基于干扰估计的航天器大角度姿态机动鲁棒次优控制

针对存在系统参数不确定与外界干扰的航天器大角度姿态机动问题,提出一种基于干扰估计的鲁棒次优控制方法。该方法通过引入总干扰的概念,将不确定参数与外界干扰对系统的影响统一为各控制通道总干扰,而后采用非线性干扰观测器实现对系统总干扰的估计;借鉴状态相关的黎卡提方程（SDRE）方法,将系统模型改写为状态相关的线性形式,并采用近似方法实现基于干扰估计的次优控制参数的在线求解。通过对航天器大角度姿态机动问题的仿真分析,校验所提方法不仅较传统SDRE方法计算效率更高,而且较大程度上提高系统对参数偏差与外界干扰的鲁棒性能。     

求解代数Riccati方程的一种新算法

本文讨论了Hamiltonian矩阵在辛相似变换下的标准形,由此给出代数Riccati方程存在非负定解的一个充分条件,提出了求解代数Riccati方程的一种新的算法。该方法节省运算量,且精度较高,尤其适合于解阶数不太高、系数矩阵为满阵的Riccati方程。最后给出了一个数值例子,并将该方法与其他方法作了比较.     

连续广义系统的镇定性分析

本文主要研究奇异系统的稳定性和镇定性问题，通过Lyapunov议程2和Ricaati方程，给出了奇异系统的渐近稳定性和镇定性的判据。     

基于Riccati方程解的再入飞行器制导律设计

提出一种再入飞行器纵向制导律设计方法。首先对纵向运动方程沿着实际轨道线性化,然后利用线性最优调节器原理设计制导律。在每个制导周期内求解代数R iccati方程,利用其正定解构造反馈控制律,与标准轨道的控制量叠加后形成全量控制,用于实际再入轨道的制导。仿真结果表明,所设计的制导律对再入初始偏差具有较强的鲁棒性,同时它也能较好地补偿由于气动参数和大气密度摄动造成的航程误差,从而保证落点精度。     

Application of SDRE technique to orbital and attitude control of spacecraft formation flying

This paper proposes the application of a nonlinear control technique for coupled orbital and attitude relative motion of formation flying. Recently, mission concepts based on the formations of spacecraft that require an increased performance level for in-space maneuvers and operations, have been proposed. In order to guarantee the required performance level, those missions will be characterized by very low inter-satellite distance and demanding relative pointing requirements. Therefore, an autonomous control with high accuracy will be required, both for the control of relative distance and relative attitude. The control system proposed in this work is based on the solution of the State-Dependent Riccati Equation (SDRE), which is one of the more promising nonlinear techniques for regulating nonlinear systems in all the major branches of engineering. The coupling of the relative orbital and attitude motion is obtained considering the same set of thrusters for the control of both orbital and attitude relative dynamics. In addition, the SDRE algorithm is implemented with a timing update strategy both for the controller and the proposed nonlinear filter. The proposed control system approach has been applied to the design of a nonlinear controller for an up-to-date formation mission, which is ESA Proba-3. Numerical simulations considering a tracking signal for both orbital and attitude relative maneuver during an operative orbit of the mission are presented.     

基于子结构消元法的柔性结构主动控制的研究

由结构动力系统的微分方程出发,建立了主动控制的数学模型,在计算结构力学与最优控制模拟关系的基础上,采用结构力学中的子结构消元法和混合能概念建立了一套时段消元公式,进而对Riccati代数方程进行了有效的求解,从而给出了一套柔性结构主动控制的研究方法。     

基于目标加速度方向观测的微分对策制导律

针对延迟信息条件下的机动目标拦截问题,研究了一种考虑目标加速度方向观测的微分对策制导律。首先,针对引入目标方向观测信息末制导博弈问题,建立了微分对策数学模型。随后,利用状态依赖黎卡提方程求解微分对策问题,得到包含无延迟目标机动项的微分对策制导律,可以更为有效地拦截机动目标。最后,在延迟信息条件下,利用目标加速度方向观测的方法补偿延迟的目标加速度,再将补偿后的目标加速度信息取代无延迟的目标加速度,得到延迟信息条件下考虑目标加速度方向观测的微分对策制导律。仿真结果表明,新的制导律可以在延迟信息条件下有效地拦截机动目标。     

Hardware-In-the-Loop Simulations of spacecraft attitude synchronization using the State-Dependent Riccati Equation technique

A nonlinear control technique pertaining to attitude synchronization problems is presented for formation flying spacecraft by utilizing the State-Dependent Riccati Equation (SDRE) technique. An attitude controller consisting of relative control and absolute control is designed using a reaction wheel assembly for regulator and tracking problems. To achieve effective relative control, the selective state-dependent connectivity is also adopted. The global asymptotic stability of the controller is confirmed using the Lyapunov theorem and is verified by Monte-Carlo simulations. An air-bearing-based Hardware-In-the-Loop Simulator (HILS) is also developed to validate the proposed control laws in real-time environments. The SDRE controller is discretized for implementation of a real-time processor in the HILS. The pointing errors are about 0.2° in the numerical simulations and about 1° in the HILS simulations, and experimental simulations confirm the effectiveness of the control algorithm for attitude synchronization in a spacecraft formation flying mission. Consequently, experiments using the HILS in a real-time environment can appropriately perform spacecraft attitude synchronization algorithms for formation flying spacecraft.     

Satellite formation reconfiguration and station-keeping using state-dependent Riccati equation technique

The current paper presents optimal reconfigurations and formation-keeping for formation flying satellites. The state-dependent Riccati equation (SDRE) technique is utilized as a non-linear controller for both the reconfiguration problem and formation-keeping problem. For the SDRE controller, a state-dependent coefficient (SDC) form is formulated to include non-linearities in the relative dynamics and J₂ orbital perturbation. The Taylor series and a transformation matrix are used to establish the SDC form. Optimal reconfiguration trajectories that minimize energy in satellite formation flying are obtained by the SDRE controller and compared with those obtained from a linear quadratic regulator (LQR) and a linear parameter varying (LPV) control method. It is illustrated that the SDRE non-linear controller of the current study obtains relocation accuracy of less than 0.1% of formation base-line length, while the LQR controller and LPV controller yield relatively large relocation errors. The formation-keeping controller developed using the SDRE technique in the current study also provides robustness under severe orbital perturbations.     

二阶离散系统LQ问题加权阵的选择

本文针对单输入条件下二阶定常线性离散系统,讨论了线性二次型(LQ)问题中加权阵的选择问题。证明并给出了当要求闭环系统是渐近稳定时,加权阵与系统开、闭环特征多项式之间以及系统开、闭环极点之间的一组解析关系式。对实例的计算结果表明,利用这组关系,可以很方便地得到加权阵。