航天器姿态控制的正规矩阵方法研究
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摘要
航天器依赖其上的控制系统以完成飞行使命。随着发展,航天器的构造越来越复杂,性能要求也越来越高,为航天器姿态控制系统的设计带来了挑战。基于此,本论文研究正规矩阵设计方法在航天器姿态控制律设计中的应用问题。
本论文以可建模为具有存储角动量和柔性附件的中心刚体的航天器为研究对象,首先建立了系统的动力学模型,并分析了其频域线性化模型的正规矩阵特性、对角优势特性、以及零极点分布特性。基于分析结果,先后研究了刚体航天器姿态稳定、柔性航天器姿态稳定、以及航天器姿态机动的正规矩阵控制问题。对乘性摄动和逆加摄动两种不确定性下的设计进行了比较。研究了闭环内输入成形技术,并将其应用于柔性航天器姿态稳定问题中。结合反馈线性化技术为航天器大角度姿态机动设计了正规矩阵控制律。基于Hamilton-Jacobi-Isaacs不等式为姿态跟随问题设计了非线性H∞正规矩阵控制律。
对航天器动力学特性的研究表明:(1)航天器的动力学模型不是正规矩阵,影响其正规矩阵特性的主要因素在于柔性运动、以及惯性积和存储角动量与轨道角速度之间的耦合;(2)航天器动力学的传输零点不受存储角动量的影响,仍然是柔性附件振动的各约束模态频率,但其系统极点不再是柔性振动的各非约束模态频率,而是由一个奇数维广义陀螺特征值问题确定;(3)最大最小主惯性矩之比满足约束的刚体,其惯性张量在任意建立的质心体坐标系内都是对角优势矩阵,这使得航天器动力学传递函数矩阵一般可视为对角优势矩阵。
在航天器姿态稳定的正规矩阵控制中,使用逆加摄动不确定性描述比使用乘性摄动有更多优势。在逆加摄动描述下,可以方便的校正使系统偏离正规矩阵特性的因素。而且,在逆加摄动描述下,正规矩阵设计条件仅对控制律中部分参数提出要求,而将其它参数释放出来以供协调三轴性能要求使用。
与传统输入成形一样,闭环内输入成形器也能抑制振动,并具有对振动频率摄动的鲁棒性,能够同时抑制设计频率及其各奇数次倍频邻域内的振动。但与传统输入成形不同,闭环内输入成形不能单独抑制设计频率的奇数次倍频。将闭环内输入成形系统视为各时滞间具有严格倍数关系的特殊的多时滞系统,给出了其渐近稳定和鲁棒稳定的LMI判据。通过分析多模态系统中各模态频率之间的关系,可以有效地缩短闭环内输入成形持续时间并简化输入成形器设计。将闭环内输入成形应用于柔性航天器,可以在获得振动抑制效果的同时,提高系统的正规性。
为将正规矩阵设计方法扩展到非线性姿态机动问题中,将其与反馈线性化技术相结合,为大角度姿态机动设计了正规矩阵控制律,并同时使用闭环内和闭环外两种输入成形器,分别抑制柔性振动和刚体振荡,提高控制快速性和精度。结合姿态跟随问题,设计了基于姿态误差模型的正规矩阵姿态机动控制,该正规矩阵控制律被证明是非线性姿态跟随问题的非线性H_∞解。
数值仿真结果验证了文中理论分析和设计结果的正确性和有效性。
Spacecraft rely heavily on the effectiveness of complex onboard control systems.Currently, the structures of spacecraft are more and more complex, and the performancerequirements are higher and higher. These challenge the designing of spacecraft attitudecontrol systems. The present thesis is focused on the application issues of the normalmatrix design approach on the attitude control of spacecraft.
The researches are based on the spacecraft that can be regarded as a central rigid-body with stored angular momentum and some ?exible appendages attached. Firstly, thesystem’s dynamical model is derived, and the characteristics of the normal matrix, diago-nally dominant, and the distribution of poles and zeros of the linearized dynamical modelin frequency domain are analyzed carefully. Based on these analysis results, the normalmatrix control problems are considered for the attitude stabilization of rigid and ?exiblespacecraft, and for the attitude maneuver of spacecraft. A comparison is made betweentwo uncertainty descriptions: the multiplicative perturbation and inverse-additive pertur-bation. The inside-the-loop input shaping is studied and applied to the attitude stabiliza-tion of ?exible spacecraft. The feedback linearization is employed in the designing ofnormal matrix control law for large angle attitude maneuvering, and the nonlinear H∞normal matrix control law is designed by using the Hamilton-Jacobi-Isaacs inequality forthe attitude tracking problem.
The research on the characteristics of spacecraft dynamics show that, (i) the dy-namics model of spacecraft is generally not the normal matrix, and the main factors thataffect the normality are the ?exible motions and the coupling between the products ofinertia, stored angular momentum, and the orbit velocity. (ii) The transmission zeros arestill the constrained modal frequencies of ?exible appendages regardless of the storedangular momentum, but the unconstrained modal frequencies are no longer the systempoles. The system poles are determined by a odd-dimension eigenvalue problem of gen-eralized gyroscopic system when the stored angular momentum occur. (iii) The inertiatensor of a rigid body in any centroid body-fixed coordinate is a diagonally dominant ma-trix if the maximum and minimum principle moments of inertia meet a given condition.Therefore, the transfer function matrix of spacecraft dynamics are generally regarded asa diagonally dominant matrix.
For the normal matrix control of spacecraft attitude stabilization, the usage of the inverse-additive perturbation can bring more advantages to the system than that of themultiplicative perturbation. With the uncertainty descriptions of the inverse-additive per-turbation, the improvement of the system’s normality is more convenient, and only partof the parameters in the control law are included in the normal-matrix design condition,therefore the others are freed and can be used in the trade-off among performance re-quirements of the three loops.
Like the traditional input shaping, the inside-the-loop input shaper can suppressthe vibrations, has robustness to the alteration of the vibration frequencies, and can si-multaneously suppress the vibrations of the design frequency and its odd-number timesfrequencies. But unlike traditional input shaping, the inside-the-loop input shaper cannot suppress the vibration of a single odd, for example, 3 or 5, times frequency. TheLMI criteria of asymptotic and robust stability are derived for the inside-the-loop inputshaping system, which is regarded as a special case of multi-delay system with delays ofmultiple relationship. The relationships among the modal frequencies in the multi-modesystem can be used in the saving of the shaping time of inside-the-loop input shaper andthe reduction of the input shaper effectively. The system’s robustness can be improvedby inserting the inside-the-loop input shaper into the attitude control loops of the ?exiblespacecraft besides the vibration suppression.
For the applications of the normal matrix design methodology to nonlinear attitudemaneuver control problems, the normal matrix control approach are combined with thefeedback linearlization. The normal matrix control law is derived for the large angle at-titude maneuver problem, and both the inside-the-loop input shaper, for the suppressionof the ?exible vibrations, and the outside-the-loop input shaper, for the reduction of therigid oscillation, are employed to promoting the precision and response speed of the sys-tem. For the attitude tracking problem, the normal matrix control law is designed basedon the attitude error dynamics model, and the control law is proved to be a nonlinear H_∞control law for the nonlinear attitude tracking problem.
The computer simulation results demonstrate the validity and effectiveness of thetheoretic analysis and design results in the present dissertation.
本论文以可建模为具有存储角动量和柔性附件的中心刚体的航天器为研究对象,首先建立了系统的动力学模型,并分析了其频域线性化模型的正规矩阵特性、对角优势特性、以及零极点分布特性。基于分析结果,先后研究了刚体航天器姿态稳定、柔性航天器姿态稳定、以及航天器姿态机动的正规矩阵控制问题。对乘性摄动和逆加摄动两种不确定性下的设计进行了比较。研究了闭环内输入成形技术,并将其应用于柔性航天器姿态稳定问题中。结合反馈线性化技术为航天器大角度姿态机动设计了正规矩阵控制律。基于Hamilton-Jacobi-Isaacs不等式为姿态跟随问题设计了非线性H∞正规矩阵控制律。
对航天器动力学特性的研究表明:(1)航天器的动力学模型不是正规矩阵,影响其正规矩阵特性的主要因素在于柔性运动、以及惯性积和存储角动量与轨道角速度之间的耦合;(2)航天器动力学的传输零点不受存储角动量的影响,仍然是柔性附件振动的各约束模态频率,但其系统极点不再是柔性振动的各非约束模态频率,而是由一个奇数维广义陀螺特征值问题确定;(3)最大最小主惯性矩之比满足约束的刚体,其惯性张量在任意建立的质心体坐标系内都是对角优势矩阵,这使得航天器动力学传递函数矩阵一般可视为对角优势矩阵。
在航天器姿态稳定的正规矩阵控制中,使用逆加摄动不确定性描述比使用乘性摄动有更多优势。在逆加摄动描述下,可以方便的校正使系统偏离正规矩阵特性的因素。而且,在逆加摄动描述下,正规矩阵设计条件仅对控制律中部分参数提出要求,而将其它参数释放出来以供协调三轴性能要求使用。
与传统输入成形一样,闭环内输入成形器也能抑制振动,并具有对振动频率摄动的鲁棒性,能够同时抑制设计频率及其各奇数次倍频邻域内的振动。但与传统输入成形不同,闭环内输入成形不能单独抑制设计频率的奇数次倍频。将闭环内输入成形系统视为各时滞间具有严格倍数关系的特殊的多时滞系统,给出了其渐近稳定和鲁棒稳定的LMI判据。通过分析多模态系统中各模态频率之间的关系,可以有效地缩短闭环内输入成形持续时间并简化输入成形器设计。将闭环内输入成形应用于柔性航天器,可以在获得振动抑制效果的同时,提高系统的正规性。
为将正规矩阵设计方法扩展到非线性姿态机动问题中,将其与反馈线性化技术相结合,为大角度姿态机动设计了正规矩阵控制律,并同时使用闭环内和闭环外两种输入成形器,分别抑制柔性振动和刚体振荡,提高控制快速性和精度。结合姿态跟随问题,设计了基于姿态误差模型的正规矩阵姿态机动控制,该正规矩阵控制律被证明是非线性姿态跟随问题的非线性H_∞解。
数值仿真结果验证了文中理论分析和设计结果的正确性和有效性。
Spacecraft rely heavily on the effectiveness of complex onboard control systems.Currently, the structures of spacecraft are more and more complex, and the performancerequirements are higher and higher. These challenge the designing of spacecraft attitudecontrol systems. The present thesis is focused on the application issues of the normalmatrix design approach on the attitude control of spacecraft.
The researches are based on the spacecraft that can be regarded as a central rigid-body with stored angular momentum and some ?exible appendages attached. Firstly, thesystem’s dynamical model is derived, and the characteristics of the normal matrix, diago-nally dominant, and the distribution of poles and zeros of the linearized dynamical modelin frequency domain are analyzed carefully. Based on these analysis results, the normalmatrix control problems are considered for the attitude stabilization of rigid and ?exiblespacecraft, and for the attitude maneuver of spacecraft. A comparison is made betweentwo uncertainty descriptions: the multiplicative perturbation and inverse-additive pertur-bation. The inside-the-loop input shaping is studied and applied to the attitude stabiliza-tion of ?exible spacecraft. The feedback linearization is employed in the designing ofnormal matrix control law for large angle attitude maneuvering, and the nonlinear H∞normal matrix control law is designed by using the Hamilton-Jacobi-Isaacs inequality forthe attitude tracking problem.
The research on the characteristics of spacecraft dynamics show that, (i) the dy-namics model of spacecraft is generally not the normal matrix, and the main factors thataffect the normality are the ?exible motions and the coupling between the products ofinertia, stored angular momentum, and the orbit velocity. (ii) The transmission zeros arestill the constrained modal frequencies of ?exible appendages regardless of the storedangular momentum, but the unconstrained modal frequencies are no longer the systempoles. The system poles are determined by a odd-dimension eigenvalue problem of gen-eralized gyroscopic system when the stored angular momentum occur. (iii) The inertiatensor of a rigid body in any centroid body-fixed coordinate is a diagonally dominant ma-trix if the maximum and minimum principle moments of inertia meet a given condition.Therefore, the transfer function matrix of spacecraft dynamics are generally regarded asa diagonally dominant matrix.
For the normal matrix control of spacecraft attitude stabilization, the usage of the inverse-additive perturbation can bring more advantages to the system than that of themultiplicative perturbation. With the uncertainty descriptions of the inverse-additive per-turbation, the improvement of the system’s normality is more convenient, and only partof the parameters in the control law are included in the normal-matrix design condition,therefore the others are freed and can be used in the trade-off among performance re-quirements of the three loops.
Like the traditional input shaping, the inside-the-loop input shaper can suppressthe vibrations, has robustness to the alteration of the vibration frequencies, and can si-multaneously suppress the vibrations of the design frequency and its odd-number timesfrequencies. But unlike traditional input shaping, the inside-the-loop input shaper cannot suppress the vibration of a single odd, for example, 3 or 5, times frequency. TheLMI criteria of asymptotic and robust stability are derived for the inside-the-loop inputshaping system, which is regarded as a special case of multi-delay system with delays ofmultiple relationship. The relationships among the modal frequencies in the multi-modesystem can be used in the saving of the shaping time of inside-the-loop input shaper andthe reduction of the input shaper effectively. The system’s robustness can be improvedby inserting the inside-the-loop input shaper into the attitude control loops of the ?exiblespacecraft besides the vibration suppression.
For the applications of the normal matrix design methodology to nonlinear attitudemaneuver control problems, the normal matrix control approach are combined with thefeedback linearlization. The normal matrix control law is derived for the large angle at-titude maneuver problem, and both the inside-the-loop input shaper, for the suppressionof the ?exible vibrations, and the outside-the-loop input shaper, for the reduction of therigid oscillation, are employed to promoting the precision and response speed of the sys-tem. For the attitude tracking problem, the normal matrix control law is designed basedon the attitude error dynamics model, and the control law is proved to be a nonlinear H_∞control law for the nonlinear attitude tracking problem.
The computer simulation results demonstrate the validity and effectiveness of thetheoretic analysis and design results in the present dissertation.
引文
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