A new approach to mixed H2/H∞ optimal PI/PID controller design

Industrial and Engineering Chemistry Research

Volumn 41, Issue 24, 2002, Pages 6107-6119

  Hwang, Chyi ^a   Hsiao, Chun Yen ^a  

^a NATIONAL CHUNG CHENG UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

CONTROL EQUIPMENT; DERIVATIVES; HYDROGEN; STABILITY;

DOMAIN BOUNDARY;

INDUSTRIAL PLANTS;

DESIGN;

ALGORITHM; ARTICLE; COMPARATIVE STUDY; FEASIBILITY STUDY; MATHEMATICAL ANALYSIS; MOLECULAR EVOLUTION; PARAMETER; PROCESS CONTROL; PROCESS DESIGN;

EID: 0037184433     PISSN: 08885885     EISSN: None     Source Type: Journal    
DOI: 10.1021/ie010963m     Document Type: Article

References (46)

1. Åström, K. J.; Hägglund, T. PID Controllers: Theory, Design, and Tuning, 2nd Ed.; ISA - The Instrumentation, Systems, and Automation Society: Research Triangle Park, NC, 1995.
2. Ziegler, J. G.; Nichols, N. B. Optimum Settings for Automatic Controllers. Trans. ASME 1942, 64 (11), 759.
3. Blickley, G. Modern Control Started with Ziegler-Nichols Tuning. Control Eng. 1990, 37, 11.
4. Bobal, V. Self-tuning Ziegler-Nichols PID controller. Int. J. Adaptive Control Signal Process. 1995, 9 (2), 213.
5. De Paor, A. M.; O'Malley, M. Controllers of Ziegler-Nichols type for unstable process with time delay. Int. J. Control 1989, 49 (4), 1273.
6. De Paor, A. M. Fiftieth anniversary celebration of the Ziegler-Nichols PID controller. Int. J. Electr. Eng. Educ. 1993, 30(4), 303.
7. Hang, C. C.; Åström, K. J. Refinements of the Ziegler-Nichols tuning formula for PID autotuners. Adv. Instrum. 1988, 43, 1021.
8. Hang, C. C.; Åström, K. J.; Ho, W. K. Refinements of the Ziegler-Nichols tuning formula. IEE Proc. D: Control Theory Appl. 1991, 138 (2), 111.
9. Mantz, R. J.; Tacconi, E. J. Complementary rules to Ziegler and Nichols's rule for a regulating and tracking controller. Int. J. Control 1989, 49 (5), 1465.
10. Ott, M. G.; Wojsznis W. K. Autotuning: From Ziegler-Nichols to model based rules. Adv. Instrum. Control 1995, 50, 323.
11. Wang, Q. G.; Lee, T. H.; Zhang, Y. Multiloop version of the modified Ziegler-Nichols method for two input-two output processes. Ind. Eng. Chem. Res. 1998, 37 (12), 4725.
12. Morari, M.; Zafiriou, E. Robust Process Control; Prentice Hall: Englewood Cliffs, NJ, 1989.
13. Rivera, E. E.; Morari, M.; Skogestad, S. Internal Model Control. 4 PID Controller Design. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 252-265.
14. Chien I. L.; Fruehauf, P. S. Consider IMC tuning to improve controller performance. Chem. Eng. Prog. 1990, 86 (10), 33-41.
15. Graham, D.; Lathrop, R. C. The Synthesis of Optimum Transient Response: Criteria and Standard Forms. AIEE Trans. II: Appl. Ind. 1953, 72, 273.
16. Zhuang, M.; Atherton, D. P. Automatic tuning of optimum PID controllers. IEE Proc. D: Control Theory Appl. 1993, 140 (3), 216-224.
17. ∞ controllers with A PID structure. Trans. ASME 1990, 112 (3), 325.
18. McFarlane, D. C.; Glover, K. Robust Controller Design Using Normalized Coprime Factor Plant Descriptions; Springer-Verlag: Berlin, 1990.
19. McFarlane, D. C.; Glover, K. A loop-shaping design procedure using H∞ synthesis. IEEE Trans. Autom. Control 1992, 37 (6), 759.
20. Grassi, E.; Tsakalis, K. S. PID Controller Tuning by frequency loop-shaping: Application to diffusion furnace temperature control. IEEE Trans. Control Syst. Technol. 2000, 8 (5), 842.
21. ∞ loop shaping. Int. J. Robust Nonlinear Control 2000, 10 (15), 1249.
22. ∞ control. IEE Proc. Control Theory Appl. 1998, 145 (6), 485.
23. ∞ optimal PID control. IEEE Control Syst. Mag. 1995, 15 (5), 51.
24. Krohling, R. Design of PID Controller for Disturbance Rejection: A Genetic Optimization Approach. In Second International Conference on Genetic Algorithms in Engineering Systems: Innovations and Applications; IEE/INSPEC: Edison, NJ, 1997; p 498.
25. Panagopoulos, H.; Åström, K. J.; Hägglund, T. Design of PID controllers based on constrained optimization. In Proceedings of the 1999 American Control Conference; IEEE Press: Piscataway, NJ, 1999; Vol. 6, p 3858.
26. Åström, K. J.; Panagopoulos, H.; Hägglund, T. Design of PI controllers based on non-convex optimization. Automatica 1998, 34 (3), 585.
27. Bao, J.; Forbes, J. F.; McLellan, P. J. Robust multiloop PID controller design: A successive semidefinite programming approach. Ind. Eng. Chem. Res. 1999, 38 (9), 3407.
28. Zheng, F.; Wang, Q. G.; Lee, T. H. On the design of multivariable PID controllers via LMI approach. Automatica 2002, 38 (3), 517.
29. Polyak, B. T.; Kogan, J. Necessary and sufficient conditions for robust stability of linear systems with multiaffine uncertainty structure. IEEE Trans. Autom. Control 1995, 40 (7), 1255-1260.
30. Chen, J. J.; Hwang, C. Value set of polynomial families with coefficients depending nonlinearly on perturbed parameters. IEE Proc. D: Control Theory Appl. 1998, 145 (1), 304-307.
31. Hwang, C.; Hsiao, C. H. Solution of a non-convex optimization arising in PI/PID control design. Automatica 2002, 38 (11), 1895-1904.
32. Conway, J. B. Functions of One Complex Variable, 2nd ed; Springer-Verlag: New York, 1978.
33. Marshall, J. E.; Gorecki, H.; Korytowski, A.; Walton, K. Time-Delay Systems Stability and Performance Criteria with Applications; Ellis Horwood: New York, 1992.
34. Price, K.; Storn, R. Differential Evolution. Dr. Dobb's J. Software Tools Prof. Programmer 1997, 22 (4), 18.
35. Golderg, D. E. Genetic Algorithms in Search, Optimization and Machine Learning; Addison-Wesley: Reading, MA, 1899.
36. Back, T. Evolutionary Algorithms in Theory and Practice; Oxford University Press: New York, 1996.
37. Azencott, R. Simulated Annealing; John Wiley & Sons: New York, 1992.
38. Price, K.; Storn, R. Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 1997, 11, 341.
39. Wang, F. S.; Chiou, J. P. Optimal control and optimal time location problems of differential - Algebraic systems by differential evolution. Ind. Eng. Chem. Res. 1997, 36 (12), 5348.
40. Lee, M. H.; Han, C. H.; Chang, K. S. Dynamic optimization of a continuous polymer reactor using a modified differential evolution algorithm. Ind. Eng. Chem. Res. 1999, 38 (12), 4825.
41. Storn, R. On the usage of differential evolution for function optimization. In Proceedings of the 1996 Biennial Conference of the North American Fuzzy Information Processing Society; IEEE Press: Piscataway, NJ, 1996; p 519.
42. Yamamura, K. Simple algorithms for tracing solution curves. IEEE Trans. Circuits Syst. 1993, 40 (8), 537.
43. Yamamura, K.; Sekiguchi, T. A modified spherical method for tracing solution curves. IEICE Trans. Fundam. 1995, E78-A (9), 1233.
44. Datta, A.; Ho, M. T.; Bhattacharyya, S. P. Structure and Synthesis of PID Controllers; Springer-Verlag: New York, 2000.
45. ∞-parameter space method. IEEE Trans. Autom. Control 1997, 42 (7), 946.
46. He, J. B.; Wang, Q. G.; Lee, T.H. PI/PID controller tuning via LQR approach. Chem. Eng. Sci. 2000, 55, 2429.