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挠性航天器振动抑制及姿态模糊控制方法研究
中文摘要

自人类发射第一颗人造卫星以来,空间技术获得了突飞猛进的发展。现代航天器上广泛存在挠性结构(如太阳能帆板和卫星天线等),挠性结构容易在航天器姿态机动过程中引起弹性振动,进而削弱姿态控制精度甚至是破坏闭环系统的稳定性。另外,外空间中持续存在的扰动力矩(如太阳辐射力矩、气动力矩、重力梯度力矩等)也会进一步加剧挠性结构的弹性振动。与此同时,受运行环境变化的影响,挠性航天器的一些物理参数很难准确获悉。显然,挠性航天器是一个多变量、刚柔模态强耦合、参数不确定且受外界扰动力矩和挠性结构弹性振动持续作用的复杂非线性系统。此外,执行机构往往还存在动作延迟、输出力矩受限等问题,在恶劣工况下甚至会发生各种故障,这些因素都大大提升了挠性航天器姿态控制系统的设计难度。 本文围绕着挠性航天器的主动振动抑制和姿态模糊控制这两个问题,进行了深入且富有创新性的研究,提出了一些新的设计方法,其主要研究内容可以归纳为: 针对航天器挠性附件的弹性振动问题,以进行单轴平转机动的挠性航天器为研究对象,提出了有限频域H〓主动控制方法,实现了弹性振动的有效抑制。与传统全频域H〓主动控制方法不同,该方法考虑到挠性结构的低频振动模态在弹性振动中往往起主导作用,故将H〓性能指标的作用区域约束在挠性结构的低频振动模态所聚集的频段,主要的控制能量被集中施加于该频段,实现了低频振动模态的充分抑制,同时也放宽了控制器设计中的约束条件,降低了设计的保守性,也因此获得了更佳的振动抑制效果。 针对挠性航天器的动力学模型,在以往研究的基础上,进一步完善了基于Takagi-Sugeno(T-S)模糊理论的建模方法,构建了挠性航天器新的T-S模糊模型,实现了使用一组局部线性模型在全局范围内以任意精度逼近挠性航天器的非线性模型的目标,为姿态模糊控制算法的研究奠定了基础。传统的姿态控制策略均依托非线性模型进行设计,然而,针对非线性系统的分析和综合的工具不足,且缺乏统一的设计方法。相比之下,针对T-S模糊系统的分析和综合方法已经非常成熟,可以借鉴现有的线性系统设计工具进行研究,这样就大大降低了挠性航天器姿态控制算法的设计难度,为解决一些在非线性模型上不易解决的控制问题提供了新思路。 针对执行机构同时存在饱和非线性及时滞影响情况下的挠性航天器的姿态控制问题,依托T-S模糊模型,提出了基于耗散理论的解决方法。其中,针对执行机构存在的时滞,构造了一类新的Lyapunov-Krasovskii泛函作为闭环系统的能量函数,充分利用了时滞信息,保证了闭环系统在输入时滞存在的条件下的渐近稳定性。此外,针对执行机构存在的饱和非线性,利用辅助矩阵的方法,补偿了饱和非线性对姿态控制的影响。耗散性能指标保证了闭环系统对挠性附件的弹性振动和外界扰动具有有效的抑制能力,提高了闭环系统的鲁棒性。此外,也分析和对比了不同耗散性能指标下的姿态控制效果,为合理设计姿态控制策略提供了指导。 针对系统存在采样信号且执行机构存在部分失效故障情况下的挠性航天器的姿态控制问题,依托T-S模糊模型,提出了一类新的采样容错控制方法。其中,针对系统中存在的采样信号,首先将闭环系统构建成连续信号和离散信号同时存在的混合系统,进而利用输入延迟的方法将其等效成一类含有特殊输入时滞的连续系统,并在此基础上进行控制算法的设计。针对执行机构存在的部分失效故障,通过数学变换,将部分失效故障中的不确定部分等效成闭环系统的一类特殊的不确定性,并利用不等式的方法进行处理。与此同时,H〓性能指标保证了闭环系统对外界扰动和挠性附件的弹性振动具有一定的抑制能力。 针对系统存在采样信号且执行机构存在随机故障情况下的挠性航天器的姿态控制问题,依托T-S模糊模型,提出了一类新的有限时间容错采样控制方法。其中,针对系统中存在的采样信号,仍然采用输入延迟的方法进行处理,且设计了一类按照采样区间分段的Lyapunov-Krasovskii泛函,能够充分刻画闭环系统中由采样保持而产生的锯齿状输入时滞,降低了所综合的控制器的保守性。针对执行机构存在的随机故障,提出了一类基于马尔科夫随机过程的控制输入模型,可以描述执行机构不同的故障模式及它们之间的随机切换行为。最后,根据所提出的有限时间的概念,建立了有限时间容错采样控制策略,使得挠性航天器的姿态在规定时间段内能够保持有界。 关键词:挠性航天器;振动抑制;姿态控制;T-S模糊系统;采样控制;有限时间

英文摘要

The space technology has received considerable development since the first spacecraft was launched. To reduce the cost, modern spacecraft widely employs flexible structures (such as solar arrays, large antennas, etc.). However, the existence of flexible structures will induce elastic vibration for flexible spacecraft. Moreover, disturbances in space (such as solar radiation torque, aerodynamic torque, gravity-gradient torque, etc.), uncertain physical parameter, actuator saturation and faults will further degrade the precision of attitude control. Clearly, flexible spacecraft is a complex nonlinear system and its attitude control problem is a difficult and challenging work. This thesis is dedicated to investigating the problem of vibration suppression and fuzzy attitude control of flexible spacecraft and proposing some novel design methods. The main contributions are summarized as follows. To solve the vibration control problem of the flexible spacecraft implementing singleaxle maneuver, a novel finite frequency H〓 control strategy is proposed, which can attenuate the elastic vibration of flexible appendages very well. Different from conventional H〓 control strategy established on entire frequency band, the proposed one notes that the low-order vibration modes of flexible appendages always play a key role in elastic vibration, so it only imposes H〓 index on the frequency range where the low-order vibration modes are located and achieves better vibration control results. The reason for it is that the main control energy is applied to chosen frequency band and the constraints of other frequency band are liberalized at the same time. When it comes to the mathematic model of flexible spacecraft, in this work TakagiSugeno (T-S) fuzzy method is employed to construct the dynamic model of flexible spacecraft. T-S fuzzy model is capable of uniformly approximating the nonlinear model of plant with any accuracy by using a set of local linear models. Based on the proposed T-S fuzzy model of flexible spacecraft, novel fuzzy attitude control strategies can be studied. It is worth mentioning that most of the existing attitude control methods for flexible spacecraft are based on nonlinear model. Since the analysis and design tools of nonlinear systems are scarce, it is difficult to design nonlinear attitude control schemes. By contrast, the analysis and deign tools for T-S fuzzy systems are resourceful, therefore, T-S fuzzy method can make it easy and open a new window for the solution to the problems which are hard to solve for nonlinear model. To solve the attitude control problem of the flexible spacecraft with actuator saturation and input delay, a novel control algorithm based on T-S fuzzy model and dissipative theorem is proposed. First, a novel Lyapunov-Krasovskii functional making full use of the information of time delay is constructed to deal with input delay, and asymptotic stability of the closed-loop system is guaranteed. Then, auxiliary-matrix method is used to compensate the effects of actuator saturation. Prescribed dissipative performance enables the closed-loop system to reject the elastic vibration of flexible appendages and external disturbances. Furthermore, the comparison of various types of performances is also implemented. To solve the attitude control problem of the flexible spacecraft with actuator faults and input sampling, a novel reliable sampled-data control algorithm based T-S fuzzy model is proposed. In this study, sampled-data control system is transformed to a continuous-time system with special input delay by input-delay method. Such that the desired controller can be designed based on this continuous-time system directly. Moreover, to cope with the partial loss of actuator effectiveness, the linear-matrix-inequality-based method is used, which converts the actuator faults into one kind of parametric uncertainty of closed-loop system. Finally, H〓 performance ensures that the closed-loop system can effectively attenuate the elastic vibration of flexible appendages and external disturbances. To solve the finite-time attitude control problem of the flexible spacecraft with stochastic actuator faults and input sampling, a novel finite-time reliable sampled-data control algorithm based on T-S fuzzy system is proposed. Here, input-delay method is also employed to handle the sampled-data control problem. Then, a novel time-dependent Lyapunov-Krasovskii functional is established, which is able to describe the sawtooth time delay induced by sample-and-hold operation, to reduce the conservatism of the synthesized controller greatly. Moreover, A novel and general input model related to Markovian variables is developed to depict the stochastic actuator faults, which is capable of covering various fault modes. Finally, with the proposed finite-time notion, the designed controller can implement finite-time attitude control of flexible spacecraft. Keywords: flexible spacecraft, vibration suppression, attitude control, T-S fuzzy system, sampled-data control, finite-time control

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