Generalized super-twisting sliding mode control with a nonlinear sliding surface for robust and energy-efficient controller of a quad-rotor helicopter

Abstract

This paper proposes a time-varying sliding surface for a second-order sliding mode controller to improve the control performance and energy efficiency of a quad-rotor helicopter. The time-varying sliding surface is designed with a nonlinear function to provide varying properties of the closed-loop dynamics in order to reduce energy consumption. It is shown that the second-order sliding mode technique, known as a generalized super twisting algorithm, providing a robust controller and a nonlinear sliding surface is effective in reducing the energy consumption. A Lyapunov stability analysis is described to prove the stability of the proposed method. The effectiveness and reliability of the proposed method are evaluated by performing experiments several times using a quad-rotor helicopter experimental testbed under wind disturbance.

Keywords

Energy efficiency nonlinear control systems robust control sliding mode control unmanned aerial vehicles quad-rotor helicopter

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References

Roberts JF, Zufferey JC and Floreano D. Energy management for indoor hovering robots. In: Proceedings of the IEEE international conference on intelligent robots and systems, Nice, France, 22–26 September 2008, pp.1242–1247.

Aleksandrov D and Penkov I. Optimal gap distance between rotors of mini quadrotor helicopter. In: Proceedings of 8th international conference of DAAAM Baltic, Tallinn, Estonia, 19–21 April 2012, pp.251–255.

Xu R and Özgüner Ü. Sliding mode control of a quadrotor helicopter. In: The 45th IEEE conference on decision and control, San Diego, CA, December 2006, pp.4957–4962.

Mohamed HAF, Yang SS and Moghawemi M. Sliding mode controller design for a flying quadrotor with simplified action planner. In: Proceedings of ICCAS-SICE, Fukuoka, Japan, August 2009, pp.1279–1283.

Patel AR, Patel MA and Vyas DR. Modeling and analysis of quadrotor using sliding mode control. In: The 44th IEEE southeastern symposium on system theory, Jacksonville, FL, March 2012, pp.111–114.

Besnard

Shtessel

Landrum

. Quadrotor vehicle control via sliding mode controller driven by sliding mode disturbance observer. J Franklin Inst 2012; 349(2): 658–684.

Bouadi

Tadjine

. Nonlinear observer design and sliding mode control of four rotors helicopter. Int J Eng Appl Sci 2007; 3(6): 333–338.

Guisser

Medromi

. A high gain observer and sliding mode controller for an autonomous quadrotor helicopter. Int J Intell Control Syst 2009; 14(3): 204–212.

Sumantri B, Uchiyama N and Sano S. Least square based sliding mode control for a quad-rotor helicopter. In: IEEE/SICE international symposium on system integration, Kobe, Japan, December 2013, pp.324–328.

10.

Xiong

Zheng

. Position and attitude tracking control for a quadrotor UAV. ISA Trans 2014; 53(3): 725–731.

11.

Vega LL, Toledo BC and Loukianov AG. Block linearization control of a quadrotor via sliding mode. In: Proceedings of American control conference, Montreal, Canada, June 2012, pp.149–154.

12.

Bouchoucha M, Seghour S and Tadjine M. Classical and second order sliding mode control solution to an attitude stabilization of a four rotors helicopter: from theory to experiment. In: IEEE international conference on mechatronics, Istanbul, Turkey, April 2011, pp.162–169.

13.

Derafa

Benallegue

Fridman

. Super twisting control algorithm for the attitude tracking of a four rotors UAV. J Franklin Inst 2012; 49: 685–699.

14.

Slotine

JJE

. Applied nonlinear control, Upper Saddle River, NJ: Prentice Hall, 1991, pp. 276–309.

15.

Hung

Gao

Hung

. Variable structure control: a survey. IEEE Trans Ind Electron 1993; 40(1): 2–22.

16.

Orowska-Kowalska

Kaminski

Szabat

. Implementation of a sliding-mode controller with an integral function and fuzzy gain value for the electrical drive with an elastic joint. IEEE Trans Ind Electron 2010; 57(4): 1309–1317.

17.

Nonaka K and Sugizaki H. Integral sliding mode altitude control for a small model helicopter with ground effect compensation. In: Proceedings of American control conference, San Francisco, CA, June 2011, pp.202–207.

18.

de Castro

Araujo

Freitas

. Wheel slip control of EVs based on sliding mode technique with conditional integrators. IEEE Trans Ind Electron 2013; 60(8): 3256–3271.

19.

Yang

Zheng

. Variable structure attitude control for an UAV with parameter uncertainty and external disturbance. Procedia Eng 2011; 15: 408–415.

20.

Beltran

Ahmed-Ali

Benbouzid

. High-order sliding-mode control of variable-speed wind turbines. IEEE Trans Ind Electron 2009; 56(9): 3314–3321.

21.

Loukianov

Canedo

Fridman

. High-order block sliding-mode controller for a synchronous generator with an exciter system. IEEE Trans Ind Electron 2011; 58(1): 337–347.

22.

Levant

. Sliding order and sliding accuracy in sliding mode control. Int J Control 1993; 58(6): 1247–1263.

23.

Moreno

. Strict Lyapunov functions for the super-twisting algorithm. IEEE Trans Automat Contr 2012; 57(4): 1035–1040.

24.

Moreno

. On strict Lyapunov functions for some non-homogeneous super-twisting algorithms. J Franklin Inst 2014; 351: 1902–1919.

25.

Sheng-Dong

. Super-twisting-algorithm-based terminal sliding mode control for a bioreactor system. Abstr Appl Anal 2014; 2014: 1–9.

26.

Moreno JA. A linear framework for the robust stability analysis of a generalized super-twisting algorithm. In: Proceedings of the 6th international conference on electrical engineering, computing science and automatic control, Toluca, Mexicon, January 2009, pp.1–6.

27.

Moreno JA and Osorio M. A Lyapunov approach to second-order sliding mode controllers and observers. In: Proceedings of the 47th IEEE conference on decision and control, Cancun, Mexico, December 2008, pp.2856–2861.

28.

Binglong

Xiangdong

Zhen

. Exponential time-varying sliding mode control for large angle attitude eigenaxis maneuver of rigid spacecraft. Chinese J Aeronaut 2010; 23: 447–453.

29.

Promkajin N and Parnichkun M. Attitude and altitude control of a four-rotor hovercraft using sliding mode control with adaptive sliding surface. In: Proceedings of IEEE-ROBIO, Phuket, Thailand, December 2011, pp.1285–1290.

30.

Tokat S, Eksin I and Guzelkaya M. Sliding mode control using a nonlinear time-varying sliding surface. In: Proceedings of the 10th IEEE international Mediterranean conference on control and automation, Lisbon, July 2002.

31.

Yorgancioglu

Komurcugil

. Decoupled sliding-mode controller based on time-varying sliding surfaces for fourth-order systems. Expert Syst Appl 2010; 37: 6764–6774.

32.

Kareem

Azeem

. A novel adaptive super-twisting sliding mode controller with a single input-single output fuzzy logic control based moving sliding surface. Int J Control Automation 2013; 6(3): 183–197.

33.

Deepak

Bandyopadhyay

Fridman

. Non-linear sliding surface: towards high performance robust control. IET Control Theory Appl 2012; 6(2): 235–242.

34.

Vázquez

Valenzuela

. Motion control of a quadrotor aircraft via singular perturbations. Int J Adv Rob Syst 2013; 10(368): 1–16.

35.

Pounds

Mahony

Corke

. Modelling and control of a large quadrotor robot. Control Eng Prac 2010; 18(7): 691–699.

36.

Bouadi

Bouchoucha

Tadjine

. Modelling and stabilizing control laws design based on sliding mode for an UAV type-quadrotor. Eng Lett 2007; 15(2): 1–6.

37.

Mokhtari A and Benallegue A. Dynamic feedback controller of Euler angles and wind parameters estimation for a quadrotor unmanned aerial vehicle. In: Proceedings of IEEE-ICRA, New Orleans, LA, 26 April–1 May 2004, vol. 3, pp.2359–2366.

38.

Hamel T, Mahony R, Lozano R, et al. Dynamic modelling and configuration stabilization for an X4-flyer. In: Proceedings of the 15th IFAC world congress, Barcelona, Spain, 21–26 July 2002, vol. 15, no. 1, pp.846–846.

39.

Mian

Daobo

. Modeling and backstepping-based nonlinear control strategy for a 6 DOF quadrotor helicopter. Chinese J Aeronaut 2008; 21: 261–268.

40.

Sumantri B, Uchiyama N and Sano S. Second order sliding mode control for a quad-rotor helicopter with a nonlinear sliding surface. In: Proceedings of the 2014 IEEE conference on control applications (CCA), Antibes, France, 8–10 October 2014, pp.742–746.

41.

Fridman

Levant

. Higher order sliding modes. Sliding mode control in engineering, New York: Marcel Dekker Inc., 2002, pp. 53–104.

42.

Sumantri

Uchiyama

Sano

. Least square based sliding mode control for a quad-rotor helicopter and energy saving by chattering reduction. Mech Syst Sig Process 2016; 66–67: 769–784.