ANALYTICAL DESIGN OF NONLINEAR CONTROL SYSTEMS

Anatoly Gaiduk, Nadežda Stojković, Elena Plaksienko

DOI Number
10.22190/FUACR1603147G
First page
147
Last page
157

Abstract

This paper presents two approaches to analytical design of nonlinear control systems using transformation of plant equations into quasilinear forms or into Jordan controlled form. Settlement expressions of corresponding analytical methods of control systems design are obtained as results. These methods can be applied if the plant’s nonlinear functions are differentiable, the plant is controllable and the additional conditions are satisfied. The suggested methods provide asymptotical stability of the equilibrium in a bounded domain of the state space or global stability and also desirable performance of transients. Examples of control systems design by the suggested analytical methods are given.

Keywords

plant, nonlinearity, nonlinear transformation, quasilinear form, Jordan controlled form, controllability, control, design, system

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References

A. Isidori, Nonlinear control systems (2nd edition). New York, Springer-Verlag, 1989.

V.O. Nikiforov, "Nonlinear control system with rejection of the external determined disturbances," Izvestiya RAN. The theory and control systems, 4, 69–73, 1997.

S. Savić, M. Raković, M. Penčić & B. Borovac, "Nonlinear motion of humanoid robot upper-body for manipulation task," FACTA UNIVERSITATIS. Series: Automatic Control and Robotics, vol. 13, 1, 1-14, 2014.

D.P. Kim, Theory of automatic control. Multivariable, nonlinear, optimal and adaptive systems. Vol. 2. Moscow, Phizmatlit, 2004.

K.J. Åström & B. Wittenmark, Adaptive control. New York, Addison-Wesley Publishing Company, 1995.

M. Krstić, I. Kanellakopoulos & P.V. Kokotović, Nonlinear and adaptive control design. New York, John Willey and Sons, 1995.

A.G. Lukyanov & V.I. Utkin, "Methods of transform of dynamic systems equations to regular form," Automation and Remote Control, 4, 5–13, 1981.

I.G. Egorov. "To stability at whole of the zero solution of two differential equations system," Differential equations, vol. 27, no. 9, pp. 1554–1549, 1991.

A A.R. Gaiduk, Theory and methods of automatic control systems analytical design, Moscow, Phizmatlit, 2012.

V.A. Podchukaev, Analytical methods of the automatic control theory, Moscow, Phizmatlit, 2002.

A.R. Gaiduk, "Design of nonlinear systems based on the Jordan controlled form, " Automation and Remote Control, 67(7), 1017–1027, 2006.

Gaiduk, A.R. "Control systems design with disturbance rejection based on JCF of the nonlinear plant equations," Facta Universitatis, Series: Automatic Control and Robotics. vol. 11, no. 2, pp. 81-90, 2012. [Online]. Available: facta.junis.ni.ac.rs/acar/acar201202/acar20120201.pdf

A.R. Gaiduk, "Astatic control design for nonlinear plants on base of JCF," Transaction on Electrical and Electronic Circuits and Systems. vol 3, Nо. 2, рр. 80-84, 2013.

G.M. Fikhtengolts, Differential and integral calculus. Vol. 3, Moscow, Nauka, 1969.

A.R. Gaiduk, N.M. Stojkovic, "Analytical design of quasilinear control systems," FACTA UNIVERSITATIS. Series: Automatic Control and Robotics, vol. 13, no 2, pp. 73-84, 2014.

P. Lankaster, Theory of matrices. New York, Academic Press, 1969.

A.R. Gaiduk, E.A. Plaksienko, I.O. Shapovalov, "Optimal control based on Jordan controlled form," in Proceedings book of 14th International Conference on Circuits, Systems, Electronics, Control & Signal, (CSECS '15) (Selcuk University, Konya, Turkey), pp. 13-18, May 2015.




DOI: http://dx.doi.org/10.22190/FUACR1603147G

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