Geri Adımlama Tekni˘gi ile Bir DC Motorun Konum ve Hız Kontrolü

Bu çalışmada Lyapunov’un ikinci kararlılık yönteminin bir özyinelemeli bir uyarlaması olan geri adımlama yöntemi fırçalı bir doğru akım motorunun denetimine uygulanmaktadır. Bozucu etkilerden bağımsız bir ortamda hem hız, hem de konum denetiminde başarı ile uygulanabildiği görülen yöntemin bozucu etkiler altındaki performasını inceleyebilmek için hem teorik hem de benzetim tabanlı analizler yapılmıştır. Teorik incelemede girdiden-duruma kararlılık kuramından yararlanılmıştır. Bu noktada girdi bozucu etkileri (bozucu torklar) temsil etmektedir. Yöntem uygulandığında, denetim kazançlarının seçiminde bir alt sınırın var olduğu ve bozucu etkilerden bağışık ortamda olduğu gibi serbest seçilmesinin uygun olmayabileceği anlaşılmaktadır. Benzetimlerde ise bozucu etkiler rastgele sinyaller olarak modellenmiş olup, denetim kazançları yükseltildiğinde bozucu etkilerin baskılanabildiği gözlemlenmektedir. Geri adımlama tekniğinin bozucu etkiler altında kararlılık analizi ile birlikte doğru akım motorunun denetimine uygulanması literatüre önemli bir katkı sunmaktadır.

Speed and position control of a DC motor based on back-stepping technique

In this study, the backstepping method which is a recursive adaptation of the Lyapunov’s second method is applied to the control of a brushed direct current motor. In a disturbance free environment, it is noted that the method works quite satisfactorily in both speed and position controls. In order to monitor its performance under the existence of disturbance torques theoretical and simulation based analyses are performed. Theoretical analysis is based on the input-to-state stability theorem where the input here refers to the external disturbance torques. When the approach is utilized, we found a lower bound and the selection of the control gains are restricted to relatively larger values. In the simulations, the disturbance torques are modeled as random signals and it is noted that the attenuation of the disturbances are improved with larger control gains. The application of backstepping control technique with a disturbance-to-state stability approach to control of direct current motors brings a novel contribution to the related literature.

PDF

___

[1] Khalil, H. K., Grizzle, J., 1996. Nonlinear systems, volume 3, Prentice hall New Jersey.

[2] Krstic, M., Kokotovic, P. V., Kanellakopoulos, I., 1995. Nonlinear and adaptive control design, John Wiley & Sons, Inc.

[3] Isidori, A., 2013. Nonlinear Control Systems: An Introduction, Springer Science & Business Media.

[4] Ali, I., Radice, G., Kim, J., 2010. Backstepping control design with actuator torque bound for spacecraft attitude maneuver, Journal of guidance, control, and dynamics, 33(1), 254–259.

[5] Karimi, A., Feliachi, A., 2008. Decentralized adaptive backstepping control of electric power systems, Electric Power Systems Research, 78(3), 484–493.

[6] Li, Y., Qiang, S., Zhuang, X., Kaynak, O., 2004. Robust and adaptive backstepping control for nonlinear systems using rbf neural networks, Neural Networks, IEEE Transactions on, 15(3), 693–701.

[7] Madani, T., Benallegue, A., 2006. Backstepping control for a quadrotor helicopter, in Intelligent Robots and Systems, 2006 IEEE/RSJ International Conference on, 3255–3260, IEEE.

[8] Yagiz, N., Hacioglu, Y., 2008. Backstepping control of a vehicle with active suspensions, Control Engineering Practice, 16(12), 1457–1467.

[9] Park, J. H., 2006. Synchronization of genesio chaotic system via backstepping approach, Chaos, Solitons & Fractals, 27(5), 1369–1375.

[10] Ling, Y., Tao, G., 1997. Adaptive backstepping control design for linear multivariable plants, International Journal of Control, 68(6), 1289–1304.

[11] Skjetne, R., Fossen, T. I., 2004. On integral control in backstepping: Analysis of different techniques, in American Control Conference, 2004. Proceedings of the 2004, volume 2, 1899–1904, IEEE.

[12] Bouabdallah, S., Siegwart, R., 2005. Backstepping and sliding-mode techniques applied to an indoor micro quadrotor, in Robotics and Automation, 2005.ICRA 2005. Proceedings of the 2005 IEEE International Conference on, 2247–2252, IEEE.

[13] Lu, J., Wei, R., Wang, X., Wang, Z., 2001. Backstepping control of discrete-time chaotic systems with application to the henon system, Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on, 48(11), 1359–1363.

[14] Nise, N. S., 2007. Control Systems Engineering, (With CD), John Wiley & Sons.

[15] Krishnan, R., 2001. Electric motor drives: modeling, analysis, and control, Prentice Hall.

[16] Sharaf, A., Alta¸s, ˙I., Özkop, E., 2007. Elektrikli araçlar için çift çevrim destekli da motor kontrol uygulaması, XII. EEBB Mühendisli˘gi Ulusal Kongresi ve Fuarı, Eski¸sehir Osmangazi Üniversitesi.

[17] Zuglem, I., Doruk, R. O., 2016. Projective dc motor control under disturbance torques, arXiv preprint arXiv:1605.08284, Gazi Üniversitesi, Mühendislik ve Mimarlık Fakülteleri Dergisinde yayına kabul edilmi¸stir.

[18] Bodson, M., Chiasson, J., Novotnak, R., 1994. Highperformance induction motor control via input-output linearization, Control Systems, IEEE, 14(4), 25–33.

[19] Mehta, S., Chiasson, J., 1998. Nonlinear control of a series dc motor: theory and experiment, Industrial Electronics, IEEE Transactions on, 45(1), 134–141.

[20] Farahani, M., Zare Bidaki, A. R., Enshaeieh, M., 2014. Intelligent control of a dc motor using a self-constructing wavelet neural network, Systems Science & Control Engineering: An Open Access Journal, 2(1), 261–267.

[21] Otkun, Ö., Do˘gan, R. Ö., Akpınar, A. S., 2015. Do˘grusal hareketli sürekli miknatisli senkron motorun yapay sinir a˘g tabanli skaler hiz denetimi, Gazi Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 30(3).

[22] Karabacak, M., Eskikurt, H. I., 2011. Speed and current regulation of a permanent magnet synchronous motor via nonlinear and adaptive backstepping control, Mathematical and Computer Modelling, 53(9), 2015–2030.

[23] Ouassaid, M., Cherkaoui, M., Zidani, Y., 2004. A nonlinear speed control for a pm synchronous motor using an adaptive backstepping control approach, in Industrial Technology, 2004. IEEE ICIT’04. 2004 IEEE International Conference on, volume 3, 1287– 1292, IEEE.

[24] Geiger, D. F., 1981. Phaselock Loops for DC Motor Speed Control, John Wiley & Sons.

[25] Yao, J., Jiao, Z., Ma, D., 2014. Adaptive robust control of dc motors with extended state observer, IEEE Transactions on Industrial Electronics, 61(7), 3630–3637.

[26] Dawson, D., Carroll, J., Schneider, M., 1994. Integrator backstepping control of a brush dc motor turning a robotic load, Control Systems Technology, IEEE Transactions on, 2(3), 233–244.

[27] Wang, J.-j., Zhao, G.-z., Qi, D.-l., 2004. Speed tracking control of permanent magnet synchronous motor with backstepping, Proceedings-Chinese Society of Electrical Engineering, 24(8), 95–98.

[28] Zhou, J., Wang, Y., 2002. Adaptive backstepping speed controller design for a permanent magnet synchronous motor, in Electric Power Applications, IEE Proceedings-, volume 149, 165–172, IET.

[29] Sontag, E. D., 1995. On the input-to-state stability property, European Journal of Control, 1(1), 24–36.

[30] Mohammadbagheri, A., Zaeri, N., Yaghoobi, M., 2011. Comparison performance between pid and lqr controllers for 4-leg voltage-source inverters, in International Conference Circuit, System and Simulation.

[31] Chowdhury, A., Debnath, D., 2013. Performance comparison between pid controller and statefeedback controller with integral action in position control of dc motor, in Mechanics, Simulation and Control III, volume 367 of Applied Mechanics and Materials, 188–193, Trans Tech Publications, .

[32] Haron, H. S., 2013. Linear quadratic regulator (LQR) controller design for DC servo motor, Ph.D. thesis, Universiti Tun Hussein Onn Malaysia.

[33] Isidori, A., Astolfi, A., 1992. Disturbance attenuation and h¥ control via measurement feedback in nonlinear systems, Automatic Control, IEEE Transactions on, 37(9), 1283–1293.

[34] Willems, J. C., Commault, C., 1981. Disturbance decoupling by measurement feedback with stability or pole placement, SIAM Journal on Control and Optimization, 19(4), 490–504.