Symbolic computing aided design of nonlinear PID controllers

  • Jesús Rodríguez-Millán
  • Juan Cardillo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1030)


In this paper we introduce a symbolic computing tool, denoted by NLPID in the sequel, for the automatic design of linear and nonlinear PID controllers for nth order nonlinear control systems. The nonlinear design algorithm is based upon Rugh's Extended Linearization Technique, and it was implemented using Mathematica® as symbolic computing platform. At its present stage of development NLPID uses Ziegler-Nichols tables to synthesize linear PID controllers, and therefore its ability to deal with first and second order plants could be limited.


Nonlinear PID Controllers Jacobian and Extended Linearization Symbolic Computing 


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  1. Aström, K. and Hägglund, T. 1988, Automatic Tuning of PID Controllers, Instrument Society of America, USA.Google Scholar
  2. Hartman, P. 1982, Ordinary Differential Equations, Birkhäuser, Basel.Google Scholar
  3. Ogata, K. 1992, Modern Control Theory, 6th Edition, Prentice-Hall, Engelwood Cliffs.Google Scholar
  4. Perko, P. 1991, Differential Equations and Dynamical Systems, Springer-Verlag, New York.Google Scholar
  5. Rodríguez-Millán, J. and Serrano, S. 1995, Symbolic Computing Aided Design of Nonlinear Controllers by Jacobian and Extended Linearization, International Congress for Industrial and Applied Mathematics: ICIAM'95, Hamburg, 3–7 July.Google Scholar
  6. Rugh, W. 1987, Design of Nonlinear PID Controllers, AIChE Journal, Vol. 33, No. 10, 1738–1742.Google Scholar
  7. Rugh, W. 1986, The Extended Linearization Approach, in Nonlinear Control and Systems, M. Fliess and M. Hazewinkel, Editors, D. Reidel Publishing Company, Dordrecht.Google Scholar
  8. Sira-Ramírez, H. 1994, Nonlinear Control by Extended Linearization, Cuadernos de Control Vol. 2–94, Postgrado de Control, Facultad de Ingeniería, ULA, Mérida. (In Spanish)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Jesús Rodríguez-Millán
    • 1
  • Juan Cardillo
    • 1
  1. 1.Facultad de Ingenieria Escuela de Sistemas - Dept. de Sistemas de ControlUniversidad de Los AndesLa HechiceraVenezuela

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