复杂机构结构太阳帆航天器动力学建模与控制问题研究
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摘要
具有独特推进优势的航天器一直是航天领域研究重点与关注焦点之一。太阳帆这类以光压为动力的新型航天器已成为航天界研究热点之一。因其具有“轻质巨大”、“几何非线性”、“结构机构复杂”等实际力学与机械特性，对太阳帆在轨运行具有重要影响。因此本文对太阳帆结构静力学、结构动力学、姿态动力学、刚柔耦合动力学与控制等问题开展研究，具体研究内容如下：
第一，对考虑结构几何非线性的太阳帆进行静力学分析及基于此的推力模型折损研究。将方形太阳帆支撑杆视为主体刚度支撑结构，认为帆面随之形变而形变。在帆面太阳角变化较缓情况下，针对帆面与支撑杆为两点和无穷点两种连接方式，对支撑杆受光压静力作用进行静力学研究。首先基于虚功原理建立单元有限元平衡方程，而后集成为整体结构有限元模型，并结合边界条件对所得方程组进行缩减处理，再基于牛顿迭代算法对缩减后的方程组进行数值求解。基于此给出太阳帆因形变而导致的推力折损分析。计算结果说明，支撑杆的非线性轴向位移较大，且相同参数条件下无穷点连接方式下的推力折损小于两点连接方式下的推力折损；
第二，对考虑结构几何非线性的太阳帆进行结构动力学建模与计算。视支撑杆为主体刚度支撑结构，对其进行光压静力、滑动质量块、摆动的控制叶片等综合作用下的振动分析。首先使用拉格朗日方程方法建立了无穷点连接方式下支撑杆轴向和横向振动微分方程组，模型具有明显的强耦合、非线性和系数矩阵时变等特点。使用隐式无条件稳定的纽马克-贝塔算法将每个时间步的动力学方程组转化为非线性代数方程组，基于牛顿迭代算法对所得方程组进行求解分析。并对滑块质量、滑块滑动速度及控制叶片作用力的角速度对结构振动响应的影响进行分析。计算结果说明滑块质量和滑动速度对支撑杆振动有一定影响，而控制叶片作用力的角速度对振动响应的影响较微弱；
第三，对考虑控制杆、滑动质量块、控制叶片等复杂机构作用下的大柔性太阳帆进行姿态动力学建模。给定太阳帆基本构型与假设，给出坐标系定义、广义坐标选取和相应坐标变换。给出有效载荷、滑块和支撑杆的位置和速度及相关能量。求取控制叶片广义外力矩。最终基于拉格朗日方程方法建立太阳帆姿态动力学方程，模型具有很强的非线性耦合特点。本章工作为太阳帆刚柔耦合动力学分析与控制奠定基础；
第四，对在轨正常运行的太阳帆进行刚柔耦合动力学与控制研究。在前述结构振动建模和姿态动力学建模基础之上经简化得到用于姿态/振动控制和动力学仿真的刚柔耦合动力学方程。以地球静止轨道上的太阳帆轨道提升任务为例，开展太阳帆姿态/振动控制研究。其中，针对太阳帆因受质心/压心偏差而致的常值干扰力矩问题，分别设计最优比例积分（PI）、线性二次调节器（LQR）控制器，并进行动力学仿真与对比分析。理论分析与仿真表明，上述两种调节器均可在姿态角、角速度动态响应性能与所需控制力矩之间进行折衷，最优PI调节器在消除太阳帆姿态角稳态偏差方面更具优势。
The spacecraft with unique propulsion advantage is one of the researchpriorities and focuses in the field of aerospace. Solar sail, which makes use ofsunlight as the propulsion thrust, has been one of the hotspots. Solar sail has thefeatures of light-weight, geometric nonlinearity, complex mechanisms and structures.The problems are important for solar sail to operate on orbit. Therefore, thedissertation will carry out research on structural statics and dynamics, attitudedynamics, and rigid-flexible coupling dynamics and control. The detail is asfollowing.
First, the dissertation analyzes the structural statics for solar sail consideringgeometric nonlinearity, then the thrust loss is carried out based on structuraldeformation. The solar sail support beam is considered as the main stiffness supportstructure and the film surface will be deformation with the support beam. The staticanalysis is carried out for the conditions of infinity and two points connectingbetween support beam and the film undergoing static force generated by lightpressure. The element equations are derived based on the principle of virtual work.Then the whole structure equations are assembled. The reduced equations arederived by considering boundary conditions. Newton-iterative algorithm is proposedto deal with the nonlinear algebraic equations. The thrust loss caused by thedeformation is given based on static analysis. The computational results indicatethat the nonlinear axial displacement is comparatively large, and the thrust loss forinfinity points connecting style is smaller than two points connecting style under thecondition of identical parameters.
Second, the dissertation studies the structural dynamics for solar sailconsidering geometric nonlinearity. The support beam is considered as the mainsupport structure. The vibration analysis of nonlinear beam undergoing static forcegenerated by light pressure, the force generated by sliding mass and control vanes iscarried out. The axial and transverse vibration equations with the properties ofstrong coupling, nonlinearity and time-varying coefficient matrix are established byLagrange equation method. The vibration equations are transformed into nonlinearalgebraic equations utilizing implicit unconditionally stable Newmark-β algorithmfor each time step. The nonlinear algebraic equations are solved by Newton-iterativealgorithm. Based on the analysis above, the vibration response affected by the massand velocity of the sliding mass, the angular velocity of the force generated bycontrol vanes are analyzed in detail. The computational results indicate that the massand velocity of sliding mass affect the vibration response, and the angular velocity of the force generated by control vanes hardly affects vibration response.
Third, the dissertation gives the attitude dynamics for large-flexible solar sailconsidering complex mechanisms such as control boom, sliding mass, control vanes.The basic configuration and assumptions, the related reference frames, thegeneralized coordinates, the coordinate transformations are given. The position andvelocity vectors of payload, sliding mass, and support beam are derived. And thegeneralized external torque caused by control vanes is given. The attitude dynamicsequations having the properties of nonlinearity and coupling are obtained byLagrange equation method. The attitude dynamic modeling is the basis for therigid-flexible coupling dynamic analysis and control.
Fourth, the dissertation carries out rigid-flexible coupling dynamics and controlstudies for solar sail. The rigid-flexible coupling dynamic equations for controllersdesign and dynamic simulations are derived based on vibration analysis and attitudedynamic modeling above-mentioned. Based on above work, the studies ofattitude/vibration control are carried out for solar sail on geostationary orbit (GEO).The controllers designed by optimal proportion and integral (PI) and linear quadraticregulator (LQR) are given for the problem of constant disturbance torque caused bythe center of pressure and the center of mass of solar sail. And the simulations andthe comparations are given. The theory analysis and simulations indicate that theLQR and optimal PI regulators can give a compromise between the dynamicresponse performance of attitude angles, angular velocities and control input torques.The PI regulator has more advantage to eliminate the steady state attitude angleserror for solar sail.
第一，对考虑结构几何非线性的太阳帆进行静力学分析及基于此的推力模型折损研究。将方形太阳帆支撑杆视为主体刚度支撑结构，认为帆面随之形变而形变。在帆面太阳角变化较缓情况下，针对帆面与支撑杆为两点和无穷点两种连接方式，对支撑杆受光压静力作用进行静力学研究。首先基于虚功原理建立单元有限元平衡方程，而后集成为整体结构有限元模型，并结合边界条件对所得方程组进行缩减处理，再基于牛顿迭代算法对缩减后的方程组进行数值求解。基于此给出太阳帆因形变而导致的推力折损分析。计算结果说明，支撑杆的非线性轴向位移较大，且相同参数条件下无穷点连接方式下的推力折损小于两点连接方式下的推力折损；
第二，对考虑结构几何非线性的太阳帆进行结构动力学建模与计算。视支撑杆为主体刚度支撑结构，对其进行光压静力、滑动质量块、摆动的控制叶片等综合作用下的振动分析。首先使用拉格朗日方程方法建立了无穷点连接方式下支撑杆轴向和横向振动微分方程组，模型具有明显的强耦合、非线性和系数矩阵时变等特点。使用隐式无条件稳定的纽马克-贝塔算法将每个时间步的动力学方程组转化为非线性代数方程组，基于牛顿迭代算法对所得方程组进行求解分析。并对滑块质量、滑块滑动速度及控制叶片作用力的角速度对结构振动响应的影响进行分析。计算结果说明滑块质量和滑动速度对支撑杆振动有一定影响，而控制叶片作用力的角速度对振动响应的影响较微弱；
第三，对考虑控制杆、滑动质量块、控制叶片等复杂机构作用下的大柔性太阳帆进行姿态动力学建模。给定太阳帆基本构型与假设，给出坐标系定义、广义坐标选取和相应坐标变换。给出有效载荷、滑块和支撑杆的位置和速度及相关能量。求取控制叶片广义外力矩。最终基于拉格朗日方程方法建立太阳帆姿态动力学方程，模型具有很强的非线性耦合特点。本章工作为太阳帆刚柔耦合动力学分析与控制奠定基础；
第四，对在轨正常运行的太阳帆进行刚柔耦合动力学与控制研究。在前述结构振动建模和姿态动力学建模基础之上经简化得到用于姿态/振动控制和动力学仿真的刚柔耦合动力学方程。以地球静止轨道上的太阳帆轨道提升任务为例，开展太阳帆姿态/振动控制研究。其中，针对太阳帆因受质心/压心偏差而致的常值干扰力矩问题，分别设计最优比例积分（PI）、线性二次调节器（LQR）控制器，并进行动力学仿真与对比分析。理论分析与仿真表明，上述两种调节器均可在姿态角、角速度动态响应性能与所需控制力矩之间进行折衷，最优PI调节器在消除太阳帆姿态角稳态偏差方面更具优势。
The spacecraft with unique propulsion advantage is one of the researchpriorities and focuses in the field of aerospace. Solar sail, which makes use ofsunlight as the propulsion thrust, has been one of the hotspots. Solar sail has thefeatures of light-weight, geometric nonlinearity, complex mechanisms and structures.The problems are important for solar sail to operate on orbit. Therefore, thedissertation will carry out research on structural statics and dynamics, attitudedynamics, and rigid-flexible coupling dynamics and control. The detail is asfollowing.
First, the dissertation analyzes the structural statics for solar sail consideringgeometric nonlinearity, then the thrust loss is carried out based on structuraldeformation. The solar sail support beam is considered as the main stiffness supportstructure and the film surface will be deformation with the support beam. The staticanalysis is carried out for the conditions of infinity and two points connectingbetween support beam and the film undergoing static force generated by lightpressure. The element equations are derived based on the principle of virtual work.Then the whole structure equations are assembled. The reduced equations arederived by considering boundary conditions. Newton-iterative algorithm is proposedto deal with the nonlinear algebraic equations. The thrust loss caused by thedeformation is given based on static analysis. The computational results indicatethat the nonlinear axial displacement is comparatively large, and the thrust loss forinfinity points connecting style is smaller than two points connecting style under thecondition of identical parameters.
Second, the dissertation studies the structural dynamics for solar sailconsidering geometric nonlinearity. The support beam is considered as the mainsupport structure. The vibration analysis of nonlinear beam undergoing static forcegenerated by light pressure, the force generated by sliding mass and control vanes iscarried out. The axial and transverse vibration equations with the properties ofstrong coupling, nonlinearity and time-varying coefficient matrix are established byLagrange equation method. The vibration equations are transformed into nonlinearalgebraic equations utilizing implicit unconditionally stable Newmark-β algorithmfor each time step. The nonlinear algebraic equations are solved by Newton-iterativealgorithm. Based on the analysis above, the vibration response affected by the massand velocity of the sliding mass, the angular velocity of the force generated bycontrol vanes are analyzed in detail. The computational results indicate that the massand velocity of sliding mass affect the vibration response, and the angular velocity of the force generated by control vanes hardly affects vibration response.
Third, the dissertation gives the attitude dynamics for large-flexible solar sailconsidering complex mechanisms such as control boom, sliding mass, control vanes.The basic configuration and assumptions, the related reference frames, thegeneralized coordinates, the coordinate transformations are given. The position andvelocity vectors of payload, sliding mass, and support beam are derived. And thegeneralized external torque caused by control vanes is given. The attitude dynamicsequations having the properties of nonlinearity and coupling are obtained byLagrange equation method. The attitude dynamic modeling is the basis for therigid-flexible coupling dynamic analysis and control.
Fourth, the dissertation carries out rigid-flexible coupling dynamics and controlstudies for solar sail. The rigid-flexible coupling dynamic equations for controllersdesign and dynamic simulations are derived based on vibration analysis and attitudedynamic modeling above-mentioned. Based on above work, the studies ofattitude/vibration control are carried out for solar sail on geostationary orbit (GEO).The controllers designed by optimal proportion and integral (PI) and linear quadraticregulator (LQR) are given for the problem of constant disturbance torque caused bythe center of pressure and the center of mass of solar sail. And the simulations andthe comparations are given. The theory analysis and simulations indicate that theLQR and optimal PI regulators can give a compromise between the dynamicresponse performance of attitude angles, angular velocities and control input torques.The PI regulator has more advantage to eliminate the steady state attitude angleserror for solar sail.
引文
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