Optimal decoupling controllers revisited

• Autorzy: Kucera V.
• Języki publikacji: EN

Abstrakty

EN

The problem of decoupling a linear system by dynamic compensation into multi-input multi-output subsystems is studied by applying proper and stable fractional representations of transfer matrices. A necessary and sufficient condition is given for a decoupling and a stabilizing controller to exist. The set of all controllers that decouple and simultaneously stabilize the system is determined in parametric form. Optimal decoupling controllers are then obtained by an appropriate selection of the parameter.

Słowa kluczowe

EN

linear systems; fractional representations; decoupling controllers; stabilizing controllers; optimal controllers

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2013
• Tom: Vol. 42, no. 1
• Strony: 139--154
• Opis fizyczny: Bibliogr. 41 poz., il.

Twórcy

autor

Kucera V.

• Czech Technical University in Prague, Faculty of Electrical Engineering, Technicka 2, 16627 Prague 6
• Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic

Bibliografia

• 1. Basile, G. and G. Marro (1970) A state space approach to non interacting controls. Ric. Autom. 1, 68-77.
• 2. Bongiorno, J.J. and D.C. Youla (2001) Wiener-Hopf design of optimal decoupling one-degree-of-freedom controllers for plants with rectangular transfer matrices. Int. J. Control 74, 1393-1411.
• 3. Denham, M.J. (1973) A necessary and sufficient condition for decoupling by output feedback. IEEE Trans. Automatic Control 18, 537.
• 4. Descusse, J. and M. Malabre (1982) Solvability of the decoupling problem for linear constant (A, B, C, D)-quadruples with regular output feedback. IEEE Trans. Automatic Control 27, 456-458.
• 5. Descusse, J. and J.M. Dion (1982) On the structure at infinity of linear square decoupled systems. IEEE Trans. Automatic Control 27, 971-974.
• 6. Descusse, J., J. F. Lafay, and V. Kuˇcera (1984) Decoupling by restricted static state feedback: The general case. IEEE Trans. Automatic Control 29, 79-81.
• 7. Desoer, C.A., R.W. Liu, J. Murray, and R. Saex (1980) Feedback system design: The fractional representation approach to analysis and synthesis. IEEE Trans. Automatic Control 25, 399-412.
• 8. Desoer, C.A. and A.N. Gündes¸ (1986) Decoupling linear multi-input / multi-output plant by dynamic output feedback: An algebraic theory. IEEE Trans. Automatic Control 31, 744-750.
• 9. Falb, P.L. and W.A. Wolovich (1967) Decoupling in the design and synthesis of multivariable control systems. IEEE Trans. Automatic Control 12, 651-659.
• 10. Filev, D.P. (1982a) Some new results in state space decoupling of multivariable systems. I. A link between geometric and matrix methods. Kybernetika 18, 215-233.
• 11. Filev, D.P. (1982b) Some new results in state space decoupling of multivariable systems. II. Extensions to decoupling of systems with D ≠ 0 and output feedback decoupling. Kybernetika 18, 330-344.
• 12. Gilbert, E.G. (1969) The decoupling of multivariable systems by state feedback. SIAM J. Control 7, 50-63.
• 13. Gómez, G.I. and G.C. Goodwin (2000) An algebraic approach to decoupling in linear multivariable systems. Int. J. Control 73, 582-599.
• 14. Hautus, M.L.J. and M. Heymann (1983) Linear feedback decoupling – Transfer function analysis. IEEE Trans. Automatic Control 28, 823-832.
• 15. Hazlerigg, A.D.G. and P.K. Sinha (1978) A non-interacting control by output feedback and dynamic compensation. IEEE Trans. Automatic Control 23, 76-79.
• 16. Howze, J.W. (1973) Necessary and sufficient conditions for decoupling Rusing output feedback. IEEE Trans. Automatic Control 18, 44-46.
• 17. Howze, J.W. and J.B. Pearson (1970) Decoupling and arbitrary pole placement in linear systems using output feedback. IEEE Trans. Automatic Control 15, 660-663.
• 18. Kavanagh, R.J. (1957) Noninteracting controls in linear multivariable systems. AIEE Trans. Applications and Industry 76, 95-100.
• 19. Koussiouris, T.G. (1979) A frequency domain approach to the block decoupling problem. Int. J. Control 29, 991-1010.
• 20. Kučera, V. (1975) Stability of discrete linear feedback systems. In: Preprints 6th IFAC Congress 1. IFAC, paper 44.1.
• 21. Kučera, V. (1979) Discrete Linear Control: The Polynomial Equation Approach. Wiley, Chichester.
• 22. Kučera, V. (1983) Block decoupling by dynamic compensation with internal properness and stability. Probl. Control Info. Theory 12, 379-389.
• 23. Kučera, V. (2011) Decoupling optimal controllers. In: Proc. 18th International Conference on Process Control, Štrbské Pleso, Slovakia. Slovak University of Technology, Bratislava, 400-407.
• 24. Kučera, V. (2012) Optimal and suboptimal decoupling controllers. In: Proc. 5th IEEE Internat. Symp. Communications, Control and Signal Processing, Roma. IEEE, New York, paper 002, 1-4.
• 25. Lee, H.P. and J.J. Bongiorno (1993) Wiener-Hopf design of optimal decoupling controllers for plants with non-square transfer matrices. Int. J. Control 58, 1227-1246.
• 26. Lin, C.A. (1997) Necessary and sufficient conditions for existence of decoupling controllers. IEEE Trans. Automatic Control 42, 1157-1161.
• 27. Mejerov, M.V. (1965) Multivariable Control Systems (in Russian). Nauka. Moscow.
• 28. Morgan, B.S. (1964) The synthesis of linear multivariable systems by state feedback. In: Proc. Joint Automatic Control Conference. ASME, New York, 468-472.
• 29. Morse, A.S. and W.M. Wonham (1970) Decoupling and pole placement by dynamic compensation. SIAM J. Control 8, 317-337.
• 30. Morse, A.S. and W.M. Wonham (1971) Status of noninteracting control. IEEE Trans. Automatic Control 16, 568-581.
• 31. Park, K.H. (2008a) H2 design of one-degree-of-freedom decoupling controllers for square plants. Int. J. Control 81, 1343-1351.
• 32. Park, K.H. (2008b) Existence conditions of decoupling controllers in the generalized plant model. In: Proc. 47th IEEE Conf. Decision and Control. IEEE, New York, 5158-5163.
• 33. Silverman, L.M. and H.J. Payne (1971) Input-output structure of linear systems with application to the decoupling problem. SIAM J. Control 9, 199-233.
• 34. Strejc, V. (1960) The general theory of autonomity and invariance of linear systems of control. Acta Technica 5, 235-258.
• 35. Voznesenskij, I.N. (1936) A control system with many outputs (in Russian). Avtomat. i Telemekh. 4, 7-38.
• 36. Vidyasagar, M. (1985) Control System Synthesis: A Factorization Approach. MIT Press, Boston.
• 37. Wolovich, W.A. (1974) Linear Multivariable Systems. Springer, New York.
• 38. Wonham, W.M. (1974) Linear Multivariable Control. Springer, New York.
• 39. Wonham, W.M. and A.S. Morse (1970) Decoupling and pole assignment in linear multivariable systems: A geometric approach. SIAM J. Control 8, 1-18.
• 40. Youla, D.C. and J.J. Bongiorno (2000) Wiener-Hopf design of optima decoupling one-degree-of-freedom controllers. Int. J. Control 73, 1657-1670.
• 41. Youla, D.C., H. Jabr, and J.J. Bongiorno (1976) Modern Wiener-Hopf design of optimal controllers – Part II: The multivariable case. IEEE Trans. Automatic Control 21, 319-338.