挠性航天器的刚柔耦合动力学建模与姿态控制
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摘要
本文以挠性多体航天器为研究对象，针对挠性航天器动力学特性复杂、系统不确定性突出、控制输入饱和、存在外部干扰以及高精度姿态控制要求等特点，采用理论分析与数值仿真相结合的方法，从刚柔耦合动力学建模与鲁棒姿态控制两个方面进行研究。主要工作如下：
1．建立了挠性航天器的一次近似动力学模型，分析了零次近似模型和传统控制模型的适用范围
首先，分析了空间梁的非线性变形场，采用JouTdain速度变分原理建立了柔性梁的有限元离散模型；然后，采用假设模态法和Lagrfdllge方法建立了带附加质量挠性航天器的一次近似动力学模型和一次近似控制模型；最后，从频率相对误差的角度分析了零次近似模型和传统控制模型的适用范围。
2．建立了符号计算与数值积分一体化仿真平台，仿真验证了动力刚化现象
该平台包括三大模块：符号计算模块、数值积分模块和数据分析模块。在该平台上，对刚柔耦合挠性航天器大范围姿态机动过程中产生的动力刚化现象进行了仿真验证。
理论分析和仿真结果表明：动力刚化现象是非惯性系下的结构动力学问题，柔性体变形场中的二次耦合项是产生这种现象的根本原因；一次近似模型比零次近似模型具有更广泛的适用性；一次近似控制模型能正确反映挠性航天器的动力学特性，可用于控制器设计；柔性体变形场的不同描述会导致附加质量对模型频率产生不同影响。
3．提出了模糊控制器的设计方法，设计了参数不确定挠性航天器的模糊区域控制器
首先，基于模糊区域模型和最大交叠规则组的概念，采用分段LVapunov函数法提出了Ts模糊控制器的系统化设计方法；其次，针对前提变量采用标准模糊分划的不确定Ts模糊区域模型，提出了PDc模糊区域控制器的设计方法；最后，基于挠性航天器的姿态动力学方程建立了Ts模型，设计了模糊区域控制器。仿真结果表明，模糊区域控制器对模型参数不确定性具有很好的鲁棒性，能够使挠性航天器完成高精度姿态机动和振动抑制。
4．提出了移动滑模控制器和自适应滑模控制器的设计方法，设计了控制受限挠性航天器的滑模控制器
首先，研究了受限滑模控制系统的滑模域与吸引域，提出了二阶线性系统非线性切换面的设计方法；其次，将弹性模态引入挠性航天器的状态空间方程，提出了分步滑模控制器和移动滑模控制器的设计方法；最后，提出了带模糊边界层的自适应滑模控制器，并采用智能材料设计了应变速率反馈补偿器抑制弹性振动。"仿真结果表明，受限滑模控制器对系统不确定性和外部干扰具有很好的鲁棒性，能够实现航天器的高精度姿态控制和振动抑制。
5．提出了挠性航天器惯量矩阵观测器和干扰观测器的设计方法，设计了基于观测器的挠性航天器姿态跟踪控制器
首先，针对目标姿态角速度L。。有界，目标姿态角加速度L。。和L2有界的姿态跟踪控制问题，采用Barbalat引理设计了基于模态观测器的非线性反馈姿态跟踪控制器；其次，提出了挠性航天器惯量矩阵观测器和干扰观测器的设计方法；最后，综合考虑模态坐标不可测、惯量矩阵未知和存在外部干扰的情况，设计了基于观测器的挠性航天器姿态跟踪控制器，它只需要姿态角和姿态角速度的反馈信息。
仿真结果表明，姿态跟踪控制器具有良好的鲁棒性，能够实现航天器的高精度姿态跟踪控制和振动抑制。综上所述，论文建立了挠性航天器的一次近似动力学模型；分析了刚柔耦合的机理和零次近似动力学模型的适用范围；针对参数不确定、存在外部干扰、模态坐标不可测和控制输入饱和等情况，设计了挠性航天器的Ts模糊区域控制器、受限滑模控制器和基于观测器的姿态跟踪控制器。得到的一些有意义的结论对挠性航天器姿态控制系统设计具有一定的参考价值。
Rigid-flexible coupling dynamics and robust control of flexible multi-body spacecraft are investigate in the paper, which involves the characteristics of complicated dynamic characters, system uncertainties, input nonlinearity, external disturbances and precision control requirements. The main contents and innovative work can be summarized as follows:
(1) The first-order approximate dynamic model of a flexible spacecraft is developed, the applicability of its traditional models for simulation and control are analyzed.
Firstly, the finite-element model of a flexible beam is developed by using Jourdain’s velocity variational principle, in which the second-order coupling term of axial deformation displacement caused by that of transverse is included. Secondly, the first-order approximate dynamic model and control model of a flexible spacecraft with attached mass are developed by using assumed mode method and Lagrange’s method. Finally, the applicability of zero-order approximate dynamic model and traditional control model are analyzed with respect to the relative error of the frequency.
(2) Simulation platform of symbolic and numerical compute programs is established, dynamic stiffening is validated based on this platform.
The platform consists of three modules: symbolic compute module, numerical integralization module and data analyze module. The dynamic stiffening of a flexible spacecraft undergoing large maneuvering is validated based on this platform. Numerical simulations and theoretical analysis show that, firstly, the second-order term of deformation field has a significant effect on the dynamic characteristics of the system and the dynamic stiffening is accounted for; secondly, the first-order approximate dynamic model is more adaptive than the zero-order approximate dynamic model; thirdly, the simplified first-order approximate dynamic model can be used for controller design; finally, the end mass has different effects on the model frequency according to different descriptions of deformation field.
(3) Fuzzy region controller of a flexible spacecraft with parameter uncertainty is developed.
Firstly, systematic design method of TS fuzzy controller is provided by using piecewise Lyapunov functions based on fuzzy region model and maximal overlapped-rules group. Secondly, a sufficient condition of quadratic stability of uncertain TS fuzzy region model is presented by using linear matrix inequality method and Schur complement theory, where the premise variables of the fuzzy model adopt standard fuzzy partition. Finally, dynamic equations of a flexible spacecraft are described as uncertain TS fuzzy model, where fuzzy region controller is obtained. Numerical simulation results show that, the fuzzy region controller can make the spacecraft accomplish the maneuvering with high precision and vibration suppression in spite of parameter uncertainty.
(4) Sliding mode controller of a flexible spacecraft with bounded input is developed
Firstly, the sliding mode domain and reaching domain of sliding mode control system with input nonlinearity are investigated, and the design of nonlinear switching surfaces is presented. Secondly, the step-by-step sliding mode controller and moving-surface sliding mode controller are provided with mode coordinates being taken accounted into the state space equations. Finally, adaptive sliding mode controller with fuzzy boundary layer is provided, strain rate feedback controller is designed to actively suppress the vibration of flexible appendages. Simulation results show that, the controllers are robust to parameters uncertainties and external disturbances which can make the spacecraft accomplish the maneuvering with high precision and stabilization.
(5) Attitude tracking controller of flexible spacecraft is developed based on estimators
Firstly, a nonlinear feedback tracking controller is designed by using Barbalat lemma and Lyapunov function, where the tracked attitude velocity is bounded and its derivation not only is bounded but also has limited energy. Secondly, both of inertia-estimator and disturbance-estimator are constructed. Finally, a nonlinear feedback controller based on estimators is developed, which only requires the feedback of the attitude angle and angular velocity of the flexible spacecraft. Simulation results show that, the nonlinear feedback tracking controller is effective.
In the paper, the first-order approximate dynamic model of a flexible spacecraft is developed, and the applicability of traditional models is analyzed. Then, TS fuzzy region controller, sliding mode controller and attitude tracking controller are provided for the attitude control of a flexible spacecraft, where mode coordinates are immeasurable, the inertia matrix is unknown, external disturbances exits and the control inputs are bounded. These conclusions can provide reference for modeling and attitude control of flexible spacecraft in the future.
1．建立了挠性航天器的一次近似动力学模型，分析了零次近似模型和传统控制模型的适用范围
首先，分析了空间梁的非线性变形场，采用JouTdain速度变分原理建立了柔性梁的有限元离散模型；然后，采用假设模态法和Lagrfdllge方法建立了带附加质量挠性航天器的一次近似动力学模型和一次近似控制模型；最后，从频率相对误差的角度分析了零次近似模型和传统控制模型的适用范围。
2．建立了符号计算与数值积分一体化仿真平台，仿真验证了动力刚化现象
该平台包括三大模块：符号计算模块、数值积分模块和数据分析模块。在该平台上，对刚柔耦合挠性航天器大范围姿态机动过程中产生的动力刚化现象进行了仿真验证。
理论分析和仿真结果表明：动力刚化现象是非惯性系下的结构动力学问题，柔性体变形场中的二次耦合项是产生这种现象的根本原因；一次近似模型比零次近似模型具有更广泛的适用性；一次近似控制模型能正确反映挠性航天器的动力学特性，可用于控制器设计；柔性体变形场的不同描述会导致附加质量对模型频率产生不同影响。
3．提出了模糊控制器的设计方法，设计了参数不确定挠性航天器的模糊区域控制器
首先，基于模糊区域模型和最大交叠规则组的概念，采用分段LVapunov函数法提出了Ts模糊控制器的系统化设计方法；其次，针对前提变量采用标准模糊分划的不确定Ts模糊区域模型，提出了PDc模糊区域控制器的设计方法；最后，基于挠性航天器的姿态动力学方程建立了Ts模型，设计了模糊区域控制器。仿真结果表明，模糊区域控制器对模型参数不确定性具有很好的鲁棒性，能够使挠性航天器完成高精度姿态机动和振动抑制。
4．提出了移动滑模控制器和自适应滑模控制器的设计方法，设计了控制受限挠性航天器的滑模控制器
首先，研究了受限滑模控制系统的滑模域与吸引域，提出了二阶线性系统非线性切换面的设计方法；其次，将弹性模态引入挠性航天器的状态空间方程，提出了分步滑模控制器和移动滑模控制器的设计方法；最后，提出了带模糊边界层的自适应滑模控制器，并采用智能材料设计了应变速率反馈补偿器抑制弹性振动。"仿真结果表明，受限滑模控制器对系统不确定性和外部干扰具有很好的鲁棒性，能够实现航天器的高精度姿态控制和振动抑制。
5．提出了挠性航天器惯量矩阵观测器和干扰观测器的设计方法，设计了基于观测器的挠性航天器姿态跟踪控制器
首先，针对目标姿态角速度L。。有界，目标姿态角加速度L。。和L2有界的姿态跟踪控制问题，采用Barbalat引理设计了基于模态观测器的非线性反馈姿态跟踪控制器；其次，提出了挠性航天器惯量矩阵观测器和干扰观测器的设计方法；最后，综合考虑模态坐标不可测、惯量矩阵未知和存在外部干扰的情况，设计了基于观测器的挠性航天器姿态跟踪控制器，它只需要姿态角和姿态角速度的反馈信息。
仿真结果表明，姿态跟踪控制器具有良好的鲁棒性，能够实现航天器的高精度姿态跟踪控制和振动抑制。综上所述，论文建立了挠性航天器的一次近似动力学模型；分析了刚柔耦合的机理和零次近似动力学模型的适用范围；针对参数不确定、存在外部干扰、模态坐标不可测和控制输入饱和等情况，设计了挠性航天器的Ts模糊区域控制器、受限滑模控制器和基于观测器的姿态跟踪控制器。得到的一些有意义的结论对挠性航天器姿态控制系统设计具有一定的参考价值。
Rigid-flexible coupling dynamics and robust control of flexible multi-body spacecraft are investigate in the paper, which involves the characteristics of complicated dynamic characters, system uncertainties, input nonlinearity, external disturbances and precision control requirements. The main contents and innovative work can be summarized as follows:
(1) The first-order approximate dynamic model of a flexible spacecraft is developed, the applicability of its traditional models for simulation and control are analyzed.
Firstly, the finite-element model of a flexible beam is developed by using Jourdain’s velocity variational principle, in which the second-order coupling term of axial deformation displacement caused by that of transverse is included. Secondly, the first-order approximate dynamic model and control model of a flexible spacecraft with attached mass are developed by using assumed mode method and Lagrange’s method. Finally, the applicability of zero-order approximate dynamic model and traditional control model are analyzed with respect to the relative error of the frequency.
(2) Simulation platform of symbolic and numerical compute programs is established, dynamic stiffening is validated based on this platform.
The platform consists of three modules: symbolic compute module, numerical integralization module and data analyze module. The dynamic stiffening of a flexible spacecraft undergoing large maneuvering is validated based on this platform. Numerical simulations and theoretical analysis show that, firstly, the second-order term of deformation field has a significant effect on the dynamic characteristics of the system and the dynamic stiffening is accounted for; secondly, the first-order approximate dynamic model is more adaptive than the zero-order approximate dynamic model; thirdly, the simplified first-order approximate dynamic model can be used for controller design; finally, the end mass has different effects on the model frequency according to different descriptions of deformation field.
(3) Fuzzy region controller of a flexible spacecraft with parameter uncertainty is developed.
Firstly, systematic design method of TS fuzzy controller is provided by using piecewise Lyapunov functions based on fuzzy region model and maximal overlapped-rules group. Secondly, a sufficient condition of quadratic stability of uncertain TS fuzzy region model is presented by using linear matrix inequality method and Schur complement theory, where the premise variables of the fuzzy model adopt standard fuzzy partition. Finally, dynamic equations of a flexible spacecraft are described as uncertain TS fuzzy model, where fuzzy region controller is obtained. Numerical simulation results show that, the fuzzy region controller can make the spacecraft accomplish the maneuvering with high precision and vibration suppression in spite of parameter uncertainty.
(4) Sliding mode controller of a flexible spacecraft with bounded input is developed
Firstly, the sliding mode domain and reaching domain of sliding mode control system with input nonlinearity are investigated, and the design of nonlinear switching surfaces is presented. Secondly, the step-by-step sliding mode controller and moving-surface sliding mode controller are provided with mode coordinates being taken accounted into the state space equations. Finally, adaptive sliding mode controller with fuzzy boundary layer is provided, strain rate feedback controller is designed to actively suppress the vibration of flexible appendages. Simulation results show that, the controllers are robust to parameters uncertainties and external disturbances which can make the spacecraft accomplish the maneuvering with high precision and stabilization.
(5) Attitude tracking controller of flexible spacecraft is developed based on estimators
Firstly, a nonlinear feedback tracking controller is designed by using Barbalat lemma and Lyapunov function, where the tracked attitude velocity is bounded and its derivation not only is bounded but also has limited energy. Secondly, both of inertia-estimator and disturbance-estimator are constructed. Finally, a nonlinear feedback controller based on estimators is developed, which only requires the feedback of the attitude angle and angular velocity of the flexible spacecraft. Simulation results show that, the nonlinear feedback tracking controller is effective.
In the paper, the first-order approximate dynamic model of a flexible spacecraft is developed, and the applicability of traditional models is analyzed. Then, TS fuzzy region controller, sliding mode controller and attitude tracking controller are provided for the attitude control of a flexible spacecraft, where mode coordinates are immeasurable, the inertia matrix is unknown, external disturbances exits and the control inputs are bounded. These conclusions can provide reference for modeling and attitude control of flexible spacecraft in the future.
引文
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