The Speed-Gradient Algorithm in the Inverse Stoker Problem for a Synchronous Electric Machine
The problem of control of the number of cycle slippings of an electric machine rotor by means of an external moment is considered by the example of a simple mathematical model. The speed-gradient method with the objective function determined by the oscillation energy function is applied to solve this problem. The use of quite a small control is a feature of this approach, which helps to save energy. We have developed an algorithm to control oscillations of an electric machine rotor, so that the rotor performs a predetermined number of cycle slippings. The simulation results illustrate the efficiency of the suggested algorithm.
KeywordsStoker problem speed-gradient algorithm energy control electric machines
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- 3.S. Ali-Habib, A. V. Morozov, and A. I. Shepeljavyi, “Estimates of cycle slippings for synchronization systems,” in Proc. Int. Conf. and Chebyshev Readings Dedicated to 175 Years since P. L. Chebyshev’s Birthday, Moscow, May 14–19, 1996 (Mosk. Gos. Univ., Moscow, 1996), Vol. 1, pp. 16–19.Google Scholar
- 6.V. Smirnova, A. Shepeljavyi, A. Proskurnikov, and A. Perkin, “Sharpened estimates for the number of slipped cycles in control systems with periodic differentiable nonlinearities,” Cybernet. Phys. 2, 222–231 (2013).Google Scholar
- 7.V. B. Smirnova, A. A. Perkin, A. V. Proskurnikov, and A. I. Shepeljavyi, “Estimation of cycle-slipping for phase synchronization systems,” in Proc. 21st Int. Symp. on Mathematical Theory of Networks and Systems (MTNS 2014), Groningen, Netherlands, July 7–11, 2014 (Univ. of Groningen, Groningen 2014), pp. 1244–1249.Google Scholar
- 10.F. F. Rodyukov, Mathematical Model of a Large-Scale Electric Power System (St. Peterb. Gos. Univ., St. Petersburg, 2006) [in Russian].Google Scholar
- 11.N. V. Kondrat’eva, G. A. Leonov, F. F. Rodyukov, and A. I. Shepeljavyi, “Nonlocal analysis of differential equations of induction motors,” Tech. Mech. 21, 75–86 (2001).Google Scholar
- 12.G. A. Leonov, N. V. Kondrat’eva, F. F. Rodyukov, and A. I. Shepeljavyi, “Nonlocal analysis of differential equations of asynchronous machine,” in Nonlinear Mechanics, Ed. by V. M. Matrosov, V. V. Rumyantsev, and A. V. Karapetyan (Fizmatlit, Moscow, 2001), pp. 257–280 [in Russian].Google Scholar
- 13.G. A. Leonov and N. V. Kondrat’eva, Stability Analysis of Electric machines of Alternating Current (St. Peterb. Gos. Univ., St. Petersburg, 2008) [in Russian].Google Scholar
- 16.B. R. Andrievsky, “Computation of the excitability index for linear oscillators,” in Proc. 44th IEEE Conf. on Decision and Control and European Control Conf., Seville, Dec. 15, 2005 (IEEE, 2005), pp. 3537–3540.Google Scholar
- 19.A. L. Fradkov and B. R. Andrievsky, “Control of wave motion in the chain of pendulums,” in Proc. 17th IFAC World Congr., Seoul, July 6–11, 2008; IFAC Proc. Vol. 41, 3136–3141.Google Scholar
- 20.P. Y. Guzenko, J. Lehnert, and E. Schöll, “Application of adaptive methods to chaos control of networks of Rössler systems,” Cybernet. Phys. 2, 15–24 (2013).Google Scholar