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Stabilization and trajectory tracking control for underactuated quadrotor helicopter subject to wind-gust disturbance. (English) Zbl 1331.93162

Summary: The control of quadrotor helicopter has been a great challenge for control engineers and researchers since quadrotor is an underactuated and a highly unstable nonlinear system. In this paper, the dynamic model of quadrotor has been derived and a so-called robust optimal backstepping control (ROBC) is designed to address its stabilization and trajectory tracking problem in the existence of external disturbances. The robust controller is achieved by incorporating a prior designed optimal backstepping control (OBC) with a switching function. The control law design utilizes the switching function in order to attenuate the effects caused by external disturbances. In order to eliminate the chattering phenomenon, the sign function is replaced by the saturation function. A new heuristic algorithm namely Gravitational Search Algorithm (GSA) has been employed in designing the OBC. The proposed method is evaluated on a quadrotor simulation environment to demonstrate the effectiveness and merits of the theoretical development. Simulation results show that the proposed ROBC scheme can achieve favorable control performances compared to the OBC for autonomous quadrotor helicopter in the presence of external disturbances.

MSC:

93C95 Application models in control theory
93C10 Nonlinear systems in control theory
70Q05 Control of mechanical systems
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory

Software:

GSA
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References:

[1] Baek S J, Lee D J, Park J H and Chong K T 2013 Design of lateral Fuzzy-PI controller for unmanned quadrotor robot. J. Inst. Control, Robotics Syst. 19: 164-170 · doi:10.5302/J.ICROS.2013.19.2.164
[2] Bolandi H, Rezaei M, Mohsenipour R, Nemati H and Smailzadeh S 2013 Attitude control of a Quadrotor with optimized PID controller. Intelligent Control Autom. 4: 335-342 · doi:10.4236/ica.2013.43039
[3] Bošković D M and Krstić M 2002 Backstepping control of chemical tubular reactors. Comp.Chem. Eng. 26: 1077-1085 · doi:10.1016/S0098-1354(02)00026-1
[4] Bouadi H, Bouchoucha M and Tadjine M 2007 Modelling and stabilizing control laws design based on sliding mode for an UAV Type-Quadrotor. Eng. Lett. 15: 342-347
[5] Bouadi H, Bouchoucha M and Tadjine M 2008 Sliding mode control based on backstepping approach for an UAV type-quadrotor. Int. J. Appl. Math. Comp. Sci. 4: 12-17
[6] Castillo P, Lozano R and Dzul A 2005 Stabilization of a mini rotorcraft with four rotors. IEEE Control Syst. Mag. 25: 45-55 · Zbl 1395.93475 · doi:10.1109/MCS.2005.1550152
[7] Chiu C H, Peng Y F and Lin Y W 2011 Intelligent backstepping control for wheeled inverted pendulum. Expert Syst. Appl. 38: 3364-3371 · doi:10.1016/j.eswa.2010.08.121
[8] De Moura Oliveira P, Pires E S and Novais P 2013 Gravitational search algorithm design of Posicast PID control systems. Soft Computing Models in Industrial and Environmental Applications (pp. 191-199): Springer · Zbl 1273.93094
[9] Erginer B and Altug E 2012 Design and implementation of a hybrid fuzzy logic controller for a quadrotor VTOL vehicle. Int. J. Control, Autom. Syst. 10: 61-70 · doi:10.1007/s12555-012-0107-0
[10] Guisser M H and Medromi H 2009 A high gain observer and sliding mode controller for an autonomous quadrotor helicopter. Int. J. Intell. Control Syst. 14: 204-212
[11] Hu Q, Xu L and Zhang A 2012 Adaptive backstepping trajectory tracking control of robot manipulator. J. Franklin Inst. 349: 1087-1105 · Zbl 1273.93094 · doi:10.1016/j.jfranklin.2012.01.001
[12] Hwang J H, Hwang S, Hong S K and Yoo M G 2012 Attitude stabilization performance improvement of the quadrotor flying robot. J. Inst. Control Robot. Syst. 18: 608-611 · doi:10.5302/J.ICROS.2012.18.6.608
[13] Jafari H, Zareh M, Roshanian J and Nikkhah A 2010 An optimal guidance law applied to quadrotor using LQR method. Trans. Japan Soc. Aeronaut. Space Sci. 53: 32-39 · doi:10.2322/tjsass.53.32
[14] Jiang Y, Hu Q and Ma G 2010 Adaptive backstepping fault-tolerant control for flexible spacecraft with unknown bounded disturbances and actuator failures. ISA Trans. 49: 57-69 · doi:10.1016/j.isatra.2009.08.003
[15] Junior J C V, De Paula J C, Leandro G V and Bonfim M C 2013 Stability control of a quad-rotor using a PID controller. Brazilian J. Instrum. Control 1: 15-20 · doi:10.3895/S2318-45312013000100003
[16] Kim H M, Park S H, Song J H and Kim J S 2010 Robust position control of electro-hydraulic actuator systems using the adaptive back-stepping control scheme. Proc. Inst. Mech. Eng. I: J. Syst. Control Eng. 224: 737-746
[17] Kristiansen R, Nicklasson P J and Gravdahl J T 2009 Satellite attitude control by quaternion-based backstepping. IEEE Trans. Control Syst. Technol. 17: 227-232 · doi:10.1109/TCST.2008.924576
[18] Krstic M, Kanellakopoulos I and Kokotovic P 1995 Nonlinear and adaptive control design, (Vol. 222): Wiley New York · Zbl 0763.93043
[19] Lee D, Ha C and Zuo Z 2013 Backstepping control of quadrotor-type UAVs and its application to teleoperation over the Internet. 12th International Conference on Intelligent Autonomous Systems, Jeju Island, vol. 194, pp. 217-225 · Zbl 1395.93475
[20] Madani T and Benallegue A 2006 Backstepping control for a quadrotor helicopter. IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3255-3260
[21] Mokhtari A, M’Sirdi N K, Meghriche K and Belaidi A 2006 Feedback linearization and linear observer for a quadrotor unmanned aerial vehicle. Adv. Robot. 20: 71-91 · doi:10.1163/156855306775275495
[22] Mukherjee P and Waslander S L 2012 Direct adaptive feedback linearization for quadrotor control. AIAA Guidance, Navigation, and Control Conference
[23] Nuchkrua T and Parnichkun M 2012 Identification and optimal control of Quadrotor. Thammasat Int. J. Sci. Technol. 17: 36
[24] Olfati-Saber R 2000 Nonlinear control of underactuated mechanical systems with application to robotics and aerospace vehicle. Ph.D. thesis, Massachusetts Institute of Technology
[25] Rashedi E, Nezamabadi-Pour H and Saryazdi S 2009 GSA: a gravitational search algorithm. Information Sci. 179: 2232-2248 · Zbl 1177.90378 · doi:10.1016/j.ins.2009.03.004
[26] Regula G and Lantos B 2011 Backstepping based control design with state estimation and path tracking to an indoor quadrotor helicopter. Electr. Eng. Comput. Sci. 53: 151-161
[27] Santos M, López V and Morata F 2010 Intelligent fuzzy controller of a quadrotor. IEEE International Conference on Intelligent Systems and Knowledge Engineering, pp. 141-146
[28] Shen Q, Jiang B and Cocquempot V 2013 Adaptive fault-tolerant backstepping control against actuator gain faults and its applications to an aircraft longitudinal motion dynamics. Int. J. Robust Nonlinear Control 23: 1753-1779 · Zbl 1274.93170 · doi:10.1002/rnc.2789
[29] Sumantri B, Uchiyama N, Sano S and Kawabata Y 2013 Robust tracking control of a quad-rotor. Helicopter utilizing sliding mode control with a nonlinear sliding surface. J. Syst. Des. Dyn. 7: 226-241
[30] Sun W, Gao H and Kaynak O 2013 Adaptive backstepping control for active suspension systems with hard constraints. IEEE/ASME Trans. Mechatronics 18: 1072-1079 · doi:10.1109/TMECH.2012.2204765
[31] Voos H 2009 Nonlinear control of a quadrotor micro-UAV using feedback-linearization. IEEE International Conference on Mechatronics, pp. 1-6
[32] Waslander S L and Wang C 2009 Wind disturbance estimation and rejection for quadrotor position control. AIAA Infotech@ Aerospace Conference and AIAA Unmanned... Unlimited Conference, Seattle, WA
[33] Xu J X, Guo Z Q and Lee T H 2012 Synthesized design of a fuzzy logic controller for an underactuated unicycle. Fuzzy Sets Syst. 207: 77-93 · Zbl 1252.93078 · doi:10.1016/j.fss.2012.04.004
[34] Yang J H and Yang K S 2012 An adaptive variable structure control scheme for underactuated mechanical manipulators. Math. Problems Eng.: 2012 · Zbl 1264.93162
[35] Yih C C 2013 Sliding mode control for swing-up and stabilization of the cart-pole underactuated system. Asian J. Control 15: 1201-1214 · Zbl 1286.93050 · doi:10.1002/asjc.577
[36] Yu R, Zhu Q, Xia G and Liu Z 2012 Sliding mode tracking control of an underactuated surface vessel. IET Control Theory Appl. 6: 461-466 · doi:10.1049/iet-cta.2011.0176
[37] Zhang Y, Zhao W, Lu T and Li J 2013 The attitude control of the four-rotor unmanned helicopter based on feedback linearization control. WSEAS Trans. Syst. 12: 229-239
[38] Zilic T, Kasac J, Situm Z and Essert M 2013 Simultaneous stabilization and trajectory tracking of underactuated mechanical systems with included actuators dynamics. Multibody Syst. Dyn. 29: 1-19 · Zbl 1271.70023 · doi:10.1007/s11044-012-9303-1
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