许璟;蔡晨晓;李勇奇;邹云
【摘 要】近年来,无人飞行器控制繁荣发展对控制精度与品质要求日益增高.为了应对这一挑战,本文基于奇异摄动的思想设计了四旋翼无人机非线性轨迹跟踪控制器.首先,基于牛顿欧拉定律建立了四旋翼无人飞行器非线性奇异摄动形式的数学模型.然后,引入奇异摄动理论,通过时间尺度分解的方法将系统解耦成内环快子系统和外环慢子系统.再者,根据非线性动态逆的思想分别建立快、慢伪线性子系统,并基于此分别设计外环轨迹跟踪、内环稳定子控制器,综合子控制器生成应用于原系统的全阶控制器以兼顾跟踪精度和鲁棒特性.针对内环快系统,采用线性二次调节控制器以实现稳定快速地控制飞行器旋转动态;针对外环慢系统,运用经典的比例-微分-积分控制器以跟踪所给定的轨迹.最后给出了仿真实例说明本文结论的有效性. 【期刊名称】《控制理论与应用》
【年(卷),期】2015(032)010
【总页数】8页(P1335-1342)
【关键词】无人飞行器;仿真器;非线性控制;奇异摄动思想;比例-微分-积分控制器;线性二次调节控制器
【作 者】许璟;蔡晨晓;李勇奇;邹云
【作者单位】红外线烘干箱南京理工大学自动化学院,江苏南京210094;南京理工大学自动化学院,江苏南京210094;南京理工大学自动化学院,江苏南京210094;南京理工大学自动化学院,江苏南京210094p2p网络电视录像专家
【正文语种】中 文发动机摇臂
军用床【中图分类】TP273
Recent advances in the investigation of unmanned vehicles have led to enormous exciting developments，particularly，with the platform of quad-rotor miniature unmanned aerial vehicles（MAVs）.As opposed to fixed wing vehicles，the quad-rotor MAV is a smalscale vehicle which might be more suitable for specific applications including search and rescue，surveillance and remote inspection.The ability to maneuver an actual MAV a
ccurately along a given geometric path is a primary objective for most appli-cations.Previous work on path tracking of MAVs has concentrated on techniques such as feedback linearization，sliding mode control，proportional integral derivative control（PID）control，linear quadratic regular（LQR）control and backstepping control methods［1-9］.In［1］，a global trajectory tracking control of UAVs without linear velocity measurements was designed based on inverse dynamic approaches. The authors in［2］proposed a backstepping design for the trajectory tracking problem of a class of underactuated systems where the states are guaranteed to con-verge to a ball near the origin.A continuous sliding mode control method based on feedback linearization was presented in［3］，and an output tracking control was designed for a quad-rotor UAV.As demonstrated in［4］，a classical PID controller made a quad-rotor able to track a given reference trajectory in presence of minor perturbations.
On the other hand，singular perturbations and time-scale techniques（SPaTSs）have been proven to be effective tools for model reduction，analysis and design of flight control systems.Modeling both kinematics and dynamics of quad-rotor MAVs results in a
model with high order，which may decrease feasibility of controller design.The main concept of SPaTSs is to lower the model order by neglecting the fast part，and to improve the the approximation by reintroducing their effects as boundary layer corrections in separate time-scales［10］.In［11］，the design and stability analysis of a hierarchical controller via using SPaTSs was presented.Flight test trajectory control systems based on time-scale techniques were designed to enable the pilot to follow complex trajectories for evaluating an aircraft within its known flight envelop and to explore the boundaries of its capabilities［12］.A cascade decomposition method was discussed in［13］for the longitudinal dynamics of a low-speed experimental UAV.
In this paper，we present a strategy of path tracking for a quad-rotor MAV to reduce position errors，and to follow a reference geometric path.Based on SPaTSs，models for inner-and outer-loops have been constructed in different time-scales.The inner-loop controller is made by integration of dynamic inversion approaches and LQR control method to enhance stability，and the two time-scale characteristics can be preserved to facilitate controller design.The outerloop controller combines a dynamic inversion controll
er with a PID controller to ensure a desired tracking performance.The dual-loop control structure is adopted to coordinate inner-loop and outer-loop controls，which can simplify the design procedure，and improve control quality and quantity of the flight system.The main contribution of this paper is outlined as follows：全息3d智能炫屏
1）Different from current works，the mathematical model of a quad-rotor MAV in this paper is represented in the singular perturbed，affine nonlinear form to facilitate controller design.
2）The dual loop control structure is then utilized to facilitate decomposition，and to attenuate the controller design difficulty of under-actuated MAVs.In thissense，inner-loopandouter-loopcontrollerdesign can be done separately in different time-scales.
3）Input control energy is saved under the assumption that small position errors are permitted.It should be noted that the position of a MAV is guaranteed within a pipe centered on the given path.
4）Due to wind effects，there exists large initial position errors off the references.The control strategyofthisworkcan eliminatetheinitialerrorsquickly，and enable the MAV track the reference path within a specified precision.
5）The modeling/control approach in this paper delivers controllers that exploit both translational and orientational dynamic capability of the aircraft，and thus are ready to be used by higher level navigation systems for complex autonomous missions.
NotationThroughout this paper，Inis the n×n identity matrix of order n.Rnand Rn×mdenote，respectively，then-dimensionalEuclideanspaceandthe set of all n×m real matrices.The superscripts“T”，“∗”，“†”denote matrix transposition，complex transpose and the Moore-Penrose inverse.The sxand cxnotations represent sinx and cosx respectively.Matrices，if not explicitly stated，are assumed to have compatible dimensions.
A quad-rotor MAV is controlled by the rotational speeds of four rotors.The Newton-Euler formulation is adopted to develop the mathematical model of the quad-rotor UAV.The vehi
cle is represented using a right hand Inertial coordinate system（I）of axes and a right hand body frame（B）.From［14］，the equations of motion can take the concrete form in the body frame（see also in Table 1），
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