Abstract
The problem is considered for control of an electromagnetic moment of the induction motor with a squirrel-cage rotor without the measurement of its rotational speed. By means of the principle of vector control, this problem reduces to developing an adaptive observer of values of the vector of the rotor magnetic-flux linkage. The method of recurrent objective inequalities (ROIs) is used, which enables one to reduce adaptation problems to counting systems of inequalities relative to the vector of the parameters estimated. For the control problem under consideration, these inequalities prove to be nonconvex, which makes it impossible to use directly the projection algorithms developed in the framework of the method of ROIs. In this connection, the common method for the stepwise reduction of the dimension of the nonlinear portion of inequalities is suggested in this work. On condition that the processes of a closed system display a certain natural property of nondegeneracy, this method permits reducing nonconvex inequalities to convex ones and ensures the achievement of the control aim on completion of the transient processes.
Similar content being viewed by others
References
Blaschke, F., Method for Controlling Asynchronous Machines, US Patent 3 824 437, July 16, 1974.
Pivnyak, G.G. and Volkov, A.V., Sovremennye chastotno-reguliruemye asinchronnye elektroprivody s shirotno-impul’snoi modulyatsiei (Modern Frequency-Controllable Asynchronous Electric Drives with Pulse-Duration Modulation), Dnepropetrovsk: Natl. Mining Univ., 2006.
Vinogradov, A., Sibirtsev, A., and Kolodin, I., Adaptive-Vector Control System of the Sensor-Free Asynchronous Electric Drive of Series ED, Silovaya Elektron., 2006, no. 3, pp. 50–55.
Yakubovich, V.A., Recurrent Finite-Convergent Algorithms for Solving the Systems of Inequalities, Dokl. Akad. Nauk SSSR, 1966, vol. 166, no. 6, pp. 1308–1311.
Yakubovich, V.A., To the Theory of Adaptive Systems, Dokl. Akad. Nauk SSSR, 1968, vol. 182, no. 3, pp. 518–521.
Yakubovich, V.A., Finite-Convergent Algorithms for Solving the Counting Systems of Inequalities and Their Application in Problems of Adaptive Systems, Dokl. Akad. Nauk SSSR, 1969, vol. 189, no. 3, pp. 495–498.
Fomin, V.N., Fradkov, A.L., and Yakubovich, V.A., Adaptivnoe upravlenie dinamicheskimi ob”ektami (Adaptive Control of Dynamic Objects), Moscow: Nauka, 1981.
Gusev, S.V. and Shishkin, S.L., Adaptive Control of Biped Robot Walking on an Inclined Plane, Proc. 5th IEEE Conf. Control Appl., Dearborn, 1996, pp. 1090–1095.
Bondarko, V.A. and Zaremba, A.T., Speed and Flux Estimation for an Induction MotorWithout Position Sensor, Proc. Am. Control Conf., San Diego, 1999, vol. 6, pp. 3890–3894.
Stuntz, R.M., Bondarko, V.A., and Zaremba, A.T., Induction Motor Control System with Speed and Flux Estimation, US Patent 6 014 006, January 11, 2000.
Kopylov, I.P., Matematicheskoe modelirovanie elektricheskikh mashin (Mathematical Modeling of Electrical Machines), Moscow: Vysshaya Shkola, 2001.
Author information
Authors and Affiliations
Additional information
Original Russian Text © V.A. Bondarko, 2010, published in Avtomatika i Telemekhanika, 2010, No. 9, pp. 120–135.
This work was supported in part by the Federal Target Program (FTP) “Personnel,” State Contract no. 02.740.11.5056.
Rights and permissions
About this article
Cite this article
Bondarko, V.A. Adaptive vector control of an induction motor on the basis of the method of recurrent objective inequalities. Autom Remote Control 71, 1849–1863 (2010). https://doi.org/10.1134/S0005117910090080
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117910090080