DESIGN OF FRACTIONAL ORDER SLIDING MODE CONTROLLER FOR 2 DOF HELICOPTER SYSTEM

This paper presents a real time control application for a prototype helicopter system by using Sliding Mode Control strategy modified with small differential deviations. Experimental and simulation studies demonstrate the performanceof the proposed controller for a class of flight systems with unstable dynamics. It is shown that the proposed controller decreases the steady state errors of the vertical and horizontal motion of the system. Small differential deviations strengthen or weaken the effect of the differential to obtain better tracking response in case of external disturbances. Numerical and experimental results match each otherto demonstratethe tracking of desired rotor angles and suppression the disturbance effects.

2 SERBESTLİK DERECELİ HELİKOPTER SİSTEMİ İÇİN KESİR DERECELİ KAYMA KİPLİ KONTROLÖR TASARIMI

Bu çalışma, küçük diferansiyel değişimler ile modifiye edilmiş Kayma Kipli Kontrol stratejisini kullanarak, prototip helicopter sistemi için gerçek zamanlı bir kontrol uygulaması sunmaktadır. Deneysel ve benzetim çalışmaları, kararsız dinamiklere sahip bir uçuş sistemi için önerilen kontrolcünün performansını ortaya koymaktadır. Önerilen kontrolcünün, sistemin dikey ve yatay hareketinin kalıcı durum hatalarını azalttığı gösterilmiştir. Küçük diferansiyel sapmalar, harici bozucu durumunda daha iyi takip cevabı elde etmek için diferansiyelin etkisini güçlendirir veya zayıflatır. Sayısal ve deneysel sonuçlar, istenen rotor açılarının takibi ve bozucu etkilerin bastırılmasını göstermek için birbirleriyle eşleşmektedir.

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B. T. Krishna and K. V. V. S. Reddy, “Active and Passive Realization of Fractance Device of Order 1/2,” Act. Passiv. Electron. Components, pp. 1–5, 2008.

A. Rahideh and M. H. Shaheed, “Mathematical dynamic modelling of a twin-rotor multiple input- multiple output system,” Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng., vol. 221, no. 1, pp. 89–101, Feb. 2007.

“Twin Rotor MIMO System Control Experiments Manuel 33-949S.” Feedback Instruments, 2006.

J. Y. Hung, W. Gao, and J. C. Hung, “Variable structure control: a survey,” Ind. Electron. IEEE Trans., vol. 40, no. 1, pp. 2–22, 1993.

V. Utkin, “Variable structure systems with sliding modes,” IEEE Trans. Automat. Contr., vol. 22, no. 2, pp. 212–222, 1977.

A. G. Radwan, A. M. Soliman, A. S. Elwakil, and A. Sedeek, “On the stability of linear systems with fractional-order elements,” Chaos, Solitons & Fractals, vol. 40, no. 5, pp. 2317–2328, 2009.

I. Podlubny, Fractional Differential Equations. San Diego: Academic Press, 1999.

D. Matignon, “Stability properties for generalized fractional differential systems,” ESAIM Proc., vol. 5, pp. 145–158, 1998.

D. Matignon, “Stability results for fractional differential equations with applications to control processing,” Comput. Eng. Syst. Appl., pp. 963–968, 1996.

A. Oustaloup et al., “An overview of the CRONE approach in system analysis, modeling and identification, observation and control,” IFAC Proc. Vol., vol. 41, no. 2, pp. 14254–14265, 2008.

I. Petras, Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation. Springer Press, 2011.

V. I. Utkin, “Sliding mode control design principles and applications to electric drives,” Ind. Electron. IEEE Trans., vol. 40, no. 1, pp. 23–36, 1993.

K. B. Oldham and J. Spanier, The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order. New York: Academic Press, 1974.

R. Caponetto, G. Dongola, L. Fortuna, and I. Petras, Fractional Order Systems: Modeling and Control Applications. Singapore: World Scientific, 2010.

M. da Graça Marcos, F. B. M. Duarte, and J. A. Tenreiro Machado, “Fractional dynamics in the trajectory control of redundant manipulators,” Commun. Nonlinear Sci. Numer. Simul., vol. 13, no. 9, pp. 1836–1844, 2008.

M. Zamani, M. Karimi-Ghartemani, N. Sadati, and M. Parniani, “Design of a fractional order PID controller for an AVR using particle swarm optimization,” Control Eng. Pract., vol. 17, no. 12, pp. 1380–1387, 2009.

G. W. Leibnitz, “Letter from Hanover, Germany, September 30, 1695 to GA L’hospital, Leibnizen Mathematische Schriften Olms Verlag,” 1962.

M. Lopez-Martinez, C. Vivas, and M. G. Ortega, “A Multivariable Nonlinear H_inf Controller for a Laboratory Helicopter,” Proc. 44th IEEE Conf. Decis. Control, pp. 4065–4070, 2005.

C. W. Tao, J. S. Taur, and Y. C. Chen, “Design of a parallel distributed fuzzy {LQR} controller for the twin rotor multi-input multi-output system,” Fuzzy Sets Syst., vol. 161, no. 15, pp. 2081–2103, 2010.

J. G. Juang, M. Te Huang, and W. K. Liu, “PID control using presearched genetic algorithms for a MIMO system,” IEEE Trans. Syst. Man Cybern. Part C Appl. Rev., vol. 38, no. 5, pp. 716–727, 2008.

A. P. S. Ramalakshmi and P. S. Manoharan, “Non-linear modeling and PID control of twin rotor MIMO system,” 2012 IEEE Int. Conf. Adv. Commun. Control Comput. Technol., pp. 366–369, Aug. 2012.

G. Kavuran and C. Yeroglu, “Sliding mode control for fractional order plants via limit cycle prediction,” in 2014 International Conference on Fractional Differentiation and Its Applications, ICFDA 2014, 2014.

B. M. Vinagre and A. J. Calderon, “On Fractional Sliding Mode Control,” in The 7th Portuguese Conference on Automatic Control, 2006.

S. Poddar, R. Kottath, V. Kumar, and A. Kumar, “Adaptive Sliding Kalman Filter using Nonparametric Change Point Detection,” Measurement, vol. 82, pp. 410–420, 2016.

E.-H. Zheng, J.-J. Xiong, and J.-L. Luo, “Second order sliding mode control for a quadrotor UAV,” ISA Trans., vol. 53, no. 4, pp. 1350–1356, 2014.

Y. Liu, T. Jia, Y. Niu, and Y. Zou, “Design of sliding mode control for a class of uncertain switched systems,” Int. J. Syst. Sci., vol. 46, no. 6, pp. 993–1002, 2015.

L. Huang, “An approach for robust control of a twin-rotor multiple input multiple output system,” 2011 IEEE Int. Conf. Robot. Autom., pp. 4423–4428, May 2011.

C. W. Tao, J. S. Taur, Y. H. Chang, and C. W. Chang, “A novel fuzzy-sliding and fuzzy-integral- sliding controller for the twin-rotor multi-inputmulti- output system,” IEEE Trans. Fuzzy Syst., vol. 18, no. 5, pp. 893–905, 2010.

B. Pratap, “Neuro sliding mode controller for twin rotor control system,” 2012 Students Conf. Eng. Syst., pp. 1–5, Mar. 2012.

J. J. Slotine and W. Li, Applied Nonlinear Control. Prentice Hall, 1991.

Q. Hu, B. Li, and Y. Zhang, “Robust attitude control design for spacecraft under assigned velocity and control constraints,” ISA Trans., vol. 52, no. 4, pp. 480–493, 2013.

S. Mondal and C. Mahanta, “Chattering free adaptive multivariable sliding mode controller for systems with matched and mismatched uncertainty,” ISA Trans., vol. 52, no. 3, pp. 335–341, 2013.

J.-G. Juang, W.-K. Liu, and R.-W. Lin, “A hybrid intelligent controller for a twin rotor MIMO system and its hardware implementation,” ISA Trans., vol. 50, no. 4, pp. 609–619, 2011.