A learning method for multivariable PID control synthesis based on estimated plant Jacobian

  • Byeong-Mook Chung
  • Yoon-Kyu Lim
  • Gregory D. Buckner
Regular Papers Control Theory
First Online:
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Accepted:

Abstract

Despite decades of research involving optimal control of multivariable systems, such controllers require accurate linear models of the plant dynamics. Real systems contain nonlinearities and high-order dynamics that may be difficult to model using conventional techniques. This paper presents a novel learning control (LC) method for PID controllers that doesn’t require explicit modeling of the plant dynamics. This method utilizes gradient descent techniques to iteratively reduce an error-related objective function. Simulations involving a hydrofoil catamaran show that the proposed PID-LC algorithm improves controller performance compared to LQR controllers derived from multivariable models.

Keywords

Hydrofoil catamaran Jacobian sign learning method PID control 
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References

  1. [1]
    A. Callender, D. R. Hartree, and A. Porter, “Time lag in control system,” Philosophical Transactions of the Royal Society of London A, vol. 235, no. 756 pp. 415–444, 1936.MATHCrossRefGoogle Scholar
  2. [2]
    J. G. Ziegler and N. B. Nichols, “Optimum setting for automatic controllers,” Trans. ASME, vol. 64, pp. 759–768, 1942.Google Scholar
  3. [3]
    Z. Y. Zhao, M. Tomizuka, and S. Isaka, “Fuzzy gain scheduling of PID controllers,” IEEE Trans. Systems, Man, & Cybernetics, vol. 23, no. 5, pp. 1392–1398, 1993.CrossRefGoogle Scholar
  4. [4]
    K. Warwick and Y.-H. Kang, “Self-tuning proportional, integral and derivative controller based on genetic algorithm least squares,” Journal of Systems and Control Engineer, vol. 212, no. 16, pp. 437–448, 1998.Google Scholar
  5. [5]
    A. Madady, “PID type iterative learning control with optimal gains,” Int. Journal of Control, Automation, and System, vol. 6, no. 2, pp. 194–203, 2008.Google Scholar
  6. [6]
    M. Athans and P. L. Falk, Optimal Control, McGraw-Hill, New York, 1966.MATHGoogle Scholar
  7. [7]
    J. M. Maciejowski, Multivariable Feedback Design, Addison-Wesley Inc., 1989.Google Scholar
  8. [8]
    T. J. Procyk, A Self-Organizing Control For Dynamic Processes, Ph.D. Thesis, Queen Mary College, Univ. of London, 1977.Google Scholar
  9. [9]
    B. M. Chung, “Control of nonlinear multivariable Systems using direct fuzzy learning method,” Journal of Intelligent & Fuzzy Systems, vol. 5, pp. 297–310, 1998.Google Scholar
  10. [10]
    Y. K. Lim and B. M. Chung, “A tuning method of multi variable PID gains using jacobian,” Proc. of IEEE Conference on Control Applications, pp. 886–891, 2003.Google Scholar
  11. [11]
    Y. Zhang, Q. G. Wang, and K. J. Astrom, “Dominant pole placement for multi-loop control systems,” Automatica, vol. 38, no. 7, pp. 1213–1220, 2002.MATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    A. P. Loh, C. C. Hang, C. K. Quek, and V. U. Vasnani, “Autotuning of multiloop propositionalintegral controllers using relay feedback,” Industrial Engineering and Chemical Research, vol. 32, pp. 1102–1107, 1993.CrossRefGoogle Scholar
  13. [13]
    Q. G. Wang, B. Zou, T. H. Lee, and Q. Bi, “Autotuning of multivariable PID controllers from decentralized relay feedback,” Automatica, vol. 33, no. 3, pp. 319–330, 1997.MATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    F. Zheng, Q. G. Wang, and T. H. Lee, “On the design of multivariable PID controllers via LMI approach,” Automatica, vol. 38, no. 3, pp. 517–526, 2002.MATHCrossRefGoogle Scholar
  15. [15]
    B. M. Chung and J. H. Oh, “Control of dynamic systems using fuzzy learning algorithm,” Fuzzy Sets and Systems, vol. 59, no. 1, pp. 1–14, 1993.MATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    F. Zhang, Matrix Theory: Basic Results and Techniques, Springer-Verlag, New York, 1999.MATHGoogle Scholar
  17. [17]
    S. Y. Lee, Theoretical and Experimental Study on the Attitude Control System of Foil-catamaran, Ph.D. Thesis, Seoul National University, Korea, 1999.Google Scholar
  18. [18]
    S. Y. Lee and K. P. Rhee, “Design of ship-motion regulators for foil catamarans in irregular sea waves,” IEEE J. of Oceanic Engineering, vol. 27, vo. 3, pp. 738–752, 2002.CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer Berlin Heidelberg 2009

Authors and Affiliations

  • Byeong-Mook Chung
    • 1
  • Yoon-Kyu Lim
    • 2
  • Gregory D. Buckner
    • 3
  1. 1.School of Mechanical EngineeringYeungnam UniversityGyeongsan, GyeongbookKorea
  2. 2.Ulsan Industry Promotion FoundationUlsanKorea
  3. 3.Department of Mechanical and Aerospace EngineeringNorth Carolina State UniversityRaleighUSA

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