.628· 工程科学学报，第40卷，第5期 helicopter.Aircr Eng Aerospace Technol,2010,82(6):340 5结论 [8]Basri M A M,Husain A R,Danapalasingam K A.Enhanced 在六旋翼飞行器非线性动力学模型的基础上， backstepping controller design with application to autonomous quadrotor unmanned aerial vehicle.Intell Rob Syst,2015,79 设计出了基于积分反步法控制与线性自抗扰控制的混 (2):295 合控制算法，从而实现了六旋翼飞行器在集总干扰下 [9]Wang C L,Chen Z Q.Sun M W.Sliding mode control of a 的轨迹跟踪控制.由理论分析和仿真试验结果可得： quadrotor helicopter.J Central S Univ Sci Technol,2017,48(4): (1)所提算法能够实现六旋翼飞行器的轨迹跟 1006 踪控制，实现对集总干扰的抑制 (王辰璐，陈增强，孙明玮.小型四旋翼飞行器的滑模控制. 中南大学学报（自然科学版），2017,48(4)：1006) (2)在阵风干扰与测量噪声的影响下，所提算 [10]Kumaz S,Cetin 0,Kaynak 0.Adaptive neuro-fuzzy inference 法能够满足六旋翼轨迹跟踪控制器设计的两点要 system based autonomous flight control of unmanned air vehicles. 求，即跟踪误差可控与小角度飞行假设 Expert Syst Appl,2010,37(2):1229 (3)在相同的期望姿态角条件下，所提的 [11]Hua Y.Research on Control Technology of a Six-Rotor Unmanned LADRC与一般的PID控制算法相比，前者滚转角的 Helicopter [Dissertation].Nanjing:Nanjing University of Science Technology,2013 跟踪精度提高了32%，表明LADRC具有更高的跟 (花寅.六旋翼无人直升机控制技术研究[学位论文].南 踪精度 京：南京理工大学，2013) (4)飞行试验表明基于BC-LADRC控制器的 [12]Liu Y P,Chen C.Wu H T,et al.Structural stability analysis 六旋翼飞行器在水平面上的轨迹跟踪误差不超过 and optimization of the quadrotor unmanned aerial vehicles via the 0.6m,姿态角的跟踪误差不超过4°.这也进一步说 concept of Lyapunov exponents.Int JAdr Manuf Technol,2018, 94(9-12):3217 明了本文所提控制算法的有效性 [13]Bouchoucha M,Seghour S,Osmani H,et al.Integral backstep- ping for attitude tracking of a quadrotor system.Elektronika ir 参考文献 Elektrotechnika,2011,116(10):75 [1]Toledo J,Acosta L,Perea D,et al.Stability and performance a- [14]Babaei R.Ehyaei A F.Robust backstepping control of a quadro- nalysis of unmanned aerial vehicles:quadrotor against Hexrotor tor UAV using extended kalman bucy filter.Int J Mechatronics, IET Control Theory Appl,2015,9(8):1190 Electrical Comput Technol,2015,5(16):2276 [2]Faessler M,Fontana F,Forster C,et al.Autonomous,vision- [15]Gao Z Q.Active disturbance rejection control:a paradigm shift based flight and live dense 3D mapping with a quadrotor micro aer- in feedback control system design//Proceedings of 2006 Ameri- ial vehicle.J Field Robot,2016,33(4):431 can Control Conference.Minneapolis,2006:2399 [3]Liu Y P,Li X Y,Wang T M,et al.Quantitative stability of [16]Gao Z Q.Scaling and bandwidth-parameterization based control- quadrotor unmanned aerial vehicles.Nonlinear Dyn,2017,87 ler tuning//Proceedings of the 2003 American Control Confer- (3):1819 ence.Denver,2006:4989 [4]Ding L,Ma R,Wu HT,et al.Yaw control of an unmanned aeri- [17]Ding L,Ma R,Shan W T,et al.Linear active disturbance rejec- al vehicle helicopter using linear active disturbance rejection con- tion control for yaw channel of a small-scale unmanned helicop- trol.Proc Inst Mech Eng Part I J Syst Control Eng,2017,231 ter.Trans Chin Soc Agric Mach,2017,48(5):22 (6):427 (丁力，马瑞，单文桃，等.小型无人直升机航向线性自抗扰 [5] Panomrattanarug B.Higuchi K,Mora-Camino F.Attitude control 控制.农业机械学报，2017,48(5)：22) of a quadrotor aircraft using LOR state feedback controller with full [18]Asadi F,Abut N.ITAE criterion based controller for buck con- order state observer//2013 Proceedings of SICE Annual Confer- verter.Int J Ady Appl Sci,2017,4(1):15 ence (SICE).Nagoya,2013:2041 [19]Gadewadikar J,Lewis F L,Subbarao K,et al.H-infinity static [6]Alexis K,Nikolakopoulos G.Tzes A.Model predictive quadrotor output-feedback control for rotorcraft.J Intell Rob Syst,2009,54 control:attitude,altitude and position experimental studies.IET (4):629 Control Theory Appl,2012,6(12):1812 [20]Dong W.Gu G Y,Zhu X Y,et al.Development of a quadrotor [7]Reza Dharmayanda H,Budiyono A,Kang T.State space identifi- test bed-modelling,parameter identification,controller design cation and implementation of H control design for small-scale and trajectory generation.Int J Ade Rob Syst,2015,12(2):7工程科学学报,第 40 卷,第 5 期 5 结论 在六旋翼飞行器非线性动力学模型的基础上, 设计出了基于积分反步法控制与线性自抗扰控制的混 合控制算法,从而实现了六旋翼飞行器在集总干扰下 的轨迹跟踪控制. 由理论分析和仿真试验结果可得: (1)所提算法能够实现六旋翼飞行器的轨迹跟 踪控制,实现对集总干扰的抑制. (2)在阵风干扰与测量噪声的影响下,所提算 法能够满足六旋翼轨迹跟踪控制器设计的两点要 求,即跟踪误差可控与小角度飞行假设. (3) 在 相 同 的 期 望 姿 态 角 条 件 下, 所 提 的 LADRC 与一般的 PID 控制算法相比,前者滚转角的 跟踪精度提高了 32% ,表明 LADRC 具有更高的跟 踪精度. (4)飞行试验表明基于 IBC鄄鄄 LADRC 控制器的 六旋翼飞行器在水平面上的轨迹跟踪误差不超过 0郾 6 m,姿态角的跟踪误差不超过 4毅. 这也进一步说 明了本文所提控制算法的有效性. 参 考 文 献 [1] Toledo J, Acosta L, Perea D, et al. Stability and performance a鄄 nalysis of unmanned aerial vehicles: quadrotor against Hexrotor. IET Control Theory Appl, 2015, 9(8): 1190 [2] Faessler M, Fontana F, Forster C, et al. Autonomous, vision鄄 based flight and live dense 3D mapping with a quadrotor micro aer鄄 ial vehicle. J Field Robot, 2016, 33(4): 431 [3] Liu Y P, Li X Y, Wang T M, et al. Quantitative stability of quadrotor unmanned aerial vehicles. Nonlinear Dyn, 2017, 87 (3): 1819 [4] Ding L, Ma R, Wu H T, et al. Yaw control of an unmanned aeri鄄 al vehicle helicopter using linear active disturbance rejection con鄄 trol. Proc Inst Mech Eng Part I J Syst Control Eng, 2017, 231 (6): 427 [5] Panomrattanarug B, Higuchi K, Mora鄄Camino F. Attitude control of a quadrotor aircraft using LQR state feedback controller with full order state observer / / 2013 Proceedings of SICE Annual Confer鄄 ence (SICE). Nagoya, 2013: 2041 [6] Alexis K, Nikolakopoulos G, Tzes A. Model predictive quadrotor control: attitude, altitude and position experimental studies. IET Control Theory Appl, 2012, 6(12): 1812 [7] Reza Dharmayanda H, Budiyono A, Kang T. State space identifi鄄 cation and implementation of H 肄 control design for small鄄scale helicopter. Aircr Eng Aerospace Technol, 2010, 82(6): 340 [8] Basri M A M, Husain A R, Danapalasingam K A. Enhanced backstepping controller design with application to autonomous quadrotor unmanned aerial vehicle. J Intell Rob Syst, 2015, 79 (2): 295 [9] Wang C L, Chen Z Q, Sun M W. Sliding mode control of a quadrotor helicopter. J Central S Univ Sci Technol, 2017, 48(4): 1006 (王辰璐, 陈增强, 孙明玮. 小型四旋翼飞行器的滑模控制. 中南大学学报(自然科学版), 2017, 48(4): 1006) [10] Kumaz S, Cetin O, Kaynak O. Adaptive neuro鄄fuzzy inference system based autonomous flight control of unmanned air vehicles. Expert Syst Appl, 2010, 37(2): 1229 [11] Hua Y. Research on Control Technology of a Six鄄Rotor Unmanned Helicopter [Dissertation]. Nanjing: Nanjing University of Science & Technology, 2013 (花寅. 六旋翼无人直升机控制技术研究[ 学位论文]. 南 京: 南京理工大学, 2013) [12] Liu Y P, Chen C, Wu H T, et al. Structural stability analysis and optimization of the quadrotor unmanned aerial vehicles via the concept of Lyapunov exponents. Int J Adv Manuf Technol, 2018, 94(9鄄12): 3217 [13] Bouchoucha M, Seghour S, Osmani H, et al. Integral backstep鄄 ping for attitude tracking of a quadrotor system. Elektronika ir Elektrotechnika, 2011, 116(10): 75 [14] Babaei R, Ehyaei A F. Robust backstepping control of a quadro鄄 tor UAV using extended kalman bucy filter. Int J Mechatronics, Electrical Comput Technol, 2015, 5(16): 2276 [15] Gao Z Q. Active disturbance rejection control: a paradigm shift in feedback control system design / / Proceedings of 2006 Ameri鄄 can Control Conference. Minneapolis, 2006: 2399 [16] Gao Z Q. Scaling and bandwidth鄄parameterization based control鄄 ler tuning / / Proceedings of the 2003 American Control Confer鄄 ence. Denver, 2006: 4989 [17] Ding L, Ma R, Shan W T, et al. Linear active disturbance rejec鄄 tion control for yaw channel of a small鄄scale unmanned helicop鄄 ter. Trans Chin Soc Agric Mach, 2017, 48(5): 22 (丁力, 马瑞, 单文桃, 等. 小型无人直升机航向线性自抗扰 控制. 农业机械学报, 2017, 48(5): 22) [18] Asadi F, Abut N. ITAE criterion based controller for buck con鄄 verter. Int J Adv Appl Sci, 2017, 4(1): 15 [19] Gadewadikar J, Lewis F L, Subbarao K, et al. H鄄infinity static output鄄feedback control for rotorcraft. J Intell Rob Syst, 2009, 54 (4): 629 [20] Dong W, Gu G Y, Zhu X Y, et al. Development of a quadrotor test bed鄄modelling, parameter identification, controller design and trajectory generation. Int J Adv Rob Syst, 2015, 12(2): 7 ·628·