一类非线性系统的反馈非线性化镇定

给出了一类非线性系统的状态反馈非线性化镇定的方法。首先构造一个人为的输出映射,使得系统的零动态渐近稳定并具有向量相对阶｛1,…,1｝;然后构造一类控制器使得零输出流形服从一类指数稳定的非线性动态方程。利用非线性H∞－控制一个基本结果证明了在较弱的条件下,所得到的闭环系统是局部渐近稳定的。最后以刚体姿态控制为例,说明了利用上述结果,可以得到一类仅仅需要知道系统惯性矩阵元素相对值的反馈方案,从而在一定程度上克服了反馈线性化方法需要精确知道系统参数的弱点。     

挠性航天器的退步直接自适应姿态跟踪控制

针对参数不确定的挠性航天器姿态跟踪控制问题,提出了一种退步直接自适应控制算法。首先验证了挠性航天器动力学子系统的近似严格正实性,并设计了具有理想控制性能的参考模型;然后对以姿态四元数描述的运动学子系统设计常系数输出反馈中间控制律,使航天器姿态四元数输出渐近跟踪参考模型输出;最后退一步,对具有参数不确定特性的动力学子系统,基于非线性直接自适应控制理论和Lyapunov稳定性理论,设计了退步直接自适应姿态跟踪控制器,并证明了闭环系统的稳定性。仿真结果表明,所提控制方法能有效抑制挠性附件的振动,对挠性航天器的控制是有效的。     

A composite control scheme for attitude maneuvering and elastic mode stabilization of flexible spacecraft with measurable output feedback

This paper treats the question of attitude maneuver control and elastic mode stabilization of a flexible spacecraft based on adaptive sliding mode theory and active vibration control technique using piezoelectric materials. More precisely, a modified positive position feedback (PPF) scheme is developed to design the PPF compensator gains in a more systematical way to stabilize the vibration modes in the inner loop, in which a cost function is introduced to be minimized by the feedback gains subject to the stability criterion at the same time. Based on adaptive sliding mode control theory, a discontinuous attitude control law is derived to achieve the desired position of the spacecraft, taking explicitly into account the mismatched perturbation and actuator constraints. In the attitude control law, an adaptive mechanism is also embedded such that the unknown upper bound of perturbation is automatically adapted. Once the controlled attitude control system reaches the switching hyperplane, the state variables can be driven into a small bounded region. An additional attractive feature of the attitude control method is that the structure of the controller is independent of the elastic mode dynamics of the spacecraft, since in practice the measurement of flexible modes is not easy or feasible. The proposed control strategy has been implemented on a flexible spacecraft. Both analytical and numerical results are presented to show the theoretical and practical merit of this approach.     

Nonlinear observer and output feedback attitude control ofspacecraft

The problem of controlling a spacecraft by measuring only the angular position (roll, pitch, and yaw) is considered. A nonlinear observer is proposed which asymptotically reconstructs all the spacecraft state variables; if the spacecraft actuators are reaction wheels, the angular velocities of the wheels also must be measured. It is shown that if the observer is used in connection with asymptotically stable state feedback controllers, the extended system (spacecraft, controller, and observer) is still asymptotically stable. Simulation results are reported to illustrate the dynamic behavior of the observer     

Adaptive Variable Structure Controller for Spacecraft Vibration Reduction

A hybrid control scheme to vibration reduction of flexible spacecraft is presented by using a variable structure technique for attitude control and piezoelectric materials for active vibration suppression. The attitude controller consists of a linear feedback term and a discontinuous feedback ones. An adaptive version of the proposed attitude controller is also achieved through releasing the limitation of knowing the bounds of the lumped perturbations in advance. An additional independent control system acting on the flexible parts can be designed for further vibration suppression. Simulation results have shown the theoretical and practical merit of this approach.     

刚体飞行器大角度机动的反馈非线性化控制

研究了刚体飞行器大角度的姿态控制问题,采用四元数描述刚体姿态,建立了刚体姿态运动的数学模型。基于反馈非线性化技术,通过构造李雅普诺夫函数推导出标量增益的线性控制律和矩阵增益的非线性控制律。两种控制律不需要知道系统参数,对模型误差具有鲁棒性。理论分析和仿真结果表明,所求控制律对闭环系统具有全局渐近稳定性。     

Nonlinear decoupling sliding mode control and attitude control ofspacecraft

Control of a class of uncertain nonlinear systems which can be decoupled by state-variable feedback is considered. A variable-structure-control (VSC) law is derived so that in the closed-loop system the output variables asymptotically track given output trajectories in spite of any uncertainty in the system. On the basis of this result, a control law is derived for the attitude control of an orbiting spacecraft in the presence of uncertainty using reaction jets. The controlled outputs are the three Euler angles which describe the orientation of the spacecraft relative to an orbital frame. Simulation results are presented to show that, in the closed-loop system, precise attitude control is accomplished in spite of the uncertainty in the system     

Singular formalism and admissible control of spacecraft with rotating flexible solar array

This paper is concerned with the attitude control of a three-axis-stabilized spacecraft which consists of a central rigid body and a flexible sun-tracking solar array driven by a solar array drive assembly. Based on the linearization of the dynamics of the spacecraft and the modal identi- ties about the flexible and rigid coupling matrices, the spacecraft attitude dynamics is reduced to a formally singular system with periodically varying parameters, which is quite different from a space- craft with fixed appendages. In the framework of the singular control theory, the regularity and impulse-freeness of the singular system is analyzed and then admissible attitude controllers are designed by Lyapunov＇s method. To improve the robustness against system uncertainties, an H∞ optimal control is designed by optimizing the H∞ norm of the system transfer function matrix. Comparative numerical experiments are performed to verify the theoretical results.     

Fault-tolerant control and vibration suppression of flexible spacecraft: An interconnected system approach

This paper considers a fault-tolerant control and vibration suppression problem of flexible spacecraft. The attitude dynamics is modeled by an interconnected system, in which the rigid part and the flexible part are coupled with each other. Such a model allows us to use the interconnected system approach to analyze the flexible spacecraft. Both distributed and decentralized observer-based fault-tolerant control schemes are developed, under which the closed-loop stability of flexible spacecraft can be ensured by using the cycle-small-gain theorem. Compared with the traditional method, this paper considers the faults occurred not only in the rigid parts, but also in the flexible parts. In addition, the application of the interconnected system approach simplifies the system model of flexible spacecraft, thereby the difficulty of theoretical analysis and engineering practice of fault-tolerant control of flexible spacecraft are greatly reduced. Simulation results show the effectiveness of the proposed methods and the comparison of different fault-tolerant control approach.     

Attitude coordination for spacecraft formation with multiple communication delays

Communication delays are inherently present in information exchange between spacecraft and have an effect on the control performance of spacecraft formation. In this work, attitude coordination control of spacecraft formation is addressed, which is in the presence of multiple communication delays between spacecraft. Virtual system-based approach is utilized in case that a constant reference attitude is available to only a part of the spacecraft. The feedback from the virtual systems to the spacecraft formation is introduced to maintain the formation. Using backstepping control method, input torque of each spacecraft is designed such that the attitude of each spacecraft converges asymptotically to the states of its corresponding virtual system. Furthermore, the backstepping technique and the Lyapunov–Krasovskii method contribute to the control law design when the reference attitude is time-varying and can be obtained by each spacecraft. Finally, effectiveness of the proposed methodology is illustrated by the numerical simulations of a spacecraft formation.     

Momentum transfer-based attitude control of spacecraft with backstepping

A nonlinear control law design based upon the backstepping approach is addressed for attitude maneuver control of spacecraft by momentum transfer (MT) in the presence of disturbance. For MT, a traditional method usually applies constant torque as an input, which tends to produce significant residual oscillation. Enhanced methods such as optimal control can somewhat reduce the residual oscillation, but may not be enough for minimum residual motion. Feedback linearization technique can drive the final nutation angle small enough, but it is rather sensitive to parameter uncertainty. The proposed method here takes advantage of nonlinear control approach with small steady-state nutation angle. Sensitivity about parameter uncertainties by feedback linearization can be reduced by the backstepping technique. Stability of the resulting control law is guaranteed by the Lyapunov stability theory. Boundedness of the control law is presented to validate practical merit of the proposed control law.     

基于反步法的挠性航天器姿态镇定

利用反步法研究了一类挠性航天器的姿态镇定问题,提出一种基于模态观测器的反步控制设计方案.首先,构造挠性模态观测器对挠性模态变量及其变化率进行观测;其次,将角速度看成虚拟控制器,设计虚拟角速度镇定运动学模型与挠性模态变量组成的子系统;最后,利用反步法设计了一种非线性控制器使得角速度能够跟踪虚拟角速度,从而实现姿态镇定的目...     

Control and stabilization of nonlinear uncertain elastic roboticarm

An approach is presented to the control of an uncertain nonlinear flexible robot arm (PUMA-type) with three rotational joints. The third link is assumed to be elastic. A torquer control law, which is a function of the trajectory error, is derived for controlling the joint angles. The knowledge of the system dynamics is not required for the derivation of the controller. This controller includes a reference model to generate command joint angle trajectories, and a dynamic system in the feedback path which requires only joint angle and rate for feedback. The torquer controller asymptotically decouples the elastic dynamics into two subsystems, representing the transverse vibration of the elastic link in two orthogonal planes. For the damping of the elastic vibration, a force control law using modal velocity feedback is synthesized. Simulation results are presented to show that the combination of the torque and force control law accomplishes reference joint angle trajectory tracking and elastic mode stabilization despite the uncertainty in the system     

柔性航天器大角度操纵的直接输出反馈控制

 本文研究了柔性航天器大角度操纵的控制问题,提出了直接输出反馈控制方法。证明了通过输出的线性反馈,用少量的控制器可以达到柔性航天器的渐近稳定调节。同时给出了所需控制器数目及其设置条件,并给出了直接输出反馈控制所对应的最优指标,从而实现了利用少量控制器控制高维非线性系统。     

Adaptive control and stabilization of elastic spacecraft

This work treats the question of large angle rotational maneuver and stabilization of an elastic spacecraft (spacecraft-beam-tip body configuration). It is assumed that the parameters of the system are completely unknown. An adaptive control law is derived for the rotational maneuver of the spacecraft. Using the adaptive controller, asymptotically decoupled control of the pitch angle of the space vehicle is accomplished, however this maneuver causes elastic deformation of the beam connecting the orbiter and tip body. For the stabilization of the zero dynamics (flexible dynamics), a stabilizer is designed using elastic mode velocity feedback. In the closed-loop system including the adaptive controller and the stabilizer, reference pitch angle trajectory tracking and vibration suppression are accomplished. Simulation results are presented to show the maneuver capability of the control system     

基于输出反馈的柔性航天器变结构跟踪控制方法

为解决柔性航天器姿态机动的控制问题,给出了基于输出反馈的变结构跟踪控制算法。针对柔性航天器的大角度机动,在建立了柔性航天器相对参考轨迹的动力学方程的基础上,设计了仅利用航天器本体的角度和角速度信息的变结构跟踪控制器,使得姿态状态跟踪误差(包括姿态跟踪误差和姿态角速度跟踪误差)以及挠性附件的模态变量从任意的初始状态出发都会到达包含原点的一个闭集内,并且姿态状态跟踪误差能收敛到零,并给出了严格的数学证明。仿真结果证明了所提控制方法的可行性和有效性。     

Non-fragile switching tracking control for a flexible air-breathing hypersonic vehicle based on polytopic LPV model

This article proposes a linear parameter varying (LPV) switching tracking control scheme for a flexible air-breathing hypersonic vehicle (FAHV). First, a polytopic LPV model is constructed to represent the complex nonlinear longitudinal model of the FAHV by using Jacobian linearization and tensor-product (T-P) model transformation approach. Second, for less conservative controller design purpose, the flight envelope is divided into four sub-regions and a non-fragile LPV controller is designed for each parameter sub-region. These non-fragile LPV controllers are then switched in order to guarantee the closed-loop FAHV system to be asymptotically stable and satisfy a specified performance criterion. The desired non-fragile LPV switching controller is found by solving a convex constraint problem which can be efficiently solved using available linear matrix inequality (LMI) techniques, and robust stability analysis of the closed-loop FAHV system is verified based on multiple Lypapunov functions (MLFs). Finally, numerical simulations have demonstrated the effectiveness of the proposed approach.     

考虑输入饱和的航天器相对运动鲁棒自适应控制

 研究了在输入饱和约束条件下的航天器相对运动的姿态和轨道一体化控制问题。首先,基于单位对偶四元数给出了航天器6自由度相对运动的数学模型,利用误差对偶四元数来描述航天器的相对姿态和相对位置。接着,针对输入饱和问题,提出了一种对航天器模型参数不确定性和外部有界干扰具有较强鲁棒性的自适应控制器,并通过李雅普诺夫方法从理论上严格证明了整个闭环系统的全局渐近稳定性。最后,通过数值仿真来验证设计方法的有效性和可行性,并且与其他方法进行了比较,结果表明设计的方法能够抑制输入饱和的问题,在性能上具有更快的收敛速度和更强的鲁棒性。     

利用变速控制力矩陀螺的航天器集成能量与姿态控制

 利用变速控制力矩陀螺(VSCMG)的航天器姿态与能量一体化控制问题。针对以VSCMG为姿态控制执行机构的刚体航天器设计了全局渐近稳定的姿态跟踪控制律。将VSCMG的框架角速度和转子角加速度作为控制输入向量设计操纵律。利用加权的最小范数解得到VSCMG的姿态控制输入向量，并用与之正交的控制输入向量来以给定的功率存储/释放能量。提出了同时表征力矩陀螺模式构型奇异和转子轮速平衡的混合指标函数。对控制自由度有冗余的系统，在混合指标函数的基础上利用梯度法构建了VSCMG的空转运动，以回避力矩陀螺模式的构型奇异，并同时减小转子转速差过大引起的转速饱和以及VSCMG零奇异的可能性。利用反馈转子动能的方法规划日照期间的储能功率，以维持系统长时间工作的能量平衡。基于某太阳同步轨道卫星的数值仿真结果验证了系统的有效性。