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[78720] Artykuł:

Input-output transformation using the feedback of nonlinear electrical circuits. Algorithms and linearization examples

(Transformacja wejścia-wyjścia za pomocą sprzężenia zwrotnego nieliniowych obwodów elektrycznych. Algorytmy i przykłady linearyzacji)
Czasopismo: Mathematical Problems in Engineering   Tom: 2018, Strony: 1-13
ISSN:  1024-123X
Opublikowano: Listopad 2018
 
  Autorzy / Redaktorzy / Twórcy
Imię i nazwisko Wydział Katedra Do oświadczenia
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kryteriów ewaluacji
Sebastian Różowicz orcid logo WEAiIKatedra Elektrotechniki Przemysłowej i Automatyki**Takzaliczony do "N"Automatyka, elektronika, elektrotechnika i technologie kosmiczne5010.00.00  
Andrzej Zawadzki orcid logo WEAiIKatedra Elektrotechniki Przemysłowej i Automatyki**Takzaliczony do "N"Automatyka, elektronika, elektrotechnika i technologie kosmiczne5010.00.00  

Grupa MNiSW:  Publikacja w czasopismach wymienionych w wykazie ministra MNiSzW (część A)
Punkty MNiSW: 20

Pełny tekstPełny tekst     DOI LogoDOI    
Słowa kluczowe:

systemy nieliniowe  zróżnicowane podejście geometryczne  transformacja przestrzeni stanów  lokalny dyfeomorfizm  linearyzacja  linearyzacja sprzężeń  Liego 

Keywords:

nonlinear systems  differential geometric approach  state space transformation  local diffeomorphism  linearization  feedback linearization  Lie algebras 


Streszczenie:

W niniejszym artykule podjęto problem nieliniowej linearyzacji wejścia-wyjścia układu elektrycznego. Przedstawiono algorytmy transformacji linearyzacji układu nieliniowego poprzez zmianę współrzędnych (lokalny dyfeomorfizm) z wykorzystaniem zamkniętej pętli sprzężenia zwrotnego wraz z warunkami niezbędnymi do linearyzacji. Omówiono etapy linearyzacji i wyniki symulacji numerycznych.



Abstract:

This paper addresses the problem of non-linear electrical circuit input-output linearization. The transformation algorithms for linearization of nonlinear system through changing coordinates (local diffeomorphism) with the use of closed feedback loop together with the conditions necessary for linearization to take place are presented. The linearization stages and the results of numerical simulations are discussed.


B   I   B   L   I   O   G   R   A   F   I   A
1. Isidori A. Nonlinear Control Systems: An Introduction. Springer, Berlin, 1989.
2. Isidori A. Nonlinear Control Systems. Springer, Berlin, 1995.
3. Nijmeijer H.
van der Schaft A. Nonlinear Dynamical Control Systems. Springer-Verlag, New York, 1990.
4. Hunt L. R.
Su R.
Meyer G. Global transformations of nonlinear systems. IEEE Trans. Automat. Contr., 1983, vol. AC-28, pp. 24–31.
5. Bourbaki N. Lie groups and Lie algebras. Springer, Berlin, 1998, Chapters 1–3, (2002) Lie groups and Lie algebras Springer, Berlin, Chapters 4–6.
6. Fujimoto K.
Sugie T. Freedom in Coordinate Transformation for Exact Linearization and Its Application to Transient Behavior Improvement. Automatica, 2001, vol. 37, pp. 137-144.
7. Guay M. Observer linearization of nonlinear systems by generalized tansformations. Asian Journal of Control, 2005, vol. 7, no. 2, pp. 187-196.
8. Jordan A.
Nowacki J.P. Global linearization of non-linear state equations. International Journal Applied Electromagnetics and Mechanics, 2004, vol. 19, pp. 637–642.
9. Bodson M.
Chiassons J. Differential-geometric methods for control of electric motors. International Journal of Circuit Theory and Applications, vol. 8, pp. 923-954, (1998).
10. Zawadzki A. Application of local coordinates rectification in linearization of selected parameters of dynamic nonlinear systems. Compel: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, 2014, Vol. 33 Issue: 5, pp.1819-1830, doi: 10.1108/COMPEL-11-2013-0358.
11. Zawadzki A.
Różowicz S. Application of input — State of the system transformation for linearization of some nonlinear generators. International Journal of Control, Automation and Systems. DOI: 10.1007/s12555-014-0026-3.
12. Zawadzki A. Comparative analysis of methods for determining the transformation linearizing the nonlinear equations of the system state. (in polish). Przegląd Elektrotechniczny, 2014, vol. 4, pp. 28-33, ISSN 0033-2097, R. 90 NR 4/2014.
13. Jakubczyk B.
Respondek W. On linearization of control systems. Bull. Acad. Polonaise, Sci., Ser., Sci., Math., 1980, vol. 28, pp. 517–522.
14. Yat-Sun P.
Wai-Yin P. Application of Elementary. Differential Geometry to Influence Analysis, International Press, 2012.
15. Celikovsky S.
Nijmeijer H. Equivalence of nonlinear systems to triangular form: the singular case. Syst. Control Lett., 1996, vol. 27, pp. 135–144.
16. Krener A.J. Approximate linearization by state feedback and coordinate change. Systems & Control Letters, 1984, vol 5(3), pp. 181-185.
17. De Luca A. Decoupling and feedback linearization of robots with mixed rigid/elastic joints. Int. J. Robust Nonlinear Control, 1998, vol. 8, pp. 965-977.
18. Isidori A.
Krener A.
Gori A. J.
Monaco S. Nonlinear decoupling via feedback: A differential geometric approach. IEEE Trans. Automat. Contr., 1981, vol. AC-26, pp. 331–345.
19. Tall I.A.
Respondek W. Feedback Linearizable Strict Feedforward Systems. Proceedings of the 47th IEEE Conference on Decision and Control, 2008, Canc´un, Mexico, pp. 2499-2504.
20. Boukas T.K.
Habetler T.G. High-Performance Induction Motor Speed Control Using Exact Feedback Linearization with State and State Derivative Feedback. IEEE Transactions on Power Electronics, 2004, vol. 19, n. 4, pp. 1022-1028.
21. Fangt B.
Kelka A.G. Exact Linearization of Nonlinear Systems by Time Scale. IEEE Transformation Proceedings of the American Control Conference, 2003, Denver, Colorado, pp. 3555-3560.
22. Liu K.P.
You W.
Li Y.C. Combining a feedback linearization approach with input shaping for flexible manipulator control. International Conference on Machine Learning and Cybernetics 1, 2003, pp. 561–565.
23. Wang D.
Vidyasagar M. Control of a class of manipulators with the last link flexible – Part I: Feedback linearization. ASME Journal of Dynamic Systems, Measurement, and Control, 1991, 113 (4) 655–661.
24. Deutscher J.
Schmid C. A state space embedding approach to approximate feedback linearization of single input nonlinear control systems. International Journal of Circuit Theory and Applications, 2006, vol. 16, pp. 421–440.
25. Devanathan R. Linearization Condition through State Feedback. IEEE Transactions on Automatic Control, 2001, vol. 46, n. 8, pp. 1257-1260.
26. Zawadzki A.
Różowicz S. Application of input-state of the system transformation for linearization of selected electrical circuits, Journal of Electrical Engineering, 2016, vol. 67, no. 3, 199–205, ISSN 1335-3632, DOI: 10.1515/jee-2016-0028.
27. Bonnard B. Quadratic control systems. Math. Control Signals Systems, 1991, vol. 4, pp. 139–1606.
28. Celikovsky S.
Nijmeijer H. Equivalence of nonlinear systems to triangular form: The singular case. Systems Control Lett., 1996, voll. 27, pp. 135–144.
29. Jakubczyk B. Equivalence and invariants of nonlinear control systems. Nonlinear Controllability and Optimal Control, H.J. Sussmann, ed., Marcel Dekker, New York, 1990, Basel, pp. 177–218.
30. Jakubczyk B.
Respondek W. Feedback classification of analytic control systems in the plane. Analysis of Controlled Dynamical Systems. Birkhäuser Boston 1991, pp. 263-273 DOI 10.1007/978-1-4612-3214-8_23
31. Bonnard B. et al. Energy minimization of single input orbit transfer by averaging and continuation. Bulletin des Sciences Mathématiques. vol 130. Issue 8, December 2006, pp. 707-719
32. Gardner R.B. The Method of Equivalence and Its Applications, CBMS Reg. Conf. Ser. In Appl. Math, Philadelphia, 1989, 58, SIAM.
33. Gardner R.B.
Shadwick W.F.
Wilkens G.R. A geometric isomorphism with applications to closed loop controls. SIAM J. Control Optim., 1989, 27, pp. 1361–1368.
34. Gardner R.B.
Shadwick W.F. The GS algorithm for exact linearization to Brunovsk´y normal form. IEEE Trans. Automat. Control, 1992, vol. 37, pp. 224–230.
35. Gardner R.B.
Shadwick W.F.
Wilkens G.R. Feedback equivalence and symmetries of Brunovsk´y normal forms. Contemp. Math., 1989, vol. 97, pp. 115–130.
36. Kupka I. On feedback equivalence, in Differential Geometry. Global Analysis, and Topology CMS Conf. Proc. 1991, 12, AMS, Providence, RI, pp. 105–117.
37. Bonnard B. Feedback equivalence for nonlinear systems and the time optimal control problem. SIAM J. Control Optim., 1991, 29, pp. 1300–1321
38. Bonnard B. Quadratic control systems. Math. Control Signals Systems, 1991, 4, pp. 139–160
39. Jakubczyk B. Feedback invariants, critical trajectories, and Hamiltonian formalism. Nonlinear Control in the Year 2000, Vol. 1, Lecture Notes in Control and Inform. Sci. 258, Springer-Verlag, London, 2001, pp. 545–568. DOI: 10.1007/BFb0110240
40. Jakubczyk B. Critical Hamiltonians and feedback invariants. Geometry of Feedback and Optimal Control, B. Jakubczyk and W. Respondek, eds., Marcel Dekker, New York, Basel, 1998, pp. 219–256.
41. Banaszuk A.
Hauser J. Approximate feedback linearization: A homotopy operator approach. Proceedings of the American Control Conference, Baltimore, Maryland, 1994, pp. 1690-1694.
42. Guardabassi G. O.
Savaresi S. M. Approximate linearization via feedback an overview. Automatica, 2001, vol. 37, pp. 1-15.
43. GuemgharK.
Srinivasan B.
Bonvin D. Approximate input-output linearization of nonlinear systems using the observability normal form. European Conference Control, 2003.
44. Brockett R. W. Feedback invariants for nonlinear systems. Proc. 6th IFAC World Congr., Helsinki, Finland, 1978, vol. 6, pp. 1115–1120.
45. Kang W. Approximate linearization of nonlinear control systems. Systems & Control Letters, 1994, vol. 23:1, pp. 43-52.
46. Krener A. J. Approximate linearization by state feedback and coordinate change. Systems & Control Letters, 1984, vol. 5(3), pp. 181-185.
47. Kang W.
Krener A.J. Extended quadratic controller normal form and dynamic state feedback linearization of nonlinear systems. SIAM J. Control Optim., 1980, 30, pp. 1319–1337.
48. Lawrence D. A.
Rugh W. J. Input-output pseudolinearization for nonlinear systems. IEEE Trans. Autom. Contr., 1984, vol. 39:11, pp. 2207-2218.
49. Respondek W.
Tall I.A. Nonlinearizable single-input control systems do not admit stationary symmetries. Systems Control Lett., 2002, 46, pp. 1–16.
50. Amadou Tall I. Multi-Input Control Systems: Explicit Feedback Linearization. 49th IEEE Conference on Decision and Control., Hilton Atlanta Hotel, Atlanta, GA, USA, 2010.
51. State and Feedback Linearization of Single-Input Control Systems Issa Amadou Tall Southern Illinois University Carbondale, MC 4408, 1245 Lincoln Drive, Carbondale IL, 62901, USA.
52. Bump D. Lie Groups, Graduate Texts in Mathematics. Springer, New York, 2004, vol. 225.
53. Serre J. P. Complex semisimple Lie algebras. Springer-Verlag, Berlin, 2001.
54. D. Cheng, A. Isidori, W. Respondek, T. J. Tarn, Exact linearization of nonlinear systems with outputs, Mathematical Systems Theory, Volume 21, Issue 1, 1988, pp 63-83.
55. Różowicz S.
Tofil Sz. The influence of impurities on the operation of selected fuel ignition systems in combustion engines. Archives of Electrical Engineering, 2016, vol. 65(2), pp. 349-360, ISSN 2300-2506 DOI: 10.1515/aee-2016-0026.

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