基于收缩反步的四旋翼飞行器控制
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摘要
针对四旋翼飞行器轨迹跟踪控制问题,将增量稳定性应用于控制器设计,提出了一种基于收缩理论与反步法的四旋翼飞行器控制算法。首先,介绍了基于微分几何的收缩理论并给出了四旋翼飞行器的动力学模型;其次,使用收缩反步控制求解出四个控制输入信号,以实现飞行器的期望轨迹跟踪。整个系统采用双回路结构,外环控制飞行器位置,内环控制飞行器姿态;最后,分析了系统的增量稳定性与李雅普诺夫稳定性。收缩反步与积分反步的对比实验表明,应用收缩反步控制算法的飞行器系统收敛性更强,能够精确地完成轨迹跟踪任务。
For the trajectory tracking control problem of quadrotor aircraft,the incremental stability is applied to the controller design. A quadrotor control algorithm based on contraction theory and integral backstepping is proposed for trajectory tracking. Firstly,the theory of contraction based on differential geometry is introduce and the dynamic model of quadrotor is given. Then,four control input signals are solved by using the contraction backstepping control to achieve the desired trajectory tracking of the aircraft. The whole system adopts a double-loop structure,the outer ring controls the position of the aircraft,and the inner ring controls the attitude of the aircraft. Finally,the incremental stability and lyapunov stability of system are analyzed. The simulation shows that the convergence of system used contraction backstepping is better than integral backstepping,and can accurately complete the trajectory tracking task.
For the trajectory tracking control problem of quadrotor aircraft,the incremental stability is applied to the controller design. A quadrotor control algorithm based on contraction theory and integral backstepping is proposed for trajectory tracking. Firstly,the theory of contraction based on differential geometry is introduce and the dynamic model of quadrotor is given. Then,four control input signals are solved by using the contraction backstepping control to achieve the desired trajectory tracking of the aircraft. The whole system adopts a double-loop structure,the outer ring controls the position of the aircraft,and the inner ring controls the attitude of the aircraft. Finally,the incremental stability and lyapunov stability of system are analyzed. The simulation shows that the convergence of system used contraction backstepping is better than integral backstepping,and can accurately complete the trajectory tracking task.
引文
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[14]胡超芳,张志鹏.基于收缩理论的一类非线性系统自适应动态面控制[J].控制与决策,2016,31(5):769-775.
[15]DANI A P,CHUNG S J,HUTCHINSON S.Observer design for stochastic nonlinear systems using contraction analysis[C]//Proceedings of the 51st IEEE Conference on Decision and Control(CDC 2012),Maui,Hawaii,USA,December 10-13,2012:6028-6035.
[2]崔道旺.四旋翼飞行器的鲁棒自适应控制研究[D].北京:北京交通大学,2016.
[3]宗群,张睿隆,董琦,等.固定翼无人机自适应滑模控制[J].哈尔滨工业大学学报,2018,50(9):147-155.
[4]王志方,付兴建,沈洁,等.电力巡检无人机的鲁棒自适应容错控制[J].武汉大学学报:工学版,2018,51(7):646-653.
[5]石川,林达.基于自适应积分反步的四旋翼飞行器控制[J].计算机应用研究,2018,35(11):3338-3342.
[6]LIU X,SHI Y,CONSTANTINESCU D.Robust distributed model predictive control of constrained dynamically decoupled nonlinear systems:a contraction theory perspective[J].Systems&Control Letters,2017,105:84-91.
[7]DELELLIS P,MARIO D B,RUSSO G.Adaptation and contraction theory for the synchronization of complex neural networks[J].The Relevance of the Time Domain to Neural Network Models.Springer Series in Cognitive and Neural Systems,2012,3:9-32.
[8]LI Y.Automatic train control with actuator saturation using contraction theory[C]//Proceedings of the 3rd International Conference on Electrical and Information Technologies for Rail Transportation(EITRT 2017),Changsha,China,October 20-22,2017:989-998.
[9]MOHAMED M,SU R.Contraction based tracking control of autonomous underwater vehicle[J].IFAC-Papers On Line,2017,50(1):2665-2670.
[10]SHARMA B B,KAR I N.Design of asymptotically convergent frequency estimator using contraction theory[J].IEEE Transactions on Automatic Control,2008,53(8):1932-1937.
[11]LOHMILLER W,SLOTINE J J E.On contraction analysis for non-linear systems[J].Automatica,1998,34(6):683-696.
[12]唐余,林达.固定翼无人机轨迹跟踪的滑模变结构控制[J].四川理工学院学报:自然科学版,2018,31(4):36-42.
[13]石川.基于积分反步法的四旋翼飞行器轨迹跟踪控制[J].四川理工学院学报:自然科学版,2017,30(4):29-35.
[14]胡超芳,张志鹏.基于收缩理论的一类非线性系统自适应动态面控制[J].控制与决策,2016,31(5):769-775.
[15]DANI A P,CHUNG S J,HUTCHINSON S.Observer design for stochastic nonlinear systems using contraction analysis[C]//Proceedings of the 51st IEEE Conference on Decision and Control(CDC 2012),Maui,Hawaii,USA,December 10-13,2012:6028-6035.