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Nonlinear Control Systems Design by Transformation Method
Аннотация
The analytical approaches to design of nonlinear control systems by the transformation of the nonlinear plant equations into quasilinear forms or into Jordan controlled form are considered. Shortly definitions of these forms and the mathematical expressions necessary for design of the control systems by these methods are submitted. These approaches can be applied if the plant’s nonlinearities are differentiable, the plant is controllable and the additional conditions are satisfied. Procedure of a control system design, i.e. definition of the equations of the control device, in both cases is completely analytical. Desirable quality of transients is provided with that, that corresponding values are given to roots of the characteristic equations of some matrixes by calculation of the nonlinear control. The proposed methods provide asymptotical stability of the equilibrium in a bounded domain of the state space or its global stability and also desirable performance of transients. Performance of the nonlinear plants equations in the quasilinear form has no any complexities, if the mentioned above conditions are satisfied. The transformation of these equations to the Jordan controlled form very much often is reduced to change of the state variables designations of the plants. The suggested methods can be applied to design of control systems by various nonlinear technical plants ship-building, machine-building, aviation, agricultural and many other manufactures. Examples of the control systems design by the proposed analytical methods are given.
Ключевые слова
nonlinear plant,
transformation,
quasilinear form,
Jordan controlled form,
controllability,
design,
control system
Об авторе
A. R. Gaiduk
Southern Federal University
Россия
Россия
Gaiduk Anatoly R., D. Sc., Professor
Department of Control Systems
Taganrog
Список литературы
1. Isidori A. Nonlinear control systems (2nd edition), New York, Springer-Verlag, 1989.
2. Nikiforov V. O. Nelineynye sistemy upravleniya c rezhektsiey vneshnikh determinirovannykh vozmuscheniy (Nonlinear control system with rejection of the external determined disturbances), Izvestiya RAN. The theory and control systems, 1997, no. 4, pp. 69—73 (in Russian).
3. Lukyanov A. G., Utkin V. I. Methods of transform of dynamic systems equations to regular form, Automation and Remote Control, 1981, no. 4, pp. 5—13.
4. Egorov I. G. K ustoychivosti v tselom nulevogo resheniya sistemy dvukh differentsial’nykh uravneniy (To stability at whole of the zero solution of two differential equations system), Differential equations, 1991, vol. 27, no. 9, pp. 1554—1549 (in Russian).
5. Savić S., Raković M., Penčić M., Borovac B. Nonlinear motion of humanoid robot upper-body for manipulation task, Facta Universitatis. Series: Automatic Control and Robotics, 2014, vol. 13, no. 1, pp. 1—14.
6. Kim D. P. Teoriya avtomaticheskogo upravleniya. Tom 2. Mnogomernye, nelineynye, optimal’nye i adaptivnye sistemy (Theory of automatic control. Vol. 2. Multivariable, nonlinear, optimal and adaptive systems), Moscow, Phizmatlit, 2004 (in Russian).
7. Åström K. J., Wittenmark B. Adaptive control, New York, Addison-Wesley Publishing Company, 1995.
8. Krstić M., Kanellakopoulos I., Kokotović P. V. Nonlinear and adaptive control design, New York, John Willey and Sons, 1995.
9. Gaiduk A. R. Teoriya i metody analiticheskogo sinteza sistem avtomaticheskogo upravleniya (Theory and methods of automatic control systems analytical design), Moscow, Phizmatlit, 2012 (in Russian).
10. Podchukaev V. A. Analiticheskie metody teorii avtomaticheskogo upravleniya (Analytical methods of the automatic control theory), Moscow, Phizmatlit, 2002 (in Russian).
11. Gaiduk A. R., Plaksienko E. A., Shapovalov I. O. Optimal control based on Jordan controlled form, Proceedings of the 14th International Conference on Circuits, Systems, Electronics, Control & Signal Processing (CSECS ‘15), Seljuk University, Konya, Turkey. May 20—22, 2015, pp. 13—18 (CSEСS-01).
12. Gaiduk A. R. Control systems design with disturbance rejection based on JCF of the nonlinear plant equations, Facta Universitatis. Series: Automatic Control and Robotics, 2012, vol. 11, no. 2, pp. 81—90. Available at: facta.junis.ni.ac.rs/acar/acar201202/acar20120201.pdf
13. Gaiduk A. R., Plaksienko E. A., Kolokolova К. В. Sintez algoritmov upravleniya nelineynymi mnogomernymi ob’’ektami na osnove UFZH (Design of control algorithms by nonlinear multivariate objects on basis JCF), Nauchnyi vestnik NGTU, 2015, no. 2 (59), pp. 59—72. DOI: 10.17212/1814-1196-2015-2-59-72 (in Russian).
14. Fikhtengolts M. Differentsial’noe i integral’noe ischislenie (Differential and integral calculus). Vol. 3, Moscow, Nauka, 1969 (in Russian).
15. Lankaster P. Theory of matrices, New York, Academic Press, 1969.
Для цитирования:
Gaiduk A.R. Nonlinear Control Systems Design by Transformation Method. Мехатроника, автоматизация, управление. 2018;19(12):755-761. https://doi.org/10.17587/mau.19.755-761
For citation:
Gaiduk A.R. Nonlinear Control Systems Design by Transformation Method. Mekhatronika, Avtomatizatsiya, Upravlenie. 2018;19(12):755-761. https://doi.org/10.17587/mau.19.755-761
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