Use of genetic algorithms for optimization in digital control of dynamic systems

ABSTRACT

This paper presents a method to optimize proportional-integral-derivative (PID) control parameters, given a discrete model of the controlled process. This method is based on Holland's genetic algorithm (GA). It does not require a mathematical model of the controller to represent its dynamic behavior. It gives a solution that is not only optimal but also meets engineering constraints. Genetic algorithms do a global search without derivatives for points in a multi-dimensional search space. This method works for non-linear as well as linear systems. The objective function of the GA is based on the integrated product of time and absolute error (ITAE). The performance of the GA is compared to that of the other optimization methods. The results show that it is simple and effective.

REFERENCES

• 1: Ziegler, J.G. and N.B. Nichols, "Optimum Settings for Automatic Controllers." Transaction ofASME, vo164, pp 759- 768, 1942. American Society of Mechanical Engineers, New York.
• 2: Kinney, Thomas B. "Tuning Process Controllers." Chemical Engineed~, pp 67-72, September 1983.
• 3: John G. Bollinger , Neil A. Duffie, Computer Control of Machines and Processes, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1988
• 4: Hemerly, Elder M., "PC-Based Packages for Identification, Optimization, and Adaptive Control," IEEE Control Systems, Feb. 1991, pp 37-43.
• 5: Karl J. Åström , Björn Wittenmark, Computer-controlled systems: theory and design (2nd ed.), Prentice-Hall, Inc., Upper Saddle River, NJ, 1990
• 6: R. C. Dorf, Modern Control Systems, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1988
• 7: Gerry, J.P. "A Comparison of PID Control Algorithms'. Control Engineering, pp 102-105, March 1987.
• 8: Goldberg, David. F_. Genetic Algorithms, Addison-Wesley Publishing Company, Inc. 1989
• 9: Goldberg, David E. "Optimal Initial Population Size for Binary-coded Genetic Algorithms'. TCGA R~ Number 850001, 1985. The Clearing House for Genetic Algorithms, Dept. of Engg. Mechanics, University of Alabama, 35486.
• 10: David E. Goldberg, Sizing populations for serial and parallel genetic algorithms, Proceedings of the third international conference on Genetic algorithms, p.70-79, December 1989, George Mason University, United States
• 11: J Grefenstette, Optimization of control parameters for genetic algorithms, IEEE Transactions on Systems, Man and Cybernetics, v.16 n.1, p.122-128, Jan./Feb. 1986 [doi>10.1109/TSMC.1986.289288]
• 12: J. David Schaffer , Richard A. Caruana , Larry J. Eshelman , Rajarshi Das, A study of control parameters affecting online performance of genetic algorithms for function optimization, Proceedings of the third international conference on Genetic algorithms, p.51-60, December 1989, George Mason University, United States
• 13: William H. Press , Brian P. Flannery , Saul A. Teukolsky , William T. Vetterling, Numerical recipes in Pascal: the art of scientific computing, Cambridge University Press, New York, NY, 1989
• 14: J. Hesser , R. Männer , O. Stucky, Optimization of steiner trees using genetic algorithms, Proceedings of the third international conference on Genetic algorithms, p.231-236, December 1989, George Mason University, United States
• 15: M. O. Odetayo , D. R. McGregor, Genetic algorithm for inducing control rules for a dynamic system, Proceedings of the third international conference on Genetic algorithms, p.177-182, December 1989, George Mason University, United States
• 16: David E. Goldberg, Genetic Algorithms and Rules Learning in Dynamic System Control, Proceedings of the 1st International Conference on Genetic Algorithms, p.8-15, July 01, 1985
• 17: Kraus, T.W. and T.J. Myron, "Self-Tuning PID Controller Uses Pattern Recognition Approach," Control Engineering, June 1984, pp 106-111.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.3 PROBABILITY AND STATISTICS
      Subjects: Probabilistic algorithms (including Monte Carlo)

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS

General Terms:
Algorithms, Design, Theory