hall, London (1989)

    Google Scholar 

  97. MacDuffee, C.C.: The Theory of Matrices. Chelsea Publishing Co., New York (1950)

    Google Scholar 

  98. Maciejowski, J.M.: Multivariable Feedback Design. Addison-Wesley, Wokingham (1989)

    MATH  Google Scholar 

  99. Magee, D.P.: Optimal filtering to improve performance in hard disk drives: Simulation results. In: Proceedings of the 1999 American Control Conference, San Diego, CA, June 1999, pp. 71–75 (1999)

    Google Scholar 

  100. McFarlane, D., Glover, K.: A loop shaping design procedure using \(\mathcal{H}_\infty\) synthesis. IEEE Transactions on Automatic Control 37, 749–769 (1992)

    Article  MathSciNet  Google Scholar 

  101. McFarlane, D.C., Glover, K.: Robust Controller Design Using Normalized Coprime Factor Plant Descriptions. Lecture Notes in Control and Information Sciences, vol. 138. Springer, Heidelberg (1990)

    MATH  Google Scholar 

  102. Medrano-Cerda, G.A.: Robust stabilization of a triple inverted pendulum-cart. International Journal of Control 68, 849–865 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  103. Medrano-Cerda, G.A.: Robust computer control of an inverted pendulum. IEEE Control Systems Magazine 19, 58–67 (1999)

    Article  Google Scholar 

  104. Meier, Z., Farwig, H., Unbehauen, H.: Discrete computer control of a triple-inverted pendulum. Optimal Control Applications & Methods 11, 157–171 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  105. Meirovitch, L.: Elements of Vibration Analysis. McGraw-Hill, New York (1986)

    Google Scholar 

  106. Messner, W., Ehrlich, R.: A tutorial on controls for disk drives. In: Proceedings of the 2001 American Control Conference, Arlington, VA, June 2001, pp. 408–420 (2001)

    Google Scholar 

  107. Meyer, D.G.: Fractional balanced reduction: Model reduction via fractional representation. IEEE Transactions on Automatic Control 35(3), 1341–1345 (1990)

    Article  MATH  Google Scholar 

  108. Moore, B.C.: Principle component analysis in linear systems: Controllability, observability, and model reduction. IEEE Transactions on Automatic Control 26, 17–31 (1981)

    Article  MATH  Google Scholar 

  109. Morari, M., Zafiriou, E.: Robust Process Control. Prentice-Hall, Englewood Cliffs (1989)

    Google Scholar 

  110. Mori, S., Nishihara, H., Furuta, K.: Control of an unstable mechanical system. Control of pendulum. International Journal of Control 23, 673–692 (1976)

    Article  Google Scholar 

  111. Murad, G.: Robust Multivariable Control of Industrial Production Processes: A Discrete- Time Multi-Objective Approach. PhD thesis, Department of Engineering, University of Leicester, Leicester, UK (1995)

    Google Scholar 

  112. Murad, G., Gu, D.-W., Postlethwaite, I.: A Direct Model Reduction Approach for Discrete-Time Non-Minimal State-Space Systems. Internal Report 94-23, University of Leicester, Leicester, UK (September 1994)

    Google Scholar 

  113. 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. IEEE Computer Society Press, Los Alamitos (1996)

    Google Scholar 

  114. Murad, G., Postlethwaite, I., Gu, D.-W., Samar, R.: On the structure of an \(\mathcal{H}_\infty\) twodegree- of-freedom internal model-based controller and its application to a glass tube production process. In: Proceedings of the Third European Control Conference, Rome, September 1995, pp. 595–600 (1995)

    Google Scholar 

  115. Murad, G., Postlethwaite, I., Gu, D.-W., Whidborne, J.F.: Robust control of a glass tube shaping process. In: Proceedings of the Second European Control Conference, Gröningen, The Netherlands, June-July 1993, vol. 4, pp. 2350–2355 (1993)

    Google Scholar 

  116. Nehari, Z.: On bounded bilinear forms. Annals of Mathematics 65, 153–162 (1957)

    Article  MathSciNet  Google Scholar 

  117. Ng, W.Y.: Interactive Multi-Objective Programming as a Framework for Computer- Aided Control System Design. Lecture Notes in Control and Information Sciences. Springer, Heidelberg (1989)

    MATH  Google Scholar 

  118. Nichols, R.A., Reichert, R.T., Rugh, W.J.: Gain scheduling for \(\mathcal{H}_infty\) controllers: A flight control example. IEEE Trans. Control Systems Technology 1, 69–53 (2001)

    Article  Google Scholar 

  119. International Society Niconet. SLICOT: Numerical Subroutine Library for Control and Systems Theory (2001), Available at http://www.win.tue.nl/niconet

  120. Packard, A., Doyle, J.C.: The complex structured singular value. Automatica, Special Issue on Robust Control 29, 71–109 (1993)

    MATH  MathSciNet  Google Scholar 

  121. Packard, A., Fan, M.K.H., Doyle, J.C.: A power method for the structured singular value. In: Proceedings of the 27th IEEE Conference on Decision and Control, Austin, Texas, December 1988, pp. 2132–2137 (1988)

    Google Scholar 

  122. Packard, A., Pandey, P.: Continuity properties of the real/complex structured singular value. IEEE Transactions on Automatic Control 38, 415–428 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  123. Pao, L.Y., Franklin, G.F.: Time-optimal control of flexible structures. In: Proceedings of the 29th IEEE Conference on Decision and Control, Honolulu, HI, December 1990, pp. 2580–2581. IEEE Computer Society Press, Los Alamitos (1990)

    Chapter  Google Scholar 

  124. Pappas, T., Laub, A.J., Sandell, N.R.: On the numerical solution of the discrete-time algebraic Riccati equation. IEEE Transactions on Automatic Control 25, 631–641 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  125. Park, J., Asada, H.: Dynamic analysis of noncollocated flexible arms and design of torque transmission mechanisms. ASME Journal of Dynamic Systems, Measurements and Control 116, 201–207 (1994)

    MATH  Google Scholar 

  126. Pernebo, L., Silverman, L.M.: Model reduction via balanced state space representations. IEEE Transactions on Automatic Control 27, 382–387 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  127. Postlethwaite, I., Lin, J.L., Gu, D.W.: Robust control of a high purity distillation column using?-K iteration. In: Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, UK, December 1991, IEEE Computer Society Press, Los Alamitos (1991)

    Google Scholar 

  128. Redheffer, R.M.: Remarks on the basis of network theory. Journal of Mathematics and Physics 28, 237–258 (1950)

    MATH  MathSciNet  Google Scholar 

  129. Redheffer, R.M.: On a certain linear fractional transformation. Journal of Mathematics and Physics 39, 269–286 (1960)

    MathSciNet  Google Scholar 

  130. Reichert, R.T.: Dynamic scheduling of modern-robust-control autopilot design for missiles. IEEE Control Systems Magazine 12, 35–42 (1992)

    Article  Google Scholar 

  131. Rugh, W.J., Shamma, J.S.: Research on gain scheduling. Automatica 36, 1401–1425 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  132. Safonov, M.G.: Stability margins of diagonally perturbed multivariable feedback systems. IEE Proceedings - Part D 129, 251–256 (1982)

    MathSciNet  Google Scholar 

  133. Safonov, M.G., Chiang, R.Y.: A Schur method for balanced-truncation model reduction. IEEE Transactions on Automatic Control 34, 729–733 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  134. Safonov, M.G., Chiang, R.Y., Limebeer, D.J.N.: Hankel model reduction without balancing – A descriptor approach. In: Proceedings of the 26th IEEE Conference on Decision and Control, Los Angeles, CA, December 1987, IEEE Computer Society Press, Los Alamitos (1987)

    Google Scholar 

  135. Safonov, M.G., Limebeer, D.J.N., Chiang, R.Y.: Simplifying the \(\mathcal{H}_\infty\) theory via loop-shifting, matrix-pencil and descriptor concepts. International Journal of Control 50, 2467–2488 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  136. Samar, R., Postlethwaite, I., Gu, D.-W.: Model reduction with balanced realizations. International Journal of Control 62, 33–64 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  137. Sánchez-Peña, R.S., Sznaier, M.: Robust Systems. Theory and Applications. John Wiley & Sons, Inc., New York (1998)

    Google Scholar 

  138. Sefton, J., Glover, K.: Pole-zero cancellations in the general \(\mathcal{H}_\infty\) problem with reference to a two block design. Systems & Control Letters 14, 295–306 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  139. Sezginer, R.S., Overton, M.L.: The largest singular value of \(e^{X}A_{O}e^{-X}\) is convex on convex sets of commuting matrices. IEEE Transactions on Automatic Control 35, 229–230 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  140. Skogestad, S.: Dynamics and control of distillation columns. A tutorial introduction. Trans. IChemE 75, 1–36 (1997)

    Article  Google Scholar 

  141. Skogestad, S., Morari, M., Doyle, J.C.: Robust control of ill-conditioned plants: High purity distillation. IEEE Transactions on Automatic Control 33, 1092–1105 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  142. Skogestad, S., Postlethwaite, I.: Multivariable Feedback Control. John Wiley and Sons Ltd, Chichester (1996)

    Google Scholar 

  143. Spillman, M.S.: Robust longitudinal flight control design using linear parameter-varying feedback. Journal of Guidance, Control, and Dynamics 23, 101–108 (2000)

    Article  Google Scholar 

  144. Sreeram, V., Anderson, B.D.O., Madievski, A.G.: New results on frequency weighted balanced reduction technique. In: Proceedings of the 1995 American Control Conference, Seattle, WA, June 1995, pp. 4004–4009 (1995)

    Google Scholar 

  145. Stoorvogel, A.A.: The \(\mathcal{H}_\infty\) Control Problem: A State Space Approach. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  146. Sutton, R., Halikias, G., Plummer, A., Wilson, D.: Modelling and \(\mathcal{H}_\infty\) control of a single-link flexible manipulator. Proceedings of the Institution of Mechanical Engineers, Part I, Journal of Systems and Control Engineering 213, 85–104 (1999)

    Article  Google Scholar 

  147. Tang, K.S., Man, K.F., Gu, D.-W.: Structured Genetic Algorithm for Robust \(\mathcal{H}_\infty\) Control Systems Design. IEEE Transactions on Industrial Electronics 43(5), 575–582 (1996)

    Article  Google Scholar 

  148. Tombs, M.S., Postlethwaite, I.: Truncated balanced realization of a stable non-minimal state space system. International Journal of Control 46(4), 1319–1330 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  149. Tsacouridis, V.A., Medrano-Cerda, G.A.: Discrete-time H  ∞  control of a triple inverted pendulum with single control input. IEEE Proceedings-Control Theory Appl. 146, 567–577 (1999)

    Article  Google Scholar 

  150. van der Linden, G.-W., Lambrechts, P.F.: \(\mathcal{H}_\infty\) control of an experimental inverted pendulum with dry friction. IEEE Control Systems Magazine 19, 44–50 (1993)

    Article  Google Scholar 

  151. Varga, A.: Balancing free square-root algorithm for computing singular perturbation approximations. In: Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, UK, December 1991, pp. 1062–1065. IEEE Computer Society Press, Los Alamitos (1991)

    Chapter  Google Scholar 

  152. Varga, A.: On stochastic balancing related model reduction. In: Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, December 2000, pp. 2385–2390 (2000)

    Google Scholar 

  153. Vidyasagar, M., Kimura, H.: Robust controllers for uncertain linear multivariable systems. Automatica 22, 85–94 (1986)

    Article  MATH  Google Scholar 

  154. Vidyasagar, M., Schneider, H., Francis, B.: Algebraic and topological aspects of feedback stabilization. IEEE Transactions on Automatic Control 27, 880–894 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  155. Walker, D.J.: Relationship between three discrete-time \(\mathcal{H}_\infty\) algebraic Riccati equation solutions. International Journal of Control 52, 801–809 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  156. Wang, F., Hurst, T., Abramovitch, D., Franklin, G.: Disk drive pivot nonlinearity modelling Part II: Time domain. In: Proceedings of the 1994 American Control Conference, Baltimore, MD, June 1994, pp. 2604–2607 (1994)

    Google Scholar 

  157. Wang, G., Sreeram, V., Liu, W.Q.: A new frequency-weighted balanced truncation method and an error bound. IEEE Transactions on Automatic Control 44, 1734–1737 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  158. Whidborne, J.F., Gu, D.-W., Postlethwaite, I.: Algorithms for solving the method of inequalities – A comparative study. In: Proceedings of the 1995 American Control Conference (June 1995)

    Google Scholar 

  159. Whidborne, J.F., Liu, G.P.: Critical Control Systems, Somerset, UK. Research Studies Press Ltd., Taunton (1993)

    Google Scholar 

  160. Whidborne, J.F., Murad, G., Gu, D.-W., Postlethwaite, I.: Robust control of an unknown plant – the IFAC 93 benchmark. International Journal of Control 61, 589–640 (1994)

    Article  Google Scholar 

  161. Whidborne, J.F., Postlethwaite, I., Gu, D.-W.: Robust controller design using \(\mathcal{H}_\infty\) loop-shaping and the method of inequalities. IEEE Transactions on Control Systems Technology 2, 455–461 (1994)

    Article  Google Scholar 

  162. Whidborne, J.F., Postlethwaite, I., Gu, D.-W.: Multiobjective control system design – a mixed optimization approach. In: Agarwal, R.P. (ed.) Recent Trends in Optimization Theory and Applications. World Scientific Series in Applicable Analysis, vol. 5, pp. 467–482. World Scientific, Singapore (1995)

    Google Scholar 

  163. Whidborne, J.F., Postlethwaite, I., Gu, D.-W.: Robust control of a paper machine. Control Engineering Practice 3, 1475–1478 (1995)

    Article  Google Scholar 

  164. White, M.T., Tomizuka, M., Smith, C.: Rejection of disk drive vibration and shock disturbances with a disturbance observer. In: Proceedings of the 1999 American Control Conference, San Diego, CA, June 1999, pp. 4127–4131 (1999)

    Google Scholar 

  165. White, W.N., Fales, R.C.: Control of a double inverted pendulum with hydraulic actuation: A case study. In: Proceedings of the 1999 American Control Conference, San Diego, CA, June 1999, pp. 495–499 (1999)

    Google Scholar 

  166. Yamakita, M., Hoshino, T., Furuta, K.: Control practice using pendulum. In: Proceedings of the 1999 American Control Conference, San Diego, CA, June 1999, pp. 490–494 (1999)

    Google Scholar 

  167. Youla, D.C., Jabr, H.A., Bongiorno, J.J.: Modern Weiner-Hopf design of optimal controllers, Part ii: The multivariable case. IEEE Transactions on Automatic Control 21, 319–338 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  168. Youla, D.C., Jabr, H.A., Lu, C.N.: Single-loop feedback stabilization of linear multivariable dynamical plants. Automatica 10, 159–173 (1974)

    Article  MATH  Google Scholar 

  169. Zakian, V., Al-Naib, U.: Design of dynamical and control systems by the method of inequalities. IEEE Proceedings - Control & Science 120, 1421–1427 (1973)

    Google Scholar 

  170. Zames, G.: Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms and approximate inverses. IEEE Transactions on Automatic Control 26, 301–320 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  171. Zames, G., Francis, B.A.: Feedback, minimax sensitivity, and optimal robustness. IEEE Transactions on Automatic Control 28, 585–600 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  172. Zarchan, P.: Tactical and Strategic Missile Guidance, 3rd edn. Progress in Astronautics and Aeronautics, vol. 176. AIAA, Washington (1998)

    Google Scholar 

  173. Zeiger, H.P., McEwen, A.J.: Approximate linear realization of given dimension via Ho’s algorithm. IEEE Transactions on Automatic Control 19, 153 (1974)

    Article  Google Scholar 

  174. Zhou, K., Doyle, J.C.: Essentials of Robust Control. Prentice Hall, Upper Saddle River (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Leicester, University Road, Leicester, LE1 7RH,  

    Da-Wei Gu

Authors
  1. Da-Wei Gu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Matthew C. Turner Declan G. Bates

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer London

About this chapter

Cite this chapter

Gu, DW. (2007). Robust Control of a Distillation Column. In: Turner, M.C., Bates, D.G. (eds) Mathematical Methods for Robust and Nonlinear Control. Lecture Notes in Control and Information Sciences, vol 367. Springer, London. https://doi.org/10.1007/978-1-84800-025-4_11

Download citation

  • DOI: https://doi.org/10.1007/978-1-84800-025-4_11

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84800-024-7

  • Online ISBN: 978-1-84800-025-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation