LINEARIZATION OF OBJECT MODEL WITH VECTOR CONTROL
Keywords:model, linearity, control, observer, robustness.
AbstractContext. A sufficient number of ways to implement vector control algorithms are very complex and in most cases tend to mismatch the vector of the resulting parameters of the control object. Therefore, there is a need to simplify complex non-linear vector control systems and apply linear dynamic models of a non-linear object with vector control for them. Currently, for a complex vector control system, there are no sufficiently accurate equivalent simple models. Development of reliable simple dynamic models will allow to design a vector control system with maximum use of linear methods of synthesis and analysis.
Objective. The goal of the paper is development of linear dynamic model of a non-linear object with vector control, which
reproduces its dynamics accurately enough for practice.
Method. The following methods were used to solve the problems posed: the state space method for describing the operation of
control systems; filtering theory, in particular, observers for estimation state vectors, uncertainties, and parameter identification;
modal control methods for the synthesis of observers and regulators; numerical simulation method to illustrate the performance of
synthesized control systems; vector control of a nonlinear object.
Results. For the investigated robust vector control system of the object with a substantial non-linearity of properties and
characteristics, simple linear equivalent mathematical models were compiled, rather accurately reproducing the operation of the
original system in all modes of operation. Simplification of mathematical models is achieved by considering the dynamics of the
entire system in a synchronous basis, robust methods for controlling parameters, and by neglecting really small errors in the work of regulators and observers. The synthesized models, as well as the original nonlinear system, have the property of robustness due to the use of combined control.
Conclusions. The simplicity and linearity of the equivalent system allows us to synthesize the control laws of the original
nonlinear system by well-developed linear methods with significantly less time spent on modeling. Numerical simulation of the
dynamics of the original nonlinear and equivalent linear systems showed a good agreement between transient and stationary
Khalil H.J. Nonlinear systems. N.-J. Prentice Hall, 1996, 750 p.
Isidori A. Nonlinear control systems. N.-Y. Springer, 1995, 657 p.
Yarymbash D. S., Yarymbash S. T., Kotsur M. I., Litvinov D. O. Computer simulation of electromagnetic field with application the
frequency adaptation method, Radio Electronics, Computer Science, Control, 2018, No. 1, pp. 65–74. DOI:https://doi.org/10.15588/1607-3274-2018-1-8.
Yelkin V.I. О redukcii nelineunyh upravljaemyh system k lineynym, Avtomatika i telemehanika, 2000, No. 2, pp. 45– 55.
Nikiforov V.О. Adaptivnoe i robastnoe upravlenie s kompencaciey vozmusheniy. SPb.,Nauka, 2003, 282 p.
Salleh Z., Sulaiman M., Omar R. Optimization of Fuzzy Logic Based for Vector Control Induction Motor Drives, IEEE 8th
Computer Science and Electronic Engineering (CEEC), UK, 28–30 September 2016: proceedings, Colchester, IEEE, 2016, pp. 83–86.
Patakor F. A., Salleh Z., Sulaiman M., Jantan N. Auto-tuning Sliding Mode Control for Induction Motor Drives, IEEE 8th
Computer Science and Electronic Engineering (CEEC), UK, 28–30 September 2016: proceedings. Colchester, IEEE, 2016, pp. 1–6.
Raumer T. V., Dion J. M., Dugard L. Applied nonlinear control of an induction motor using digital signal processing, IEEE Trans.
Control System Technology, 1994. Vol. 2, No. 4, pp. 327–335. DOI: https://doi.org/10.1002/acs.4480070511.
Kuroe Y., Yoneda Y. Design of a new controller for induction motors based on exact linearization, Industrial Electronics, Control
and Instrumentation, Japan, 28 October-1 November 1991: proceedings. Kobe, IECON, 1991, Vol. 1, pp. 621–626.
Blaschke F. Das Prinzip der Feldorientiening die Grundlage fur die Transvector – Regelung von Asynchronmaschienen. Siemens-Zeitschrift, 1971, 757 p.
Potapenko Y. М., Potapenko Y. Y. Robastnye algoritmy vectornogo upravlenija asinhronnym privodom. Zaporizhzhya, ZNTU, 2009, 352 p.
Karnauhov N. F. Electromehanicheskie i mehatronnye sistemy. Rostov-na-Donu, Feniks, 2006, 320 p.
Karnauhov N. F. Impulsnye preobrazovayeli ispolnitelnyh ustroystv electromehatronnyh sistem, Uchebnoe posobie. Rostovna-
Donu, DGTU, 1994, 71 p.
Peresada S., Tilli A., Tonielli A. New passivity based speedfluxtracking controllers for induction motor, Annual Conference of
the IEEE Industrial Electronics Society, Japan, 22–28 October 2000: proceedings. Nagoya, IECON, 2000, Vol. 2, pp. 1099–1104.
Peresada S., Tilli A., Tonielli A. Theoretical and Experimental Comparison of indirect field-oriented Controllers for Induction
Motors, IEEE Transactions On Power Electronics, 2003, Vol. 18, No. 1, pp. 151–163. DOI: 10.1109/TPEL.2002.807123.
Peresada S., Kovbasa S., Dymko S. Indirect Field-Oriented Torque Control of Induction Motors with Maximum Torque per Ampere Ratio, Transactions of Kremenchuk State University, 2010, Vol. 2, No. 3, pp. 33 – 36.
Wasynchuk O., Sudhoff S. D., Corsine K. A., Tichenor J. et al. A Maximum Torque per Ampere Control Strategy for Induction Motor Drives, IEEE Transactions on Energy Conversion, 1998, Vol. 13, No. 2, pp. 163–169. DOI 10.1109/60.678980.
Grcar B., Cafuta P., Stumberger G. et al. Non-Holonomy in Induction Machine Torque Control, IEEE Transactions on Control
Systems Technology, 2011, Vol. 19, No. 2, pp. 367–375. DOI: 10.1109/TCST.2010.2042718.
Famouri P., Cathey J. J. Loss Minimization Control of an Induction Motor Drive, IEEE Transactions Industrial Applicaions, 1991,
Vol. 27, pp. 32–37. DOI: 10.1109/28.67529
Dymko S., Peresada S., Leidhold R. Torque Control of Saturated Induction Motor with Torque per Ampere Ratio Maximization,
IEEE International Conference on Intelligent Energy and Power Systems, Ukraine, 2–6 June 2014: proceedings. Kiev, IEPS, 2014,
pp. 251–256. DOI: 10.1109/IEPS.2014.6874189.
Kwon C., Sudhoff S. D. An Improved Maximum Torque per amp Control Strategy for Induction Machine Drives, IEEE Applied
Power Electronics Conference and Exposition, USA, 6–10 March 2005, proceedings. Austin, APEC, 2005, Vol. 2, pp. 740–745. DOI:10.1109/APEC.2005.1453052.
Marino R., Peresada S., Valigi P. Adaptive input-output linearizing control of induction motors, IEEE Transactions on Automatic
Control, 1993, Vol. 38, № 2, pp. 208–221. DOI:10.1109/9.250510.
Peresada S., Kovbasa S., Korol S., Zhelinskyi N. Feedback linearizing field-oriented control of induction generator: Theory and
experiments, Tekhnichna Elektrodynamika, 2017, No. 2017, Issue 2, pp. 48–56.
Ambrish D., Madhusudan S., Narendra K. DSP based feedback linearization control of vector controlled induction motor drive,
IEEE International Conferenceon Power Electronics, Intelligent Controland Energy Systems, India 4–6 July 2016, proceedings.
Delhi, ICPEICES, 2016, pp. 36–42. DOI:10.1109/ICPEICES.2016.7853631.
Sobczuk D. L. Feedback Linearization Control of Inverter Fed
Induction Motor-DSP Implementation, IEEE International Symposium on Industrial Electronics, Italy, 8–11 July 2002:
proceedings. L’Aquila, IEEE, 2002, pp. 678–682. DOI: 10.1109/ISIE.2002.1026373.
Sobczuk D., Malinowski M. Feedback linearization control of inverter fed induction motor with sliding mode speed and flux
observers, Annual Conference on IEEE Industrial Electronics, France, 6–10 November 2006: proceedings. Paris, IEEE, 2006, Vol.
, No. 5, pp. 1299–1304. DOI: 10.1109/IECON.2006.348089.
Marquez H. J. Nonlinear control systems. New Jersey, John Wiley & Sons, 2003, 376 p.
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