带有输入饱和的挠性航天器姿态跟踪鲁棒控制研究
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摘要
在实际的航天任务中,燃料的消耗、有效载荷的运动以及挠性附件(如太阳能帆板、天线等)的振动,致使航天器的惯量参数是时变的且不能精确获知;同时在轨航天器又不可避免地受到各种外部干扰的作用(如太阳光压、气动力矩等),这些因素使得航天器姿态控制系统是一个变参数、强耦合以及存在外干扰的多变量非线性系统。此外由于执行机构自身的物理限制,导致其输出是饱和受限的,这种饱和特性的存在将大大降低航天器姿态控制性能,严重时将导致闭环系统不稳定,从而使整个航天任务失败。因此针对上述问题,设计一种控制方法确保带有执行机构饱和非线性的挠性航天器姿态跟踪控制具有很好的跟踪性能便显得十分重要。正是在这种背景下,本论文结合国家自然科学基金(60774062)、高等学校博士学科点专项科研基金(20070213061)等基础研究课题,从理论和应用两方面对挠性航天器的动力学建模、姿态跟踪控制等方面进行了深入的研究,其研究内容主要包括以下几个方面:
首先,根据欧拉定理分别建立了用欧拉角和四元数描述的挠性航天器姿态运动学方程;并基于真—伪坐标形式的Lagrange方程,利用Hamilton原理建立了挠性航天器的动力学模型,且应用模态分析法,进一步将挠性航天器的耦合方程规范化,使之适用于姿态跟踪控制系统的分析与设计。
其次,针对转动惯量未知、存在外部干扰以及控制输入饱和受限的轮控挠性航天器姿态跟踪问题,基于其线性化后的姿态运动学方程,利用自适应反步控制提出了两种不同的姿态跟踪鲁棒控制方法:第一种控制方法将反步控制与L_2增益控制相结合,它通过设计一个鲁棒控制器和构造一个附加的输入误差信号系统,使所设计的控制器在其幅值不超过执行机构最大输出力矩的同时,保证闭环系统的一致最终有界稳定性且姿态跟踪性能对外部干扰具有??2小增益。为了克服第一种方法只能保证姿态有界跟踪的缺点,充分利用滑模控制对系统不确定性的鲁棒控制能力,又提出了一种自适应反步滑模控制策略,并基于Lyapunov方法证明了该控制方法能够实现对期望姿态的全局渐近跟踪控制。仿真结果表明上述所设计的两种方法在实现姿态高精度跟踪控制的同时,对系统不确定性和外部干扰具有很强的鲁棒性。
同时,针对挠性航天器模型中存在参数不确定性、控制输入受限及外部干扰的姿态跟踪控制问题,提出了一种非线性姿态输出反馈控制方法。该方法用神经网络来逼近和估计系统中的不确定项、未知挠性部件振动模态以及外部干扰;运用有界的反正切函数来设计控制器,从而保证所设计的控制器在执行机构输出受限且不需要任何角速度测量信息的情况下实现对姿态跟踪误差的一致最终有界稳定控制。仿真结果表明,尽管不需要角速度反馈且存在受限的控制输入,所设计的控制器不但可以快速地、高精度地完成姿态跟踪操作,而且对系统不确定性具有很强的鲁棒性。
最后,将上述研究结果应用于某型挠性航天器进行大量的数学仿真,仿真结果进一步验证本文设计的三种姿态跟踪控制方案能够有效地处理系统不确定性、外部干扰以及控制输入饱和受限问题。
In practical space missions, note that during operation the mass properties of thespacecraft may be uncertain or may change due to onboard payload motion, rotation offlexible appendages such as solar arrays, or fuel consumptions, and an orbital spacecraftis also affected by external disturbances, such as solar radiation, aerodynamic drags, etc.All these issues lead to the uncertain coupling nonlinear attitude system with multi-inputand multi-output. Moreover, due to physical limitation, momentum exchange devices orthrusters as actuator for the spacecraft attitude control plant fail to render infinite controltorque and thus the actuator outputs are constantly bounded or constrained. Once the ac-tuator reaches its input limit, the efforts to further increase the actuator output would notresult in any variation in the output, and then this usually deteriorates the system perfor-mance and even results in system instability. Consequently, it is very desirable to takeinput saturation into account during the attitude controller design. In this thesis, dynamicmodeling of spacecraft with ?exible appendages and attitude tracking control are deeplystudied, which is funded by the National Natural Science Foundation of China(ProjectNumber: 60774062) and the Research Fund of the Doctoral Program of Higher Educa-tion of China(Project Number: 20070213061), and the main contents of this thesis arepresented as follows:
Firstly, flexible spacecraft attitude kinematics described by Euler angle and unitquaternion is presented based upon Euler Theorem, and an approximately analytical dy-namic model of spacecraft is derived using Hamilton’s principle with discretization bythe assumed mode method. The obtained mathematical model is then converted to statespace form for the purpose of attitude tracking control design.Secondly, two robust adaptive backstepping attitude tracking control schemes aredeveloped for a moment exchange devices controlled spacecraft based on the linearizedattitude kinematics, in which the unknown inertia matrix, disturbances torques and in-put saturation are considered. The first control strategy combines backstepping techniquewith L_2 gain control. In this approach, a robust controller and an auxiliary input signalerror system are incorporated to treat the input saturation problem. Although ??2 trackingperformance with the desirable attenuation level to disturbances can be achieved with this proposed control scheme, it can only guarantee uniformly ultimately bounded stability ofattitude tracking error. For the purpose of achieving globally asymptotically attitude track-ing control, an adaptive backstepping sliding mode control scheme is then proposed withthe advantages of sliding mode control for its robustness to system unmodeled dynamic.Furthermore, the benefits of these two control approaches are analytically authenticatedand also validated via simulation study.
Moreover, a theoretical framework for attitude tracking control using quaternionmeasurements only is developed and applied to the flexible spacecraft with external dis-turbance, parameter uncertainties and control input constraint taken into account simul-taneously. In contrast to the most existing approaches, the proposed controller does notrequire the knowledge of body angular velocity and the flexible modal vibrations as well.By employing neural network approximate technique, the problem of unknown systemdynamics is explicitly addressed in the control design. In the closed-loop systems, it isshown that uniform ultimate boundedness of all signals is guaranteed, and the attitudecan track the reference trajectories as close as possible. Moreover, the derived adaptiveattitude tracking controller can ensure that the controller rigorously enforces actuator-magnitude saturation constraints. Numerical simulation results are also presented whichnot only highlights the ensuring closed-loop performance benefits from the control lawderived here but also illustrates its robustness in face of external disturbances and systemuncertainties.
Last but not least, the details of system responses are numerically simulated in anorbital flexible spacecraft in conjunction with the above proposed three novel attitudetracking control laws. It is shown that parametric uncertainty and unmodeled dynamicof the attitude system, external disturbances and even input saturation can be explicitlyaddressed by our proposed controllers with perfect attitude tracking performance guar-anteed. Moreover, theirs benefits of theoretical and engineering practice are also high-lighted.
首先,根据欧拉定理分别建立了用欧拉角和四元数描述的挠性航天器姿态运动学方程;并基于真—伪坐标形式的Lagrange方程,利用Hamilton原理建立了挠性航天器的动力学模型,且应用模态分析法,进一步将挠性航天器的耦合方程规范化,使之适用于姿态跟踪控制系统的分析与设计。
其次,针对转动惯量未知、存在外部干扰以及控制输入饱和受限的轮控挠性航天器姿态跟踪问题,基于其线性化后的姿态运动学方程,利用自适应反步控制提出了两种不同的姿态跟踪鲁棒控制方法:第一种控制方法将反步控制与L_2增益控制相结合,它通过设计一个鲁棒控制器和构造一个附加的输入误差信号系统,使所设计的控制器在其幅值不超过执行机构最大输出力矩的同时,保证闭环系统的一致最终有界稳定性且姿态跟踪性能对外部干扰具有??2小增益。为了克服第一种方法只能保证姿态有界跟踪的缺点,充分利用滑模控制对系统不确定性的鲁棒控制能力,又提出了一种自适应反步滑模控制策略,并基于Lyapunov方法证明了该控制方法能够实现对期望姿态的全局渐近跟踪控制。仿真结果表明上述所设计的两种方法在实现姿态高精度跟踪控制的同时,对系统不确定性和外部干扰具有很强的鲁棒性。
同时,针对挠性航天器模型中存在参数不确定性、控制输入受限及外部干扰的姿态跟踪控制问题,提出了一种非线性姿态输出反馈控制方法。该方法用神经网络来逼近和估计系统中的不确定项、未知挠性部件振动模态以及外部干扰;运用有界的反正切函数来设计控制器,从而保证所设计的控制器在执行机构输出受限且不需要任何角速度测量信息的情况下实现对姿态跟踪误差的一致最终有界稳定控制。仿真结果表明,尽管不需要角速度反馈且存在受限的控制输入,所设计的控制器不但可以快速地、高精度地完成姿态跟踪操作,而且对系统不确定性具有很强的鲁棒性。
最后,将上述研究结果应用于某型挠性航天器进行大量的数学仿真,仿真结果进一步验证本文设计的三种姿态跟踪控制方案能够有效地处理系统不确定性、外部干扰以及控制输入饱和受限问题。
In practical space missions, note that during operation the mass properties of thespacecraft may be uncertain or may change due to onboard payload motion, rotation offlexible appendages such as solar arrays, or fuel consumptions, and an orbital spacecraftis also affected by external disturbances, such as solar radiation, aerodynamic drags, etc.All these issues lead to the uncertain coupling nonlinear attitude system with multi-inputand multi-output. Moreover, due to physical limitation, momentum exchange devices orthrusters as actuator for the spacecraft attitude control plant fail to render infinite controltorque and thus the actuator outputs are constantly bounded or constrained. Once the ac-tuator reaches its input limit, the efforts to further increase the actuator output would notresult in any variation in the output, and then this usually deteriorates the system perfor-mance and even results in system instability. Consequently, it is very desirable to takeinput saturation into account during the attitude controller design. In this thesis, dynamicmodeling of spacecraft with ?exible appendages and attitude tracking control are deeplystudied, which is funded by the National Natural Science Foundation of China(ProjectNumber: 60774062) and the Research Fund of the Doctoral Program of Higher Educa-tion of China(Project Number: 20070213061), and the main contents of this thesis arepresented as follows:
Firstly, flexible spacecraft attitude kinematics described by Euler angle and unitquaternion is presented based upon Euler Theorem, and an approximately analytical dy-namic model of spacecraft is derived using Hamilton’s principle with discretization bythe assumed mode method. The obtained mathematical model is then converted to statespace form for the purpose of attitude tracking control design.Secondly, two robust adaptive backstepping attitude tracking control schemes aredeveloped for a moment exchange devices controlled spacecraft based on the linearizedattitude kinematics, in which the unknown inertia matrix, disturbances torques and in-put saturation are considered. The first control strategy combines backstepping techniquewith L_2 gain control. In this approach, a robust controller and an auxiliary input signalerror system are incorporated to treat the input saturation problem. Although ??2 trackingperformance with the desirable attenuation level to disturbances can be achieved with this proposed control scheme, it can only guarantee uniformly ultimately bounded stability ofattitude tracking error. For the purpose of achieving globally asymptotically attitude track-ing control, an adaptive backstepping sliding mode control scheme is then proposed withthe advantages of sliding mode control for its robustness to system unmodeled dynamic.Furthermore, the benefits of these two control approaches are analytically authenticatedand also validated via simulation study.
Moreover, a theoretical framework for attitude tracking control using quaternionmeasurements only is developed and applied to the flexible spacecraft with external dis-turbance, parameter uncertainties and control input constraint taken into account simul-taneously. In contrast to the most existing approaches, the proposed controller does notrequire the knowledge of body angular velocity and the flexible modal vibrations as well.By employing neural network approximate technique, the problem of unknown systemdynamics is explicitly addressed in the control design. In the closed-loop systems, it isshown that uniform ultimate boundedness of all signals is guaranteed, and the attitudecan track the reference trajectories as close as possible. Moreover, the derived adaptiveattitude tracking controller can ensure that the controller rigorously enforces actuator-magnitude saturation constraints. Numerical simulation results are also presented whichnot only highlights the ensuring closed-loop performance benefits from the control lawderived here but also illustrates its robustness in face of external disturbances and systemuncertainties.
Last but not least, the details of system responses are numerically simulated in anorbital flexible spacecraft in conjunction with the above proposed three novel attitudetracking control laws. It is shown that parametric uncertainty and unmodeled dynamicof the attitude system, external disturbances and even input saturation can be explicitlyaddressed by our proposed controllers with perfect attitude tracking performance guar-anteed. Moreover, theirs benefits of theoretical and engineering practice are also high-lighted.
引文
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