Designing PID controllers with a minimum IAE criterion by a differential evolution algorithm

Chemical Engineering Communications

Volumn 170, Issue , 1998, Pages 83-115

  Cheng, Shih Lian ^a   Hwang, Chyi ^b  

^a NATIONAL CHENG KUNG UNIVERSITY   (Taiwan)

^b NATIONAL CHUNG CHENG UNIVERSITY   (Taiwan)

Author keywords

Differential evolution algorithm; Integral of absolute error; Numerical optimization; PID controller

Indexed keywords

ALGORITHMS; CONTROL SYSTEM SYNTHESIS; FUNCTIONS; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; SYSTEM STABILITY; THREE TERM CONTROL SYSTEMS;

DIFFERENTIAL EVOLUTION ALGORITHM; INTEGRAL OF ABSOLUTE ERROR (IAE) PERFORMANCE INDEX; OBJECTIVE FUNCTIONS;

PROCESS CONTROL;

EID: 0032305101     PISSN: 00986445     EISSN: None     Source Type: Journal    
DOI: 10.1080/00986449808912737     Document Type: Article

References (49)

1. Al-Assadi, S. A. K. and Al-Chalabi, L. A. M. (1987) "Optimal Gain for Proportional Integral Derivative Feedback", IEEE Control Systems Magazine, 7(6), 16-19.
2. Åström, K. (1970) Introduction to Stochastic Control Theory, Academic Press, New York.
3. Åström, K. J. (1983) "Computer-Aided Modeling, Analysis, and Design of Control Systems a Perspective", IEEE Control Systems Magazine, 3(2), 4-16.
4. Åström, K. J. and Hägglund, T. (1988) Automatic Tuning of PlD Controllers, Instrument Society of America, Research Triangle Park, NC, U.S.A.
5. Azencott, R. (1992) Simulated Annealing, John Wiley and Sons. Inc., New York.
6. Babister, A. W. (1957a) "Response Functions of Linear Systems with Constant Coefficients Having One Degree of Freedom", Quart. J. Mech. and Appl. Math., X (Pt. 3), 360-368.
7. Babister, A. W. (1957b) "Determination of the Optimum Response of Linear Systems (Zero Displacement Error Systems)", Quart. J. Mech. and Appl. Math., X (Pt. 4), 504-512.
8. Babister, A. W. (1958) "Determination of the Optimum Response of Linear Systems (Zero-Velocity-Error and Zero-Acceleration-Error Systems)", Quart. J. Mech. and Appl. Math., XI(Pt. 1), 119-128.
9. Back, T. (1996) Evolutionary Algorithms in Theory and Practice, Oxford University Press, New York.
10. Bobal, V. (1995) "Self-Tuning Ziegler-Nichols PID Controller", Int. J. Adaptive Control and Signal Processing, 9(2), 213-226.
11. Barmish, B. R., Hollot, C. V., Kraus, F. J. and Tempo, R. (1992) "Extreme Point Result for Robust Stabilization of Interval Plants with First Order Conpensators", IEEE Trans. Automatic Control, 37(6), 707-714.
12. Calistru, C. N. (1995) "Symbolic Optimization Approach for Tuning of PID Controllers", Proc. IEEE Conf, on Control Applications, pp. 174-175.
13. 2 Problem with Multivariable Gain and Phase Margin Constraints", Proc. 1992 American Control Conference, pp. 3124-3129.
14. Cohen, G. H. and Coon, G. A. (1953) "Theoretical Investigation of Retarded Control", Trans. of the American Society of Mechanical Engineers, 75, 827-834.
15. Coughanowr, D. R. (1991) Process Systems Analysis and Control, McGraw-Hill, New York.
16. De Paor, A. M. (1993) "Fiftieth Anniversary Celebration of the Ziegler-Nichols PID Controller", int. J. of Electrical Engineering Education, 30(4), 303-316.
17. Eisenberg, L. (1966) "Stability of Linear Systems with Transport Lag", IRE Convention Record, Part 4, pp. 207-218.
18. Golderg, D. E. (1989) Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, MA, U.S.A.
19. Gorecki, H. and Korytowski, A. (1993) Advances in Optimization and Stability Analysis of Dynamical Systems, Lecture Notes No. 1353, Publications of AGH, Krakow, Poland.
20. Hang, C. C. and Åström, K. J. (1988) "Refinements of the Ziegler-Nichols Tuning Formula for PID Auto-Tuners", Advances in Instrumentation, 43(pt 3), 1021 - 1030.
21. Hang, C. C., Aström, K. J. and Ho, W. K. (1991) "Refinements of the Ziegler-Nichols Tuning Formula", IEE Proc., Part D: Control Theory and Applications, 138(2), 111 - 118.
22. Hwang, C., Lu, M. J. and Shieh, L. S. (1991) "Improved FFT-Based Numerical Inversion Laplace Transforms via Fast Hartley Transform Algorithm", Computers and Mathematics with Applications, 22(1), 13-24.
23. Hwang, C., Shih, Y. P. and Wu, R. Y. (1997) "An Efficient FFT-Based Algorithm for Power Series Expansions", Computers Chem. Engng., 21(9), 1043-1049.
24. Hwang, S. H. (1993) "Adaptive Dominant Pole Design of PID Controllers Based on a Single Closed-Loop Test", Chemical Engineering Communications, 124, 131-152.
25. Imaeda, M., Hashimoto, K. and Ma, S. C. (1987) "Optimal Tuning of Digital PID Controller Based on the Integration of Absolute Error", Kagaku Kogaku Ronbunshu, 13(3), 370-372.
26. Krishnaswamy, P. R., Chan, B. E. M. and Rangaiah, G. P. (1987) "Closed-Loop Tuning of Process Control Systems", Chem. Eng. Sci., 42(9), 2173-2182.
27. Lanzkron, R. W. and Higgins, T. J (1959) "D-Decomposition Analysis of Automatic Control Systems", IEEE Trans. Automatic Control, 4, 150-171.
28. Lee, J., Cho, W. and Edgar, T. F. (1990) "An Improved Technique for PID Controller Tuning from Closed-Loop Tests", AIChE J., 36(12), 1891 -1895.
29. Mantz, R. J. and Tacconi, E. J. (1989) "Complementary Rules to Ziegler and Nichols' Rules for a Regulating and Tracking Controller", Int. J. Control, 49(5), 1465-1471.
30. Michalewicz, Z. (1992) Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, Berlin.
31. Nishkawa, Y., Sannomiya, N., Ohta, T. and Tanaka, H. (1984) "A Method for Auto-Tuning of PID Control Parameters", Automatica, 20(3), 321-332.
32. Park, H. L, Sung, S. W., Lee, I. and Lee, J. (1997) " A Simple Autotuning Method Using Proportional Controller", Chem. Eng. Comm., 161, 185-204.
33. Polak, E. (1964) "A Note on D-Decomposition Theory", IEEE Trans. Automatic Control, 9(1), 107-109.
34. Polonyi, M. J. G. (1989) "PID Controller Tuning Using Standard Form Optimization", Control Engineering, 102- 106, March.
35. Poulin, E. and Pomerleau, A. (1996) "PID Tuning for Integrating and Unstable Processes", IEE Proc., Part D: Control Theory and Applications. 143(5), 429-435.
36. Price, K. and Storn, R. (1997) "Differential evolution", Dr. Dobb's Journal, 22, 24, 78, 18-20, April.
37. Safronova, I. N. and Volgin, V. V. (1989) "The Method of Multiple Roots in Optimizing a Control System with a PID-Algorithm", Thermal Engineering, 36(10), 580-582.
38. Schwefel, H. P. (1995) Evolution and Optimum Seeking, John Wiley and Sons, Inc., New York.
39. Sobol, I. M. (1979) "On the Systematic Search in a Hypercube", SIAM J. Numer. Anal., 16(5), 790-793.
40. Shafiei, Z. and Shenton, A. T. (1994) "Tuning of PID-Type Controllers for Stable and Unstable Systems with Time Delay", Automalica, 30(10), 1609- 1615.
41. Vu, K. M. (1992) "Optimal Setting for Discrete PID Controllers", IEE Proc., Part D: Control Theory and Applications, 139(1), 31-40.
42. Walton, K. and Gorecki, H. (1984) "On the Evaluation of Cost Functionals with Particular Emphasis on Time Delay Systems", IMA J. Mathematical Control and Information, 1(3), 283-306.
43. Wang, P and Kwok, D. P. (1994) "Optimal Design of PID Process Controllers Based on Genetic Algorithms", Control Engineering Practice, 2(4), 641 -648.
44. Wong, L. P. and Seborg, D. E. (1985) "Optimal Proportional Plus Integral Control for Regulator and Tracking Problems", Optimal Control Appl. Methods, 6(4), 335-350.
45. Yang, Y., Jia, C., Chen, J. and Lu, Y. (1991) "Optimization Method for PID Controller Design", Computers in Industry, 16(1), 81 -85.
46. Yuwana, M. and Seborg, D. E. (1982) "A New Method for On-Line Controller Tuning", AIChE J., 28(3), 434-440.
47. Ziegler, J. G. and Nichols, N. B. (1942) "Optimum Settings for Automatic Controllers", Trans. of the American Society of Mechanical Engineers, 64(11), 759-768.
48. Zhuang, M. and Atherton, D. P. (1991) "Optimal PID Controller Settings Using Integral Performance Criteria", Proc. 1991 American Control Conference, 3, 3042-3043.
49. Zhuang, M. and Atherton, D. P. (1993) "Automatic Tuning of Optimum PID Controllers", IEE Proc. Part D: Control Theory and Applications, 140(3), 216-224.