Magnetic torque attitude control of a satellite using the state-dependent Riccati equation technique

A non-linear attitude control method for a satellite with magnetic torque rods using the state-dependent Riccati equation (SDRE) technique has been developed. The magnetic torque caused by the interaction with the Earth's magnetic field and the magnetic moment of torque rods plays a role of the control torque. The detailed equations of motion for this system are presented using angular velocity and quaternions. The SDRE controller is developed for the non-linear systems which can be formed in pseudo-linear representations using the state-dependent coefficient (SDC) method without linearization procedure. The aim of this control system is to achieve a stable attitude within 5°, and minimize the control effort. The stability regions for the SDRE controlled satellite system are estimated through the investigation of the stability conditions developed for pseudo-linear systems and the application of Lyapunov's theorem. For comparisons, the Linear Quadratic Regulator (LQR) method using the solution of the algebraic Riccati equation (ARE) is also applied to this non-linear system. The performance of the SDRE non-linear control system demonstrates more robustness and stability than the LQR control system when subjected to a wide range of initial conditions.     

基于对偶四元数的双星编队相对位姿测量

为了描述编队卫星中主从星的相对位置和姿态信息,提出了基于对偶四元数的编队卫星相对位姿测量算法。以双星编队飞行的位姿运动为主线,运用对偶四元数工具,充分发挥其能以最简洁的形式表示一般性刚体运动的优点,对卫星轨道和姿态进行分析并建立了对偶四元数位姿模型。同时设计类GPS测量技术来测量编队卫星的相对位置和姿态,该技术载波相位波长和伪码码元比GPS的更短,可获得更高精度的相对测量信号。由于状态方程和观测方程的非线性特征,使用UKF滤波来消除随机噪声对量测过程的干扰。实验结果表明,所设计的算法能够有效估计系统误差,卫星的位置误差和四元数误差收敛于零,验证了该算法的有效性。     

Orbit and attitude control of spacecraft formation flying

Formation flying is a novel concept of distributing the functionality of large spacecraft among several smaller, less expensive, cooperative satellites. Some applications require that a controllable satellite keeps relative position and attitude to observe a specific surface of another satellite among the cluster. Specially, the target space vehicle is malfunctioning. The present paper focuses on the problem that how to control a chaser satellite to fly around an out-of-work target satellite closely in earth orbit and to track a specific surface. Relative attitude and first approximate relative orbital dynamics equations are presented. Control strategy is derived based on feedback linearization and Lyapunov theory of stability. Further, considering the uncertainty of inertia, an adaptive control method is developed to obtain the correct inertial ratio. The numerical simulation is given to verify the validity of proposed control scheme.     

Robust attitude control for rapid multi-target tracking in spacecraft formation flying

A robust attitude tracking control scheme for spacecraft formation flying is presented. The leader spacecraft with a rapid mobile antenna and a camera is modeled. While the camera is tracking the ground target, the antenna is tracking the follower spacecraft. By an angular velocity constraint and an angular constraint, two methods are proposed to compute the reference attitude profiles of the camera and antenna, respectively. To simplify the control design problem, this paper first derives the desired inverse system （DIS）, which can convert the attitude tracking problem of 3D space into the regulator problem. Based on DIS and sliding mode control （SMC）, a robust attitude tracking controller is developed in the presence of mass parameter uncertainties and external disturbance. By Lyapunov stability theory, the closed loop system stability can be achieved. The numerical simulations show that the proposed robust control scheme exhibits significant advantages for the multi-target attitude tracking of a two-spacecraft formation.     

飞网抛射过程母卫星姿态干扰分析与姿态控制

空间飞网是一种新型的空间碎片或漂浮物回收装置. 飞网抛射过程会对母体卫星产生较大的干扰,影响卫星的姿态稳定,因此需要设计具有抗干扰能力的控制律来保证卫星姿态的稳定. 针对空间飞网直接抛射展开过程,分析了影响飞网抛射效果的主要因素,并建立了飞网发射所产生的干扰力矩模型. 针对卫星的控制要求,建立了卫星姿态控制系统的模型,设计了滑模变结构控制器,并给出数学推导过程. 最后,通过仿真对姿态干扰及控制器控制性能进行了分析研究,结果表明,设计的控制器能够保证卫星的稳定,满足设计指标要求.     

基于有限时间收敛的双臂空间机器人捕获卫星主动对接力/位姿阻抗控制

针对双臂空间机器人捕获卫星主动对接力/位姿阻抗控制进行了研究.为防止捕获过程中机械臂末端执行器与卫星接触、碰撞时产生的冲击载荷对机器人关节造成冲击破坏,在各关节电机与机械臂之间加入了一种弹簧阻尼缓冲机构.该机构可通过弹簧实现冲击力矩的卸载,阻尼器则用于因弹簧引起的柔性振动的抑制.为解决捕获过程中的非完整动力学约束及捕获后混合体系统的协调控制问题,结合牛顿第三定律、捕获点的速度约束及闭链几何约束,获得捕获后混合体系统的动力学方程,且通过动量守恒关系计算碰撞冲击效应与碰撞冲击力.通过分析对接装置在载体坐标系下的运动学关系,建立对接装置相对载体的运动雅可比矩阵,并基于此建立基于力的二阶线性阻抗模型,实现对接装置输出力的精确控制.考虑到主动对接操作过程要求控制器具有收敛速度快,控制精度高的特点,通过结合终端滑模与超扭滑模的特点,提出一种非奇异快速终端滑模阻抗控制策略.该策略即能实现主动对接操作中位姿与输出力的快速响应,又能有效地抑制滑模的抖振以保证控制精度.通过Lyapunov定理证明系统的稳定性;利用数值模拟验证缓冲装置的抗冲击性能及所提阻抗控制策略的有效性.     

Detumbling strategy and coordination control of kinematically redundant space robot after capturing a tumbling target

This paper focuses on the motion planning to detumble and control of a space robot to capture a non-cooperative target satellite. The objective is to construct a detumbling strategy for the target and a coordination control scheme for the space robotic system in post-capture phase. First, the dynamics of the kinematically redundant space robot after grasping the target is presented, which lays the foundation for the coordination controller design. Subsequently, optimal detumbling strategy for the post-capture phase is proposed based on the quartic B\(\acute{\text{ e }}\)zier curves and adaptive particle swarm optimization algorithm subject to the specific constraints. Both detumbling time and control torques were taken into account for the generation of the optimal detumbling strategy. Furthermore, a coordination control scheme is designed to track the designed reference path while regulating the attitude of the chaser to a desired value. The space robot successfully dumps the initial velocity of the tumbling satellite and controls the base attitude synchronously. Simulation results are presented for detumbling a target with rotational motion using a seven degree-of-freedom redundant space manipulator, which demonstrates the feasibility and effectiveness of the proposed method.     

基于视线运动模型的椭圆轨道交会最优控制

针对航天器自主交会对接实际存在的接近方位角约束, 在视线坐标系内讨论了椭圆轨道最优交会控制设计问题. 根据椭圆轨道视线动力学模型具有时变非线性的特点, 分别采用状态相关Riccati方程(state-dependent riccati equation, SDRE)方法和\theta-D方法进行了最优交会控制器设计. 考虑到实际施加的控制力沿原轨道坐标系各轴向更易于实现, 结合SDRE方法中系统输入矩阵可与系统状态量相关, 进而设计了控制力沿轨道坐标系轴向的最优交会控制器. 数值仿真表明: 两种方法均实现了带有方位角约束的交会; \theta-D控制算法计算效率更高, 而SDRE控制算法精度较高, 且可以实现控制力沿轨道坐标系各轴定向施加.      

New-type of flying control for spinning TVC vehicle

A new kind of problem for TVC vehicle spinning in the boost stage had been researched. The study of non-linear flying dynamics modeling and dynamic properties of TVC vehicles reveal dominant coupled factors that affect the attitude stability and attitude precision of the pitch channel and yaw channel. The paper emphasizes the inertial delay coupled effects between vehicle＇s pitch servo system and yaw servo system, which have always been neglected. An uncoupled plan and control algorithm are put forward from the standpoint of engineering implementation to provide theoretical guidance and reference for further research on this complicated flying control.     

SDRE-based near optimal nonlinear controller design for unified chaotic systems

This paper proposes a near optimal controller design method for unified chaotic systems based on state-dependent Riccati equation (SDRE) approach. A parameterization of the optimal nonlinear control gain is given in terms of the solution matrix of an SDRE. A simple algorithm to compute the near optimal control gain is proposed. The proposed near optimal control design method is also extended to the synchronization problem for unified chaotic systems. Finally, the effectiveness of the proposed design method is verified via numerical simulations.     

Numerical analyses and experimental validations of coexisting multiple attractors in Hopfield neural network

In this paper, a finite-time controller is proposed for the quadrotor aircraft to achieve hovering control in a finite time. The design of controller is mainly divided into two steps. Firstly, a saturated finite-time position controller is designed such that the position of quadrotor aircraft can reach any desired position in a finite time. Secondly, a finite-time attitude tracking controller is designed, which can guarantee that the attitude of quadrotor aircraft converges to the desired attitude in a finite time. By homogenous system theory and Lyapunov theory, the finite-time stability of the closed-loop systems is given through rigorous mathematical proofs. Finally, numerical simulations are given to show that the proposed algorithm has a faster convergence performance and a stronger disturbance rejection performance by comparing to the PD control algorithm.     

Observer-based controller for discrete-time systems: a state dependent Riccati equation approach

In this paper, an observer-based controller for discrete-time nonlinear dynamical systems is proposed. After transforming the nonlinear system to a linear structure having state-dependent coefficient matrices (SDC), a recursive regularized least-square (RLS) state estimator is developed. The observed states are then used to generate either a constrained or unconstrained state feedback controller using the state dependent Riccati equation (SDRE) approach. The stability of the observer-based control system is rigorously analyzed in a theoretical frame work. Applications to different numerical examples as well as to a practical case study demonstrate the effectiveness of the proposed procedure.     

Self-tuning PID controller to three-axis stabilization of a satellite with unknown parameters

This paper addresses the three-axis stabilization of a satellite system in the presence of the gravity gradient and orbital eccentricity. Multivariable non-linear dynamics of the satellite system are converted into three well-known non-linear canonical independent models with unknown parameters. The new model is efficient and practical for designers to implement and analyze different control methodologies on satellite systems. A self-tuning PID controller is designed on the basis of the new proposed model to produce control signals for three reaction wheels in three axes. An adaptive algorithm is applied to tune and update gains of the PID controller and stability of the closed-loop system is guaranteed by using Lyapunov approach. Numerical simulations are performed to demonstrate feasibility and effectiveness of the self-tuning PID controller and a comparison with a fixed gain PD controller and a variable-structure controller is made.     

猎雷声纳基阵姿态稳定系统自适应反步法控制

针对带非线性摩擦力矩和负载扰动的高精度猎雷声纳基阵姿态稳定系统,提出了一种基于神经网络的自适应反步法控制方法。其中神经网络用于估计未知非线性摩擦力矩,进而设计反步法控制器和参数自适应律来对神经网络估计误差和负载扰动进行补偿。最后应用Lyapunov方法证明了所提出的自适应控制器能保证闭环系统的稳定性,并且可以通过选择适当的控制器参数来调整收敛率。仿真结果表明,基于神经网络的自适应反步法控制方法与PID控制相比,系统的动、静态性能指标及鲁棒性得到了全面的改善,与双闭环PID控制相比,跟踪精度提高了3倍多。     

Distributed time-varying formation tracking of multi-quadrotor systems with partial aperiodic sampled data

In this article, a distributed formation tracking controller is proposed for Multi-agent systems (MAS) consisting of quadrotors. It is considered that each quadrotor in the MAS only shares its translation position information with its neighbors. Moreover, position information is transmitted at nonuniform and asynchronous time instants. The control system is divided into an outer-loop for the position control and an inner-loop for the attitude control. A continuous-discrete time observer is used in the outer-loop to estimate both position and velocity of the quadrotor and its neighbors using discrete position information it receives. Then, these estimated states are used to design the position controller in order to enable quadrotors to generate the required geometric shape. A finite-time attitude controller is designed to track the desired attitude as dictated by the position controller. Finally, a closed-loop stability analysis of the overall system including nonlinear coupling is performed.

     

基于虚拟力概念的柔性臂空间机器人模糊退步自适应控制算法设计

讨论了漂浮基柔性臂空间机器人系统的动力学模拟、运动轨迹跟踪控制算法设计及柔性振动主动抑制。采用多体动力学建模方法并结合假设模态法,建立了漂浮基柔性臂空间机器人的系统动力学模型。基于该模型,针对系统惯性参数未知情况,提出了刚性运动基于模糊基函数网络自适应调节的退步控制算法,以完成柔性臂空间机器人载体姿态及机械臂各关节铰的协调运动。然后,为了主动抑制系统柔性振动,运用虚拟力的概念,构造了同时反映柔性模态和刚性运动轨迹的混合期望轨迹,通过改造原有的控制算法,提出了基于虚拟力概念的模糊退步自适应控制算法;这样不但保证了之前刚性运动控制方案对模型不确定的鲁棒性,而且能主动抑制柔性振动,从而提高了轨迹跟踪性能。理论分析及数值仿真算例均表明了控制方法的可行性。     

Avoiding Switching Upon Failure of a Sensor in the Lateral Control System of a Quadcopter

International Applied Mechanics - An algorithm of designing a controller of the lateral movement of a quadcopter is offered. This algorithm guarantees the stability of the system in the case of...     

Adaptive neural tracking control for a class of perturbed pure-feedback nonlinear systems

This paper focuses on the problem of the adaptive neural control for a class of a perturbed pure-feedback nonlinear system. Based on radial basis function (RBF) neural networks’ universal approximation capability, an adaptive neural controller is developed via the backstepping technique. The proposed controller guarantees that all the signals in the closed-loop system are bounded and the tracking error eventually converges to a small neighborhood around the origin. The main advantage of this note lies in that a control strategy is presented for a class of pure-feedback nonlinear systems with external disturbances being bounded by functions of all state variables. A numerical example is provided to illustrate the effectiveness of the suggested approach.     

AIRSHIP ATTITUDE TRACKING SYSTEM

The attitude tracking control problem for an airship with parameter uncertainties and external disturbances was considered in this paper. The mathematical model of the airship attitude is a multi-input/multi-output uncertain nonlinear system. Based on the characteristics of this system, a design method of robust output tracking controllers was adopted based on the upper-bounds of the uncertainties. Using the input/output feedback linearization approach and Liapunov method, a control law was designed, which guarantees that the system output exponentially tracks the given desired output. The controller is easy to compute and complement. Simulation results show that, in the closed-loop system, precise attitude control is accomplished in spite of the uncertainties and external disturbances in the system.     

太阳帆日心悬浮轨道附近的相对运动

研究悬浮轨道附近的编队飞行问题,推导了悬浮轨道附近的相 对运动方程. 由于编队太阳帆之间的距离与帆到太阳的距离的比值为小量,将相对运动方程 在悬浮轨道附近线性化,得到了线性化方程. 基于该线性化方程,考虑了悬浮轨道附近的几 种编队控制方法,只需通过调节太阳帆的姿态来进行简单的控制. 其中包括一种被动编队控 制策略,该控制策略具有实现简单、稳定区域大的特点,具有很好的工程应用前景. 最后基 于非线性方程对每种编队策略进行了数值仿真验证,数值结果表明该控制方法能实现编 队.