柔性航天器在轨振动主动控制研究
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摘要
采取多种展开形式的大型航天器往往具有较强的柔性，对其在空间工作时产生的振动需要进行抑制以满足航天器任务的需求。本文针对柔性航天器进行了动力学建模、模型修正、非线性姿态与振动控制、鲁棒振动控制及振动控制实现策略等方面的研究，旨在为柔性航天器振动控制的实际工程应用提供理论依据和技术支持。主要研究内容如下：
1.根据混合坐标法和拉格朗日方程推导了柔性航天器的动力学模型，并提出一种附加质量法分析薄板在空气场中的非线性振动问题。针对航天器柔性结构在地面实验中的非线性振动问题，引入Green-Lagrange应变修正非线性薄板的一阶剪切变形，采用虚功原理建立薄板有限元模型，再通过速度势函数和格林函数计算空气场加载在薄壳上的压力获得附加质量，利用附加质量对原结构进行修正。将所获得的柔性结构地面非线性动力学分析结果用于修正柔性航天器模型，从而获得相对精确的在轨工作时的动力学模型。
2.基于压电智能材料和模态控制方法构造了三轴稳定柔性航天器的姿态控制和振动控制系统。利用频带隔离思想，设计了柔性结构的正位置反馈（PositivePosition Feedback，PPF）振动主动控制器。建立了压电智能板的有限元模型，并导出压电作动器的模态控制力以及结构的模态位移。考虑到姿态确定系统、姿态控制执行器及PPF控制器，建立了三轴稳定柔性航天器姿态控制与振动控制的全数字仿真模型，通过算例验证了模型以及控制方法的有效性。
3.设计了抗干扰能力较强的基于状态相关Ricatti方程（State-DependentRiccati Equation，SDRE）的姿态控制器，并利用自适应方法增强了一阶PPF控制器的鲁棒性。根据航天器姿态角与姿态角速度两类变量变化速度的不同，将姿态动力学、运动学分解为内、外两个控制回路，再将非线性动力学伪线性化，每个回路设计相应的积分型SDRE控制器。同时，研究了一阶PPF控制器特性，利用自适应思想设计了柔性结构的自适应PPF振动控制器，增强了控制系统的鲁棒性，并且较好地解决了控制器性能和精度之间的矛盾。通过算例验证了所提出的姿态与振动控制器的有效性。
4.基于线性矩阵不等式（Linear Matrix Inequality，LMI）提出了一种非线性系统的鲁棒控制方法，并利用所得方法和结论设计了鲁棒二阶PPF控制器。针对基于模糊T-S模型的输入受限非线性系统，导出控制性能指标的上界，再通过李雅普诺夫方程给出优化的充分条件，证明闭环系统的稳定性。将稳定性约束和控制输入约束变换成易求解的LMIs形式。利用这一结论，将LMI方法引入到PPF控制器设计中。在带有PPF控制器的闭环系统中，考虑到柔性结构动力学中不确定项和作动器能力的限制，将问题转化为具有LMI约束的特征值问题进行求解，从而得到优化后的PPF控制律，增强了振动控制的鲁棒性。通过算例验证了所设计的鲁棒PPF控制器的有效性。
5.面向工程应用，设计了基于多重主动调谐质量阻尼器（Multiple ActiveTuned Mass Dampers，MATMD）的柔性结构振动主动控制实现策略，以增强控制系统的可靠性。针对某柔性航天器结构，设计了以板簧和惯性质量块组成的多重调谐质量阻尼器（Multiple Tuned Mass Dampers，MTMD）。利用位移放大系数优化选择了惯性元件、弹性元件和阻尼元件参数。将压电作动器引入板簧的主动控制中，结合PPF控制方法，推导出基于压电作动器的模态控制方程。通过实例对比，证明了所设计的MATMD振动控制策略的优越性和可靠性。
Since large spacecrafts extensively deployed exhibit strong flexibility, the vibrationgenerated during space work must be depressed to satisfy the task demands. Dynamicmodeling, model updating, nonlinear attitude control and vibration control, robustvibration control and vibration control implementation strategies for flexible spacecraftsare studied in this research and the results can find theoretical and technicalfundamentals for the engineering application of the vibration control for flexiblespacecrafts. The main contributions are described as follows:
1. The dynamic model of a flexible spacecraft is derived by a hybrid coordinatemethod and Lagrange equation, and an added mass method is presented to analyze thevibration in the air. With regard to non-linear vibration of a spacecraft flexible structurein ground testing, Green-Lagrange strain is introduced to correct first-order shearingdeformation of its non-linear sheet. Then a finite element model is built by virtual workprinciple. Added mass is gained by calculating the pressure with velocity potentialfunction and Green equation. On this basis, the original structure is modified withadditional mass. The method of updating flexible spacecraft model is proposed usinganalysis result of flexible structure ground vibration. A relatively refined dynamic modelof the in-orbit spacecraft is obtained.
2. Based on the piezoelectric smart materials and modal controls method, attitudecontrol and vibration control systems for the three-axis-stabilized flexible spacecraftsare established. Based on a bandwidth insulation method, a positive position feedback(PPF) active vibration controller for the flexible structure is designed. The finiteelement model of piezo-intelligent plate is built, and mode control force and modedisplacement are deduced. Taking account of the attitude determination system andattitude control actuators, a full digital simulation model of the three-axis stabilizedflexible spacecraft is built. Simulation results verify the validity of the proposed modeland control methods.
3. In order to improve anti-interference ability of the attitude control system, anovel state-dependent Riccati equation (SDRE)-based attitude controller is designed.The robustness of the control system is enhanced by introducing the idea ofself-adaptation. Since the rate of change of the angular velocity variable and the rate ofchange of angular displacement variable are different, attitude dynamics and kinematicmodel are decomposed into the inside and outside control loops. Nonlinear dynamics is pseudo-linearized, and hence the corresponding integral SDRE controller is designedfor each loop. The characteristics of first-order PPF controller are studied, By means ofan adaptive PPF controller, not only the robustness of the control system is enhanced,but also the tradeoff between control precision and control performance could be solved.Numerical example shows the effectiveness and feasibility of the proposed methods.
4. Based on Linear Matrix Inequalities (LMI), a robust control method for nonlinearsystem is proposed, furthermore, a robust second-order PPF controller is designed. Forthe nonlinear systems based on a fuzzy T-S model with control input constraints, theupper bound of the quadratic performance index is derived. Stability constraints andcontrol input constraints are further formulated into LMIs which are easily obtained. AnLMI method is introduced into PPF controller design. In the closed-loop systems withthe PPF controller, by considering the uncertainty of the flexible structure dynamic andthe actuators’ capacity limit, the control problem is transformed into solving theeigenvalue problem with LMI constraints. Therefore, an optimal PPF controller isobtained, and robustness of vibration control is enhanced. The simulation results showthe effectivity of the robust PPF controller.
5. Aiming at achieving higher reliability in engineering application, the strategy ofactive vibration control for the flexible structure is presented using multiple active tunedmass dampers (MATMD). For a flexible spacecraft structure, multiple tuned massdampers (MTMD) consisting leaf springs and inertial masses are designed. By using ofdisplacement amplification factor, the parameters of mass, springiness element anddamping element are optimally chosen. The piezoelectric actuators are introduced intoactive control. Combined with the PPF method, a modal control equation withpiezoelectric actuators is deduced. The simulation results with three cases are compared,showing the advantage and reliability of the MATMD.
1.根据混合坐标法和拉格朗日方程推导了柔性航天器的动力学模型，并提出一种附加质量法分析薄板在空气场中的非线性振动问题。针对航天器柔性结构在地面实验中的非线性振动问题，引入Green-Lagrange应变修正非线性薄板的一阶剪切变形，采用虚功原理建立薄板有限元模型，再通过速度势函数和格林函数计算空气场加载在薄壳上的压力获得附加质量，利用附加质量对原结构进行修正。将所获得的柔性结构地面非线性动力学分析结果用于修正柔性航天器模型，从而获得相对精确的在轨工作时的动力学模型。
2.基于压电智能材料和模态控制方法构造了三轴稳定柔性航天器的姿态控制和振动控制系统。利用频带隔离思想，设计了柔性结构的正位置反馈（PositivePosition Feedback，PPF）振动主动控制器。建立了压电智能板的有限元模型，并导出压电作动器的模态控制力以及结构的模态位移。考虑到姿态确定系统、姿态控制执行器及PPF控制器，建立了三轴稳定柔性航天器姿态控制与振动控制的全数字仿真模型，通过算例验证了模型以及控制方法的有效性。
3.设计了抗干扰能力较强的基于状态相关Ricatti方程（State-DependentRiccati Equation，SDRE）的姿态控制器，并利用自适应方法增强了一阶PPF控制器的鲁棒性。根据航天器姿态角与姿态角速度两类变量变化速度的不同，将姿态动力学、运动学分解为内、外两个控制回路，再将非线性动力学伪线性化，每个回路设计相应的积分型SDRE控制器。同时，研究了一阶PPF控制器特性，利用自适应思想设计了柔性结构的自适应PPF振动控制器，增强了控制系统的鲁棒性，并且较好地解决了控制器性能和精度之间的矛盾。通过算例验证了所提出的姿态与振动控制器的有效性。
4.基于线性矩阵不等式（Linear Matrix Inequality，LMI）提出了一种非线性系统的鲁棒控制方法，并利用所得方法和结论设计了鲁棒二阶PPF控制器。针对基于模糊T-S模型的输入受限非线性系统，导出控制性能指标的上界，再通过李雅普诺夫方程给出优化的充分条件，证明闭环系统的稳定性。将稳定性约束和控制输入约束变换成易求解的LMIs形式。利用这一结论，将LMI方法引入到PPF控制器设计中。在带有PPF控制器的闭环系统中，考虑到柔性结构动力学中不确定项和作动器能力的限制，将问题转化为具有LMI约束的特征值问题进行求解，从而得到优化后的PPF控制律，增强了振动控制的鲁棒性。通过算例验证了所设计的鲁棒PPF控制器的有效性。
5.面向工程应用，设计了基于多重主动调谐质量阻尼器（Multiple ActiveTuned Mass Dampers，MATMD）的柔性结构振动主动控制实现策略，以增强控制系统的可靠性。针对某柔性航天器结构，设计了以板簧和惯性质量块组成的多重调谐质量阻尼器（Multiple Tuned Mass Dampers，MTMD）。利用位移放大系数优化选择了惯性元件、弹性元件和阻尼元件参数。将压电作动器引入板簧的主动控制中，结合PPF控制方法，推导出基于压电作动器的模态控制方程。通过实例对比，证明了所设计的MATMD振动控制策略的优越性和可靠性。
Since large spacecrafts extensively deployed exhibit strong flexibility, the vibrationgenerated during space work must be depressed to satisfy the task demands. Dynamicmodeling, model updating, nonlinear attitude control and vibration control, robustvibration control and vibration control implementation strategies for flexible spacecraftsare studied in this research and the results can find theoretical and technicalfundamentals for the engineering application of the vibration control for flexiblespacecrafts. The main contributions are described as follows:
1. The dynamic model of a flexible spacecraft is derived by a hybrid coordinatemethod and Lagrange equation, and an added mass method is presented to analyze thevibration in the air. With regard to non-linear vibration of a spacecraft flexible structurein ground testing, Green-Lagrange strain is introduced to correct first-order shearingdeformation of its non-linear sheet. Then a finite element model is built by virtual workprinciple. Added mass is gained by calculating the pressure with velocity potentialfunction and Green equation. On this basis, the original structure is modified withadditional mass. The method of updating flexible spacecraft model is proposed usinganalysis result of flexible structure ground vibration. A relatively refined dynamic modelof the in-orbit spacecraft is obtained.
2. Based on the piezoelectric smart materials and modal controls method, attitudecontrol and vibration control systems for the three-axis-stabilized flexible spacecraftsare established. Based on a bandwidth insulation method, a positive position feedback(PPF) active vibration controller for the flexible structure is designed. The finiteelement model of piezo-intelligent plate is built, and mode control force and modedisplacement are deduced. Taking account of the attitude determination system andattitude control actuators, a full digital simulation model of the three-axis stabilizedflexible spacecraft is built. Simulation results verify the validity of the proposed modeland control methods.
3. In order to improve anti-interference ability of the attitude control system, anovel state-dependent Riccati equation (SDRE)-based attitude controller is designed.The robustness of the control system is enhanced by introducing the idea ofself-adaptation. Since the rate of change of the angular velocity variable and the rate ofchange of angular displacement variable are different, attitude dynamics and kinematicmodel are decomposed into the inside and outside control loops. Nonlinear dynamics is pseudo-linearized, and hence the corresponding integral SDRE controller is designedfor each loop. The characteristics of first-order PPF controller are studied, By means ofan adaptive PPF controller, not only the robustness of the control system is enhanced,but also the tradeoff between control precision and control performance could be solved.Numerical example shows the effectiveness and feasibility of the proposed methods.
4. Based on Linear Matrix Inequalities (LMI), a robust control method for nonlinearsystem is proposed, furthermore, a robust second-order PPF controller is designed. Forthe nonlinear systems based on a fuzzy T-S model with control input constraints, theupper bound of the quadratic performance index is derived. Stability constraints andcontrol input constraints are further formulated into LMIs which are easily obtained. AnLMI method is introduced into PPF controller design. In the closed-loop systems withthe PPF controller, by considering the uncertainty of the flexible structure dynamic andthe actuators’ capacity limit, the control problem is transformed into solving theeigenvalue problem with LMI constraints. Therefore, an optimal PPF controller isobtained, and robustness of vibration control is enhanced. The simulation results showthe effectivity of the robust PPF controller.
5. Aiming at achieving higher reliability in engineering application, the strategy ofactive vibration control for the flexible structure is presented using multiple active tunedmass dampers (MATMD). For a flexible spacecraft structure, multiple tuned massdampers (MTMD) consisting leaf springs and inertial masses are designed. By using ofdisplacement amplification factor, the parameters of mass, springiness element anddamping element are optimally chosen. The piezoelectric actuators are introduced intoactive control. Combined with the PPF method, a modal control equation withpiezoelectric actuators is deduced. The simulation results with three cases are compared,showing the advantage and reliability of the MATMD.
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