On the theory of λ-matrices based MIMO control system design

Bekhiti, B.; Dahimene, A.; Nail, B.; Hariche, K.

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Tytuł artykułu

On the theory of λ-matrices based MIMO control system design

Autorzy

Bekhiti B. , Dahimene A. , Nail B. , Hariche K.

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In this paper we have described a new design algorithm for the whole set of latent-structure assignments via the approaches of block structure of λ-matrices placement. The procedure that has been developed is based on decoupling of the interactions between control loops in a multivariable plant. The procedure is performed using matrix polynomial solvent reconstruction for the decoupling purposes. However, for the design of the trajectory tracking controller, each input-output pair is treated respectively by designing SISO controllers. A second procedure is the MIMO PID compensator design via the model-matching method. This latter algorithm has been developed in order to avoid the internal or the hidden instability, which may occur in the ﬁrst method, due to the block zeros - block poles cancellation.

Słowa kluczowe

block roots λ-matrices decoupling MIMO PID compensator model matching

Wydawca

Systems Research Institute, Polish Academy of Sciences

Czasopismo

Control and Cybernetics

Rocznik

2015

Tom

Vol. 44, no. 4

Strony

421--442

Opis fizyczny

Bibliogr. 48 poz., rys., tab.

Twórcy

autor

Bekhiti B.

Signal and System Laboratory, Electronics and Electrotechnics Institute University of Boumerdes, Algeria, IGEE Ex:(INELEC)

autor

Dahimene A.

Signal and System Laboratory, Electronics and Electrotechnics Institute University of Boumerdes, Algeria, IGEE Ex:(INELEC)

autor

Nail B.

Science and Technology Department, University of Ziane Achour Moudjbara Street, BP 3117, Djelfa, Algeria

autor

Hariche K.

Signal and System Laboratory, Electronics and Electrotechnics Institute University of Boumerdes, Algeria, IGEE Ex:(INELEC)

Bibliografia

1. Ahn, S. M. (1982) Stability of a Matrix Polynomial in Discrete Systems. IEEE Trans. on Auto. Contr., AC-27, 1122–1124, Oct.
2. Andry, A.N., Shapiro, E.Y., Chung, J.C. (1983) Eigenstructure assignment for linear systems. IEEE Trans. Aerosp. Electron. Syst. 19 (5) 711–729.
3. Barnett, S. (1971) Matrices in Control Theory. Van Nostrand Reinhold, New York.
4. Bekhiti, B., Dahimene, A., Nail, B., Hariche, K. and Hamadouche, A. (2015) On the Block Roots of Matrix Polynomialsbased MIMO Control System Design. In: 4th International Conference on Electrical Engineering ICEE Boumerdes. IEEE 978–1–4673–6673–1/15/ $ 31.00, 1–6.
5. Bekhiti, B., Dahimene, A., Nail, B. and Hariche, K. (2016) The Left and Right Block Placement Comparison Study: Application to Flight Dynamics. Informatics Engineering, an International Journal (IEIJ), 4 (1), March.
6. Chen, C.T. (1984) Linear System Theory and Design. Holt, Reinhart and Winston.
7. Dahimene, A. (2009) Incomplete matrix partial fraction expansion. Control and Cybernetics 38, 3.
8. Denman, E.D. (1977) Matrix polynomials, roots, and spectral factors. Applied Math. Comput. 3: 359–368.
9. Denman, E.D. and Beavers, A.N. (1976) The matrix sign function and computations in systems. Appl.Math. Comput. 2: 63–94.
10. Dennis, J.E., Traub, J.F. and Weber, R.P. (1976) The algebraic theory of matrix polynomials. J. Numer. Anal. 13: 831–845.
11. Dennis, J.E., Traub, J.F. and Weber, R.P. (1978) Algorithms for solvents of matrix polynomials. J. Numer. Anal. 15: 523–533.
12. DiStefano, J.J., Stubberud, A.R., and Williams, I.J. (1967) Theory and Problems of Feedback and Control Systems. Mc Graw Hill.
13. Fredriksson, J., Egardt, B. (2001) Backstepping control with local LQ performance applied to a turbocharged diesel engine. In: Proc. 40th IEEE Conference on Decision and Control, 1, 111–116, IEEE.
14. Friedrich, I., Liu, C.S., Oehlerking, D. (2009) Coordinated EGR-rate model-based controls of turbocharged diesel engines via an intake throttle and an EGR valve. In: IEEE Conference on Vehicle Power and Propulsion, VPPC 09, 7-10 Sept. 2009, 340–347. IEEE.
15. Gohberg, I.,Kaashoek M.A., and Rodman, L. (1978) Spectral analysis of operator polynomial and a generalized Vandermondee matrix. 1. The ﬁnite-dimensional case. In: Topics in Functional Analysis. Advances in mathematics, Supplementary Studies, 3. Academic Press, London, 91– 128.
16. Gohberg, I., Lancaster, P. and Rodman, L. (1982) Matrix Polynomials. Academic Press. Haiyan, W. (2006) Control oriented dynamic modeling of a turbocharged diesel engine. In: Sixth Int. Conference on Intelligent Systems Design and Applications ISDA 06, 2, 16-18 Oct. 2006, 142–145, IEEE.
17. Hariche, K. (1986) Interpolation Theory in the Structural Analysis of λmatrices. Chapter 3, Ph. D. Dissertation, University of Houston.
18. Hariche, K., Denman, E. D. (1988) On Solvents and Lagrange Interpolating λ-Matrices. Applied Mathematics and Computation 25, 321–332.
19. Hariche, K., Denman, E. D. (1989) Interpolation Theory and λ-Matrices. Journal of Mathematical Analysis and Applications 143, 53.
20. Harvey, C.A., Stein, G. (1978) Quadratic weights for asymptotic regulator properties. IEEE Trans. Autom. Control 23 (3), 378–387.
21. Hippe, P., O’Reilly, J. (1987) Parametric compensator design. Int. J. Control 45 (4), 1455–1468.
22. Jung, M., Glover, K., Christen, U. (2005) Comparison of uncertainty parameterizations for robust control of turbocharged diesel engines. Control Eng. Pract. 13(1), 15–25.
23. Kailath, T., Li, W. (1980) Linear Systems. Prentice Hall.
24. Kucera, V. (1979) Discrete Linear Control: The Polynomial Equation Approach. John Wiley.
25. Liu, G.P., Patton, R.J. (1998) Eigenstructure Assignment for Control System Theory. John Wiley & Sons.
26. Magdi, S. Mahmoud and Yuanqing Xia (2012) Applied Control Systems Design. Springer Verlag, London Limited.
27. Moore, B.C. (1976) On the ﬂexibility oﬀered by state feedback in multivariable systems beyond closed loop eigenvalue assignment. IEEE Trans. Autom. Control 21 (5) 689–692.
28. Pereira, E. (2003) On solvents of matrix polynomials. Appl. Numer. Math., 47, 197–208.
29. Pereira, E. (2003) Block eigenvalues and solution of diﬀerential matrix equation, Mathematical Notes, Miskolc, 4, 1, 45–51.
30. Resende, P., Kaskurewicz, E. (1989) A Suﬃcient Condition for the Stability of Matrix Polynomials. IEEE Trans. on. Autom. Contr., AC-34, 539–541, May.
31. Singh, M.G. and Elloy, J.-P. (1980) Applied Industrial Control. Volume 1. Pergamon Press.
32. Shieh, L.S., Sacheti, S. (1978) A Matrix in the Block Schwarz Form and the Stability of Matrix Polynomials. Int. J. Control, 27, 245–259.
33. Shieh, L.S. and Chahin, N. (1981) A computer-aided method for the factorization of matrix polynomials. Internat. Systems Sci. 12: 1303-1316.
34. Shieh, L.S., Tsay, Y. T. and Coleman, N. I. (1981) Algorithms for solvents and spectral factors of matrix polynomials. Internat. J. Control 12: 1303–1316.
35. Shieh, L.S. and Tsay, Y. T. (1981) Transformation of solvent and spectral factors of matrix polynomial, and their applications. Internat. J. Control 34: 813–823.
36. Tsai, J.S.H., Shieh, I.S., and Shen, T.T.C. (1988) Block power method for computing solvents and spectral factors of matrix polynomials. Internat. Computers and Math. Appl. 16: 683–699.
37. Shieh, L.S. and Tsay, Y.T. (1982) Block modal matrices and their applications to multivariable control systems. IEE Proc. D Control Theory Appl. 2: 41–48.
38. Shieh, L.S., Chang, F.R. and McInnis, B.C. (1986) The Block partial fraction expansion of a matrix fraction description with repeated Block poles. IEEE Trans. Automat. Control. 31: 23–36.
39. Shieh, L.S. and Tsay, Y.T. (1984) Algebraic-geometric approach for the modal reduction of large-scalemultivariable systems. IEE Proc. D Control Theory Appl, 131(1): 23–26.
40. Shieh, L.S. and Tsay, Y.T. (1982) Transformation of a class of multivariable control systems to Block companion forms. IEEE Trans. Automat. Control 27: 199–203.
41. Shieh, L.S., Tsay, Y.T. and Yates, R.E. (1983) State-feedback decomposition of multivariable systems via Block pole placement. IEEE Trans. Autom. Control 28(8), 850–852.
42. Solak, M.K. (1987) Divisors of Polynomial Matrices: Theory and Applications. IEEE Trans. on Auto. Contr., AC-32, 916–919, Oct.
43. Tsai, J.S.H. and Chen, C.M. and Shieh, L.S. (1992) A Computer-Aided Method for Solvents and Spectral Factors of Matrix Polynomials. Applied mathematics and computation, 47: 211–235.
44. Yaici, M. and Hariche, K. (2014a) On eigenstructure assignment using Block poles placement. European Journal of Control, September, 20 (5), 217–226.
45. Yaici, M., Hariche, K. (2014b) On Solvents of Matrix Polynomials. International Journal of Modeling and Optimization, 4, 4, August, 273–277.
46. Yaici, M. Hariche, K. and Clark, T. (2014) A Contribution to the Polynomial Eigen Problem. International Journal of Mathematics, Computational, Natural and Physical Engineering, 8, 10.
47. Wang, Q.G. (2003) Decoupling Control. Springer Verlag, Berlin–Heidelberg.
48. Wonham, W.M. (1976) On pole assignment in multi-input controllable linear systems. IEEE Trans. Autom. Control 12, 660–665.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.

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Bibliografia

Identyfikator YADDA

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