基于有限时间范数的末制导系统性能分析
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摘要
近年来,为了进一步提高末制导精度,寻的末制导系统的性能综合分析及指标分配工作越来越受到广泛的重视。传统的性能分析主要依靠飞行试验数据或者数字仿真技术,存在着分析与设计脱节、性能指标单一以及分析周期较长等缺点,已无法满足现代精确末制导武器系统的需求。因此,亟待根据末制导系统的特点,从系统与控制的角度建立科学的定量指标体系及相应的分析方法。为此,本文针对末制导系统的性能综合分析问题,进行了以下几个方面的研究:
首先,分析末制导系统的有限时间、非零初始条件和强时变等特点,在此基础上,建立末制导系统的线性时变模型,并在延拓的L_p空间内对末制导系统的输入和输出信号进行度量,从系统与控制的角度对末制导系统的性能进行描述,为后续的研究工作奠定基础。
其次,针对末制导过程中的随机误差和目标机动,提出一种基于有限时间广义H_2范数的性能分析框架。提出线性时变系统的有限时间广义H_2范数,以Hermitian Riccati矩阵微分方程(HRMDE)的形式给出有限时间广义H_2性能准则,并对HRMDE的数值解法进行比较研究。利用成形滤波器对导引头量测噪声及目标机动进行数学建模,进而基于有限时间广义H_2范数对末制导系统的均方根脱靶量进行分析。
然后,对末制导系统的能量需求问题进行深入的研究,提出参数不确定系统的有限时间H_∞鲁棒性能分析准则,并基于线性时变系统的有限时间H_∞范数揭示中末交班误差以及目标机动对末制导能量需求的影响,给出目标最劣的机动形式以及最大的弹目能量消耗之比。仿真分析能量需求与末制导回路动态品质的关系,并对制导设计问题进行相关的讨论。
再次,针对末制导过程中的需用过载问题,提出基于有限时间L,范数的性能分析方法。对线性时变系统的有限时间L_1范数进行相关的研究,提出有限时间L_1性能准则。基于伴随理论,提出线性连续系统诱导L_∞范数求解的一般性方法,并讨论系统BIBO稳定性与有限时间L_1性能的区别和联系。基于有限时间L_1范数对末制导的最大需用过载进行分析,揭示末制导各个子系统的性能与末制导需用过载的关系。
最后,针对复杂末制导系统的指标分配问题,在对末制导系统性能综合分析的基础上,提出具体的指标分配思路和方法。在总结前面研究成果的基础上,将控制系统的参数化思想与有限时间范数结合起来,从而解决末制导系统的指标分配问题。在指标分配过程中,根据制导精度要求,基于系统的有限时间范数,确定可行指标分配方案的集合。在此基础上,考虑研制成本、难度、周期等因素,给出某型末制导系统的最佳指标分配方案。
综上所述,全文紧密围绕末制导系统的性能综合分析问题,提出基于有限时间广义H_2、H_∞和L_1范数的线性时变系统性能分析方法,从而建立比较完善的末制导系统性能的定量指标体系,并对末制导的均方根脱靶量、能量需求、需用过载以及指标分配等关键问题进行较为深入的研究,仿真验证定量指标体系的科学性和分析方法的有效性。
In the past few years, to improve the accuracy of the terminal guidance system, the performance analysis and index distribution of the homing TGS have been paid more and more attention. Conventional performance analysis methods greatly depend on flying trial data or digital simulation technology, which have some drawbacks such as disjunctions between analysis and design, single performance index, long analysis period, and so on. Since they can not satisfy any more the requirements from modern precision terminal guidance weapon systems, it is in urgent need, based on the characteristics of TGS, to establish a scientific and quantitative index system and its corresponding comprehensive analysis methods from the system and control point of view. Therefore, the performance analysis method for homing TGS is focused in this dissertation, and the main contributions are the following:
Firstly, the characteristics, which are finite-time, non-zero initial conditions and strongly time-varying, are analyzed. Based on this, the linear time-varying (LTV) model is established for TGS. Then, the input-output signals of TGS are measured in an extend L_p space. These works lay the foundation for deeper researches on TGS.
Secondly, in light of stochastic errors in terminal guidance process and random maneuvers of targets, a new performance analysis framework is presented based on the finite-time generalized H_2 method. The finite-time generalized H_2 performance measure is proposed for a LTV system and the corresponding criterion is given in the form of Hermitian Riccati matrix differential equation (HRMDE). The comparison on numerical solutions of HRMDE is approached. Seeker noises and target maneuvers are described via shaping filters. The root-mean miss distance is analyzed by applying the proposed finite-time generalized H_2 method.
Thirdly, the energy requirement of homing TGS is investigated. The finite-time H_∞robust performance analysis criterion is proposed for a system with parameter uncertainties. The energy requirement caused by handover errors from midcourse guidance to terminal guidance and target maneuvers is illustrated by applying finite-time H_∞analysis method. The worst maneuver form of the target and the missile-target maximum energy consumption ratio are given. Furthermore, simulation results quantitatively reveal the relation between the energy requirement and terminal guidance loop dynamics. Also, the trade-offs between the energy requirement and miss distance are analyzed by choosing different weight functions.
Fourthly, with required overload problems in terminal guidance process, a new finite-time L_1 analysis method is proposed. The finite-time L_1 performance measure and criterion of LTV system are studied. Based on the adjoint theory, a general method is proposed for computing the Loo-induced norm of linear continuous system. The relation and distinction between finite-time L_1 performance and BIBO stability are also discussed. The relation between subsystem performance and maximum required overload is analyzed quantitatively by applying the proposed finite-time L_1 method.
Finally, to solve the index distribution problem of a complicated TGS, considerations and methods for the index distribution are given in detail by solving the finite-time mixed gain measure. By combining the system parameterization method and mixed gain measure, the index distribution problem is formulated as the typical control issue. In the index distribution process, the set of the feasible index distribution schemes is determined via finite-time mixed gain measure method, taking into consideration the guidance accuracy requirement. Furthermore, the optimal index distribution scheme of the certain TGS is given considering the cost, the difficulty, the development period, and so on.
In summary, we focus on the performance comprehensive analysis problem of homing TGS in this dissertation. Proposing the finite-time H_2, H_∞, and L_1 analysis methods of LTV system aside, it comes up with relatively perfect quantitative performance index system and corresponding comprehensive analysis methods of TGS. It also looks into the key issues such as root-mean miss distance, energy requirement, required overload and index distribution. The superiority and effectivity of these proposed methods have been verified by computer simulations.
首先,分析末制导系统的有限时间、非零初始条件和强时变等特点,在此基础上,建立末制导系统的线性时变模型,并在延拓的L_p空间内对末制导系统的输入和输出信号进行度量,从系统与控制的角度对末制导系统的性能进行描述,为后续的研究工作奠定基础。
其次,针对末制导过程中的随机误差和目标机动,提出一种基于有限时间广义H_2范数的性能分析框架。提出线性时变系统的有限时间广义H_2范数,以Hermitian Riccati矩阵微分方程(HRMDE)的形式给出有限时间广义H_2性能准则,并对HRMDE的数值解法进行比较研究。利用成形滤波器对导引头量测噪声及目标机动进行数学建模,进而基于有限时间广义H_2范数对末制导系统的均方根脱靶量进行分析。
然后,对末制导系统的能量需求问题进行深入的研究,提出参数不确定系统的有限时间H_∞鲁棒性能分析准则,并基于线性时变系统的有限时间H_∞范数揭示中末交班误差以及目标机动对末制导能量需求的影响,给出目标最劣的机动形式以及最大的弹目能量消耗之比。仿真分析能量需求与末制导回路动态品质的关系,并对制导设计问题进行相关的讨论。
再次,针对末制导过程中的需用过载问题,提出基于有限时间L,范数的性能分析方法。对线性时变系统的有限时间L_1范数进行相关的研究,提出有限时间L_1性能准则。基于伴随理论,提出线性连续系统诱导L_∞范数求解的一般性方法,并讨论系统BIBO稳定性与有限时间L_1性能的区别和联系。基于有限时间L_1范数对末制导的最大需用过载进行分析,揭示末制导各个子系统的性能与末制导需用过载的关系。
最后,针对复杂末制导系统的指标分配问题,在对末制导系统性能综合分析的基础上,提出具体的指标分配思路和方法。在总结前面研究成果的基础上,将控制系统的参数化思想与有限时间范数结合起来,从而解决末制导系统的指标分配问题。在指标分配过程中,根据制导精度要求,基于系统的有限时间范数,确定可行指标分配方案的集合。在此基础上,考虑研制成本、难度、周期等因素,给出某型末制导系统的最佳指标分配方案。
综上所述,全文紧密围绕末制导系统的性能综合分析问题,提出基于有限时间广义H_2、H_∞和L_1范数的线性时变系统性能分析方法,从而建立比较完善的末制导系统性能的定量指标体系,并对末制导的均方根脱靶量、能量需求、需用过载以及指标分配等关键问题进行较为深入的研究,仿真验证定量指标体系的科学性和分析方法的有效性。
In the past few years, to improve the accuracy of the terminal guidance system, the performance analysis and index distribution of the homing TGS have been paid more and more attention. Conventional performance analysis methods greatly depend on flying trial data or digital simulation technology, which have some drawbacks such as disjunctions between analysis and design, single performance index, long analysis period, and so on. Since they can not satisfy any more the requirements from modern precision terminal guidance weapon systems, it is in urgent need, based on the characteristics of TGS, to establish a scientific and quantitative index system and its corresponding comprehensive analysis methods from the system and control point of view. Therefore, the performance analysis method for homing TGS is focused in this dissertation, and the main contributions are the following:
Firstly, the characteristics, which are finite-time, non-zero initial conditions and strongly time-varying, are analyzed. Based on this, the linear time-varying (LTV) model is established for TGS. Then, the input-output signals of TGS are measured in an extend L_p space. These works lay the foundation for deeper researches on TGS.
Secondly, in light of stochastic errors in terminal guidance process and random maneuvers of targets, a new performance analysis framework is presented based on the finite-time generalized H_2 method. The finite-time generalized H_2 performance measure is proposed for a LTV system and the corresponding criterion is given in the form of Hermitian Riccati matrix differential equation (HRMDE). The comparison on numerical solutions of HRMDE is approached. Seeker noises and target maneuvers are described via shaping filters. The root-mean miss distance is analyzed by applying the proposed finite-time generalized H_2 method.
Thirdly, the energy requirement of homing TGS is investigated. The finite-time H_∞robust performance analysis criterion is proposed for a system with parameter uncertainties. The energy requirement caused by handover errors from midcourse guidance to terminal guidance and target maneuvers is illustrated by applying finite-time H_∞analysis method. The worst maneuver form of the target and the missile-target maximum energy consumption ratio are given. Furthermore, simulation results quantitatively reveal the relation between the energy requirement and terminal guidance loop dynamics. Also, the trade-offs between the energy requirement and miss distance are analyzed by choosing different weight functions.
Fourthly, with required overload problems in terminal guidance process, a new finite-time L_1 analysis method is proposed. The finite-time L_1 performance measure and criterion of LTV system are studied. Based on the adjoint theory, a general method is proposed for computing the Loo-induced norm of linear continuous system. The relation and distinction between finite-time L_1 performance and BIBO stability are also discussed. The relation between subsystem performance and maximum required overload is analyzed quantitatively by applying the proposed finite-time L_1 method.
Finally, to solve the index distribution problem of a complicated TGS, considerations and methods for the index distribution are given in detail by solving the finite-time mixed gain measure. By combining the system parameterization method and mixed gain measure, the index distribution problem is formulated as the typical control issue. In the index distribution process, the set of the feasible index distribution schemes is determined via finite-time mixed gain measure method, taking into consideration the guidance accuracy requirement. Furthermore, the optimal index distribution scheme of the certain TGS is given considering the cost, the difficulty, the development period, and so on.
In summary, we focus on the performance comprehensive analysis problem of homing TGS in this dissertation. Proposing the finite-time H_2, H_∞, and L_1 analysis methods of LTV system aside, it comes up with relatively perfect quantitative performance index system and corresponding comprehensive analysis methods of TGS. It also looks into the key issues such as root-mean miss distance, energy requirement, required overload and index distribution. The superiority and effectivity of these proposed methods have been verified by computer simulations.
引文
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