Design of Nonlinear Guidance and Control for Maneuvering Target Interception with Passive Ranging System

攔截洲際彈道飛彈(ICBM)，一直是飛彈防禦系統重要的課題，尤其在於其距離遠、目標小、飛行速度快且具機動能力，對於攔截目標的飛彈導引控制的設計極具挑戰，近年來引起許多學者的研究。本論文針對飛彈系統的三個部分：尋標器(追蹤法則)、導引律及自動駕駛儀等來進行設計。首先，在尋標器的追蹤法則設計中，本論文使用被動式測距法則來實現設計目的，也就是利用交互式多模型(Interacting Multiple Models)結合擴展卡曼濾波器(Extended Kalman Filter)，運作在修正球座標(Modified Spherical Coordinate)與直角座標之間，來估測與追蹤目標移動的軌跡及其相關資訊；導引律的部分，考量目標估測所產生的誤差及系統強健性，本論文運用二階順滑模態控制(Second-Order Sliding Mode Control)來進行設計，亦可大幅降低應用傳統順滑模態控制所隨之而來的抖振(Chattering)現象。在自動駕駛儀設計部分，則利用順滑模態控制來實現其控制設計，並在整合導引系統時，考量飛彈姿態誤差造成的影響來修正導引律，並用李亞普諾夫定理(Lyapunov Stability Theory)來分析及證明設計之穩定性。再者，考量實際飛彈攔截的場景需求，本論文由一對一擴展到多對一的合作攔截，運用多員追逃賽局理論(Multi-Player Pursuit-Evasion Game)來設計個別飛彈的導引律，以達成飽和(同時)攻擊的目的。為了驗證所設計控制器的性能，本論文也納入空氣動力模式來設計模擬程式與場景設計，透過不同場景的模擬並和傳統順滑模態控制做比較，來驗證本論文所提出的設計，並分析與討論所提出設計的可行性與穩定性。This dissertation proposes a novel integrated approach to the interception of a maneuvering target within a 3-D space. The estimator/seeker system of the intercepting missile tracks the trajectory of the target with a passive ranging law to ensure stealth capability. The passive ranging mechanism comprises a coordinate transform from Cartesian coordinates to modified spherical coordinates (MSC) as well as an extended Kalman filter (EKF) with an Interacting Multiple Model (IMM). The aim of the system is to derive accurate estimates of the target’s position, even when the target performs evasive maneuvers. Based on these estimates, the proposed guidance law incorporates second-order sliding mode control (SOSMC), such that the missile will approach the target continuously until intercepting it. Moreover, considering the practical situation in missile-target engagement, we extend one-on-one interception to multi-missile interception via multi-player pursuit-evasion (MPPE) game theory. The stability of the integrated guidance/autopilot system was and a variety of simulations were conducted to verify the efficacy of the proposed system.論文口試委員審定書 …………………………………………………………….....ii 誌謝 …………………………………………………………………………………….iii 中文摘要 ………………………………………………………………………………...v Abstract ……………………………………………………………………………vi List of Figures ………………………………………………………………………vii List of Tables………………………………………………………………………ix Chapter 1 Introduction 1.1 Classification of Missiles ………………………………………………1 1.2 Motivation of Missile Interception Research……………………3 1.3 Survey of Related Works………………………………………6 1.4 Contributions…………………………..…………………………..……..11 1.5 Organization…..…………………………………………………......12 Chapter 2 Preliminaries and Problem Description 2.1 Missile Control System…………………………………………………………14 2.2 Airframe and Actuators ……………………………………………15 2.3 Aerodynamics…………………………………….………………………21 2.4 Mathematical Background………………………………………………25 2.5 Problem Description……………………………………………………33 Chapter 3 Missile Seeker/Estimator Design 3.1 Fundamentals of Seeker/Estimator………………………………………36 3.2 Passive Ranging Law……………………………………………………37 3.3 MSC-EKF Estimation………………………………………………………39 3.4 Interactive Multiple Models Filter………………………………………47 3.5 Simulation Results and Discussion……………………………………56 Chapter 4 Missile Guidance Law Design 4.1 Fundamentals of Missile Guidance....…………………………………63 4.2 Modeling for Target Interception………………………………………67 4.3 Second-Order Sliding Mode Guidance Law……………………………72 Chapter 5 Integrated Guidance/Autopilot System Stability Analysis 5.1 Autopilot System…….………......…………………...…………………..80 5.2 Integrated Guidance/Autopilot System…………………………………..87 5.3 Simulation Results and Discussion………..……………………………96 Chapter 6 Multi-Missiles Interception Problem 6.1 Problem Formulation......…………………...………..………………….112 6.2 Derivation of Time-to-Go Intercepting…………………………114 6.3 Multi-Player Pursuit and Evasion Game………………………………116 6.4 Stability Analysis of the Guidance Strategy…120 6.5 Simulation Results and Discussion……………………………………124 Chapter 7 Conclusions and Future Works…………………………………12