ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Analytical Design of Multivariable Control Systems by Dynamical Decomposition Method

Journal of Applied Nonlinear Dynamics 3(4) (2014) 325--332 | DOI:10.5890/JAND.2014.12.004

Anatoly R. Gaiduk; Kseniya V. Besklubova; Elena A. Plaksienko

Department of Control Systems, Southern Federal University, Taganrog, 347928, Russia

Department of Mathematics and Informatics, Taganrog Management and Economy Institute, 347900, Russia

Abstract

Design of multivariable control systems for complex technical plants with several interrelated channels and controlled variables is difficult problem. Usually here it is necessary to provide either independent (autonomous, unrelated) or coherent control of output variables. This design problem can be solved by using the analytical method implying exact, dynamical decomposition of the multivariable plant to the set of an independent single input–single output channels. The dynamic decomposition method is based on decomposing property of the adjunct matrix and provides realized of control action as function of output variables, reference input and measured disturbances (control on output and inputs) of the system. The efficiency of this analytical method is shown by the numerical example of control system design for the turbojet engine of the gas-pumping station with three interrelated channels.

Acknowledgments

The work presented here is supported by the grant of RFBR No.13-08-00249.

References

1.  [1] Voznesenski, I.N. (1938), About regulation of machines with the big number of control parameters, Automatics and telemechanics, 4, 4-5. (In Russia).
2.  [2] Morgan, B.S. (1964), The synthesis of linear multivariable systems by state variable feedback, IFEE Trans. Aut. Control, 9(4), 405-411.
3.  [3] Volovich, W.A. (1974), Linear Multivariable Systems, Springer-Verlag, New York.
4.  [4] Tyan, V.K. (2008), Reduction of synthesis procedure of multivariable linear control systems to synthesis one-dimensional with typical object, Mechatronic, Automation, Control, 4, 2-7. (In Russia).
5.  [5] Wonham, W.M. (1980), Linear Multivariable Systems: A Geometric Approach, 2rd ed., Springer-Verlag, New York.
6.  [6] Chen, C.T. (1999), Linear system. Theory and Design, 3rd ed., Oxford University Press, New York.
7.  [7] Misrikhanov, M. Sh. and Ryabchenko, V.N. (2003), Design of multicoherent control for dynamic systems: Review. Vestnik IGEU, 5, 17-21. (In Russia).
8.  [8] Misrikhanov, M. Sh. (2007), Invariant Control of Multivariable Systems: The Algebraic Approach, Science, Moscow. (In Russia).
9.  [9] Gaiduk, A.R. (1980), Design of control systems on transfer function, Automatics and Telemechanics, 1, 11-16. (In Russia).
10.  [10] Gaiduk, A.R. and Plaksienko, E.A. (2008), Design of dynamic systems on desired quality performances, Mechatronic, Automation, Control, 4, 7-12. (In Russia).
11.  [11] Gaiduk, A.R. (1998), Design of control systems of multivariable plants, News of the Academy of sciences. The Theory and Control Systems, 1, 9-17. (In Russia).
12.  [12] Gaiduk, A.R., Plaksienko, E.A., and Besklubova, K.V. (2013), Multivariable Dynamic System Control Under Condition of Autonomy and Coherence, Dynamical systems. Theory, Łódź December 2-5, 2013, Poland, 195-204.
13.  [13] Ilyasov, B.G., Saitova, G.A. and Halikova E.A. (2010), Stability Analysis of a Multicoherent Control Systems for Gas Turbine Engine, Proc. 3-th multiconference , OAS CSRI : Saint Petersburg, 35-38.