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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
Czasopismo
Rocznik
Tom
Strony
421--442
Opis fizyczny
Bibliogr. 48 poz., rys., tab.
Twórcy
autor
- Signal and System Laboratory, Electronics and Electrotechnics Institute University of Boumerdes, Algeria, IGEE Ex:(INELEC)
autor
- Signal and System Laboratory, Electronics and Electrotechnics Institute University of Boumerdes, Algeria, IGEE Ex:(INELEC)
autor
- Science and Technology Department, University of Ziane Achour Moudjbara Street, BP 3117, Djelfa, Algeria
autor
- 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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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