Non-smooth structured control design with application to PID loop-shaping of a process

International Journal of Robust and Nonlinear Control

Volumn 17, Issue 14, 2007, Pages 1320-1342

  Apkarian, Pierre ^a,b   Bompart, Vincent ^a,b   Noli, Dominikus ^b  

^a ONERA   (France)

^b INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

Author keywords

H synthesis; Non smooth optimization; NP hard problems; PID; Structured controllers

Indexed keywords

AD HOC NETWORKS; COMPUTATIONAL COMPLEXITY; CONTROL EQUIPMENT; ENGINEERS; MATHEMATICAL PROGRAMMING;

NON-SMOOTH OPTIMIZATION; STRUCTURED CONTROLLERS;

FEEDBACK CONTROL;

EID: 34548711232     PISSN: 10498923     EISSN: 10991239     Source Type: Journal    
DOI: 10.1002/rnc.1175     Document Type: Article

References (39)

1. ∞ control problems. IEEE Transactions on Automatic Control 1989; AC-34(8):831-847.
2. Tsitsiklis JN, Blondel V. NP-hardness of some linear control design problems. SIAM Journal on Control 1997; 35(6):2118-2127.
3. Balakrishnan V, Boyd S. Global optimization in control system analysis and design. In Control and Dynamic Systems: Advances in Theory and Applications, Leondes CT (ed.), vol. 53. Academic Press: New York, 1992.
4. Wong T, Bigras P. Structured controller design with evolutionary optimization. AIA2003, Benalmadena, Spain, September 2003; 163-168.
5. Boyd S, ElGhaoui L, Feron E, Balakrishnan V. Linear Matrix Inequalities in Systems and Control Theory. SIAM Studies in Applied Mathematics, vol. 15. SIAM: Philadelphia, 1994.
6. Grigoriadis KM, Skelton RE. Low-order control design for LMI problems using alternating projection methods. Automatica 1996; 32(8):1117-1125.
7. Ebihara Y, Tokuyama K, Hagiwara T. Structured controller synthesis using LMI and alternating projection method. International Journal of Control 2004; 77(12):1137-1147.
8. El Ghaoui L, Balakrishnan V. Synthesis of fixed-structure controllers via numerical optimization. Proceedings of IEEE Conference on Decision and Control, Lake Buena Vista, FL, 1994; 2678-2683.
9. Iwasaki T. The dual iteration for fixed-order control. IEEE Transactions on Automatic Control 1999; 44(4):783-788.
10. Han J, Skelton RE. An LMI optimization approach for structured linear controllers. Proceedings of IEEE Conference on Decision and Control, Maui, HI, 2003; 5143-5148.
11. Hassibi A, How J, Boyd S. A pathfollowing method for solving BMI problems in control. Proceedings of American Control Conference, San Diego, U.S.A., 1999; 1385-1389.
12. Bao J, Forbes JF, McLellan PJ. Robust multiloop PID controller design: a successive semidefinite programming approach. Industrial and Engineering Chemistry Research 1999; 38(9):3407-3413.
13. ∞ loop shaping PID controllers. Technical Report, Cambridge University, Cambridge, U.K., October 2000.
14. Miyamoto S, Vinnicombe G. Robust decentralized control design based on coprime factorization representations and LMI optimization. Proceedings of the 36th SICE Annual Conference, Tokushima, Japan, 1997; 1007-1012.
15. Tan W, Chen T, Marquez HJ. Robust controller design and PID tuning for multivariable processes. Asian Journal of Control 2002; 4(4):439-451.
16. ∞ control problem. Automatica 2006; 42(1):93-100.
17. Rotkowitz M, Lall S. A characterization of convex problems in decentralized control. IEEE Transactions on Automatic Control 2006; 51(2):274-286.
18. Xin Q, Salapaka MV, Voulgaris PG, Khammash M. Structured optimal and robust control with multiple criteria: a convex solution. IEEE Transactions on Automatic Control 2004; 49(10):1623-1640.
19. Boyd S, Barratt C. Linear Controller Design: Limits of Performance. Prentice-Hall: Englewood Cliffs, NJ, 1991.
20. Scherer C. Structured finite-dimensional controller design by convex optimization. Linear Algebra and Applications 2002; 351-352C:639- 669.
21. Mäkilä PM, Toivonen HT. Computational methods for parametric LQ minimization: a survey. IEEE Transactions on Automatic Control 1987; AC-32(8):658-671.
22. Polak E, Wardi Y. A nondifferentiable optimization algorithm for the design of control systems subject to singular value inequalities over a frequency range. Automatica 1982; 18(3):267-283.
23. ∞ synthesis. IEEE Transactions on Automatic Control 2006; 51(1):71-86.
24. ∞ synthesis. European Journal of Control 2006; 12(3):229-244.
25. Apkarian P, Noll D. Nonsmooth optimization for multiband frequency domain control design. Automatica 2006, to appear.
26. ∞ synthesis. IEEE Transactions on Automatic Control 1992; 37(6):759-769.
27. Noll D, Apkarian P. Spectral bundle methods for nonconvex maximum eigenvalue functions: first-order methods. Mathematical Programming Series B 2005; 104(2):701-727.
28. Apkarian P, Noll D. IQC analysis and synthesis via nonsmooth optimization. Systems and Control Letters 2006; 55(12):971-981.
29. ∞ synthesis. 5th IFAC Symposium on Robust Control Design, Toulouse, France, July 2006.
30. Clarke FH. Optimization and Nonsmooth Analysis. Canadian Mathematical Society Series. Wiley: New York, 1983.
31. ∞ spaces. IEEE Transactions on Automatic Control 1989; AC-34(3):268-276.
32. Polak E. Optimization: Algorithms and Consistent Approximations. Applied Mathematical Sciences. Springer: New York, 1997.
33. ∞-norm. Systems and Control Letters 1990; 15:1-7.
34. ∞ loop shaping design procedure. Proceedings of the 3rd World Congress on Intelligent Control and Automation, Hefei, China, vol. 5, June 2000; 3385-3388.
35. Fujita M, Hatake K, Matsumura F. Loop shaping based robust control of a magnetic bearing. IEEE Control Systems Magazine 1993; 13(4): 57-65.
36. Raisch JJ, Lang L, Groebel M. Loop shaping controller design for a binary distillation column. Control'91, Edinburgh, U.K., vol. 2, March 1991; 1271-1276.
37. Helton JW, Merino O. Coordinate optimization for bi-convex matrix inequalitites. Proceedings of IEEE Conference on Decision and Control, San Diego, CA, 1997; 3609-3613.
38. Bompart V, Apkarian P, Noll D. Nonsmooth technique for stabilizing linear systems. 2006, submitted for publication.
39. Suykens J, Vandewalle K, De Moor B. Intelligence and cooperative search by coupled local minimizers. International Journal of Bifurcation and Chaos 2001; 11(8):2133-2144.