考虑时滞特性的航天器非线性姿态控制方法研究

发布时间：2018-06-25 13:00

本文选题：航天器姿态控制 + 时滞　；参考：《哈尔滨工业大学》2017年博士论文

【摘要】：航天器姿态控制系统在工作时,执行器环节和姿态量测环节不可避免的会引入时滞。控制系统性能会因此受到影响,甚至导致失稳现象。由于航天器姿态模型具有强耦合非线性,时滞的引入使系统更加复杂,其特征方程具有无穷多个特征根,系统模型从有限维常微分方程变成无穷维时滞微分方程,因此经典的频域或基于Lyapunov函数的时域方法不再适用。近年来,随着时滞系统理论的发展,由Krasovskii所建立的Lyapunov-Krasovskii稳定性理论已成为研究时滞非线性系统的主要时域方法,该理论被引申到航天器姿态控制领域,用于对时滞影响下的姿态控制策略的研究。在这种背景下,本论文针对干扰力矩、时滞参数未知及模型参数不确定性影响下的航天器姿态控制问题进行了深入研究,主要内容如下:为便于使用Lipschitz假设条件处理航天器姿态模型中的非线性项,选择修正罗德里格斯参数(Modified Rodrigues Parameters,MRPs)作为姿态描述参数,并结合MRPs的映射集,对航天器姿态进行全局非奇异描述,最终建立航天器姿态运动学模型和动力学模型及其性质。给出设计航天器姿态控制策略用到的时滞系统稳定性理论基础和后续研究需要的不等式关系。为解决存在执行器未知时滞影响的刚性航天器姿态控制问题,设计线性状态反馈控制器,基于Lipschitz假设,结合L-K泛函构造和自由权矩阵方法,得到线性矩阵不等式形式的局部稳定性结论。在此基础上,考虑了航天器模型参数不确定影响,进一步设计了状态反馈控制器,数字仿真结果说明所设计控制器有效。针对姿态量测过程中存在时滞的航天器姿态控制问题,利用已有的时滞线性系统稳定性结论,基于反步法设计了保证闭环系统全局稳定性的非线性控制策略。进一步,考虑量测时滞未知和外部干扰力矩对航天器姿态控制的共同影响,利用扩张状态观测器(Extended State Observer,ESO)结合反步法设计了非线性控制器。对于同时存在量测时滞和执行器时滞的航天器姿态稳定问题,为克服航天器姿态运动数学模型中非线性项对姿态控制器设计造成的困难,对反步法进行改进,应用模型简化方法对航天器姿态运动模型进行变换,并设计非线性控制器保证变换后的系统稳定。通过L-K稳定性理论分析并证明变换前姿态控制系统稳定。对于执行器引入长时滞输入的情况,采用时滞补偿思路实现航天器姿态控制。建立执行器时滞状态的一阶双曲偏微分方程模型,从而得到航天器姿态系统的偏微分方程-常微分方程(Partial Differential Equation-Ordinary Differential Equation,PDE-ODE)级联耦合模型。对该PDE-ODE模型进行二维反步变换,包括对航天器姿态常微分方程模型的反步变换和对执行器状态偏微分方程的反步变换,给出了映射之间的变换关系和逆变换关系。在此基础上,设计了边界控制器。最后证明目标系统的指数稳定性并通过映射关系证明了原系统的稳定性。虽然该方法要求时滞量精确已知,但仿真表明所设计的非线性控制器对时滞偏差和重力梯度力矩干扰都具有鲁棒性。考虑执行器时滞未知情况下航天器姿态控制问题,设计了时滞自适应估计器对前述边界控制律进行改进,仿真结果表明改进后的非线性边界控制律能够保证姿态控制系统稳定。
[Abstract]:When the spacecraft attitude control system is working, the performance of the actuator and the attitude measurement will inevitably lead to the delay. The performance of the control system will be affected and even lead to instability. Due to the strong coupling nonlinearity of the spacecraft attitude model, the introduction of time delay makes the system more complex, and its characteristic equation has infinitely many special characteristics. The system model is transformed from finite dimensional ordinary differential equation into infinite dimensional delay differential equation, so the classical frequency domain or time domain method based on Lyapunov function is no longer applicable. In recent years, with the development of time-delay system theory, the theory of Lyapunov-Krasovskii stability established by Krasovskii has become the main study of time-delay nonlinear systems. In time domain method, the theory is extended to the field of spacecraft attitude control, which is used in the study of attitude control strategy under the influence of time delay. Under this background, this paper studies the attitude control of spacecraft under the influence of the disturbance torque, the unknown time delay parameters and the uncertainty of the model parameters. The main contents are as follows: Using the Lipschitz hypothesis to deal with the nonlinear term in the spacecraft attitude model, the modified Rodrigues parameter (Modified Rodrigues Parameters, MRPs) is selected as the attitude description parameter, and the global nonsingular description of the spacecraft attitude is carried out with the mapping set of MRPs, and the attitude kinematic model and dynamic model of the spacecraft are finally established. In order to solve the problem of attitude control of a rigid spacecraft with unknown delay in the actuator, a linear state feedback controller is designed, based on the Lipschitz hypothesis, and combined with the L-K functional structure and self. By the weight matrix method, the local stability conclusions of linear matrix inequalities are obtained. On this basis, the state feedback controller is designed in consideration of the uncertainty of the parameters of the spacecraft model. The numerical simulation results show that the designed controller is effective. Based on the stability conclusion of the linear system with time delay, a nonlinear control strategy is designed to guarantee the global stability of the closed loop system based on the backstepping method. Further, considering the common influence of the unknown time delay and the external disturbance torque on the attitude control of the spacecraft, the extended state observer (Extended State Observer, ESO) is used to combine the anti step method. The nonlinear controller is designed. In order to overcome the problem of attitude stabilization of spacecraft with time delay and actuator delay, the difficulty of solving the attitude controller design in the mathematical model of spacecraft attitude motion is overcome. The inverse step method is improved, and the model simplification of the model is used to transform the attitude motion model of the spacecraft. The nonlinear controller is designed to ensure the stability of the system after transformation. The stability of the attitude control system before transformation is analyzed and proved by the L-K stability theory. The attitude control of the spacecraft is realized by the delay compensation idea. The first order hyperbolic partial differential equation model of the actuator is established. To the partial differential equation (Partial Differential Equation-Ordinary Differential Equation, PDE-ODE) cascade coupling model of the spacecraft attitude system, the two-dimensional inverse transformation of the PDE-ODE model is carried out, including the backstepping transformation of the attitude ordinary differential equation model of the spacecraft and the backstepping of the partial differential equation of the actuator state. On the basis of this, the boundary controller is designed. Finally, the exponential stability of the target system is proved and the stability of the original system is proved by the mapping relation. Although the method requires the time delay to be accurately known, the nonlinear controller designed by the simulation shows the delay deviation. And the gravity gradient torque interference is robust. Considering the attitude control problem of the spacecraft under the unknown delay of the actuator, a time-delay adaptive estimator is designed to improve the foregoing boundary control law. The simulation results show that the improved nonlinear boundary control law can ensure the stability of the attitude control system.
【学位授予单位】：哈尔滨工业大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：V448.2

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