飛彈終端攔截系統之非線性控制法則設計

Abstract

本論文主要是在研究歸向飛彈終端攔截之導引律設計與分析。我們由系統的強健穩定性的觀點，提出兩種強健控制理論將其運用在飛彈導引律之設計。在飛機攔截過程當中，由於目標逃逸的加速度一般來說是未知的，則可視為外在的干擾處理。首先我們利用滑順控制對於外界干擾具有強健性的特性，提出一種可變結構控制法則，來抑制外界干擾對系統的影響。此外，我們利用另一種H-infinity控制理論來設計飛彈導引律，期望外界干擾對於系統影響的程度能被限制在某個預設值內。利用數值模擬分析，我們在時域上對攔截時間和燃料耗損等兩項指標作一綜合性的探討。在性能比較上，我們將提出的兩種飛彈導引律設計與TPN、IPN作比較，由模擬結果可以發現，可變結構控制法則可以得到較佳的性能，且飛彈攔截的性能可以由設計者所設計的參數所控制。

In this thesis, we study the interception problem of homing missiles. From the robust stabilization point of view, we propose two of robust control techniques and use them on the design of missile guidance law. When the missile pursuits the target, the acceleration of target is usually unknown and can be regarded as external disturbance. According to the robustness of sliding-mode control, we use Variable Structure Control scheme to design missile guidance law. Moreover, H-infinity control scheme is also proposed for missile interception. We wish the ratio of output energy and input energy will less than or equal to the prescribed value. We use the capture time and the cumulative velocity increment as two performance indices. For the purpose of performance comparison, we compare the performance indices of two missile guidance laws with those of TPN and IPN. From simulation results, we can find that VSC can achieve good performance against both non-maneuvering and maneuvering target and the performance can be controlled by the parameters chosen by the designer. ABSTRACT ii ACKNOWLEDGMENT iii TABLE OF CONTENTS iv LIST OF FIGURES vii LIST OF TABLES x 1. INTRODUCTION 1 1.1. Motivation 1 1.2. The Interception Problem of Homing Missiles 3 1.3. Outline 3 2. PRELIMINARIES 5 2.1. Variable Structure Control 5 2.1.1. Introduction 5 2.1.2. Sliding Surfaces 6 2.1.3. Variable Structure Control Design 11 2.1.3.1. The Method of Equivalent Control 11 2.1.3.2. Controller Design 12 2.2. Nonlinear H-infinity Control Theory 13 2.2.1. Introduction 13 2.2.2. The Analysis of L-2 gain Stability 14 2.2.3. Nonlinear State-Feedback H-infinity Control 15 3. MISSILE GUIDANCE PROBLEM 18 3.1. Missile Kinematics 18 3.1.1. Problem Formulation 18 3.1.2. State Equation of Motion 21 3.2. Target Model 22 3.2.1. Weaving Target 22 3.2.2. Circular Target 22 3.3. Review of Proportional Navigation 24 3.3.1. True Proportional Navigation 24 3.3.2. Ideal Proportional Navigation 24 4. VARIABLE STRUCTURE CONTROL DESIGN 26 4.1. System Equations of Missile Guidance 26 4.2. Choice of Sliding Surface 26 4.3. Design of Control Law 27 4.3.1. Equivalent Control 27 4.3.2. Augmenting the Equivalent Control 28 4.4. Smoothing the Control Law 29 4.5. Simulation Results and Analysis 34 4.5.1. Non-maneuvering Target 34 4.5.2. Maneuvering Target 35 4.5.2.1. Weaving Target 35 4.5.2.2. Circular Target 35 4.5.3 Analysis 37 5. H-infinity CONTROL DESIGN 48 5.1. Formulation of Robust Guidance Problems 48 5.2. Control Law Design 50 5.2.1. Hamilton-Jacobi Partial Differential Inequality 50 5.2.2. Control Law 53 5.3. Simulation Results 54 5.3.1. Non-maneuvering Target 54 5.3.2. Maneuvering Target 55 5.3.2.1. Weaving Target 55 5.3.2.2. Circular Target 55 5.4. Performance Comparison 56 5.4.1. Non-maneuvering Target 56 5.4.2. Maneuvering Target 57 5.4.2.1. Weaving Target 57 5.4.2.2. Circular Target 57 5.4.3. Analysis 58 6. CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH 66 BIBLIOGRAPHY 68