本論文在探討發展小型無人直昇機"翔蛉"(H-Ling，為雷虎翼手
龍90 級)的參數化模型及利用各種系統鑑別的技術來鑑別參數，包括ARX、CIFER 和PEM。此項計畫的最終目標是建立一個全功能的自主飛行旋翼機。我們首先簡短回顧了小型直昇機的運動方程式，然後簡單介紹每個方法的數學原理。藉由收集到的試飛數據，我們將直昇機的線性參數全數鑑別出來。本文透過比較各種鑑別理論所得的結果，來呈現這些結果的一致性，也間接證明那些結果的正確性。本文最後列出所有線性係數的組成細節，並且使用PEM 來對那些非線性參數進行鑑別，由於試飛資料的不夠完善，非線性的鑑別工作效果並不理想。

In this paper we are going to develop a parameterized model for a small-scale unmanned helicopter H-Ling (a Thunder Tiger Raptor-90) and its identification using various techniques, including ARX, CIFER and PEM. The ultimate goal of this project is to extend the current work to build a fully functional autonomous rotorcraft. The equations of motion of a small-scaled rotorcraft are briefly reviewed first. We then briefly introduce the mathematics of ARX and PEM. With the flight test data, we obtain the identified parameters of the dynamical model.Numerical simulations and table of identified parameters are provided to show the consistency and correctness of our results.
In the last part of this thesis we decompose the linear derivatives into detailed components, some of which are nonlinear. We were to identify those nonlinear components, but the results are not convincing enough due to the poor quality of flight test data.

Nomenclature iii
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Research Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Dynamics Model 4
2.1 Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Linearizatiom of the Equations of Motion . . . . . . . . . . . . . . . . . . . 8
2.3 Rotor Tip-Path-Plane Equation . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Yaw Dynamics and Flybar Dynamics . . . . . . . . . . . . . . . . . . . . . 12
2.5 Transfer function in hover . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.6 Overall model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 System Identi¯cation 16
3.1 Data Collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 What is System Identi¯cation . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.3 Introduction to ARX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.4 Introduction to PEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5 Comparison between ARX and PEM . . . . . . . . . . . . . . . . . . . . . 21
4 Identi¯ed Results of Linearized System 23
4.1 Flight Test Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2 Identi¯ed with ARX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.3 Identi¯ed with CIFER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.4 Identi¯ed Parameters with ARX , CIFER , PEM . . . . . . . . . . . . . . 35
5 Nonlinear Dynamics 38
5.1 Nonlinear Parameters list . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
5.2 Known and Unknown Parameters . . . . . . . . . . . . . . . . . . . . . . . 43
5.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
6 Conclusion 47
Bibliography 48

List of Tables
4.1 Scaling rules of Froude and March . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 Parameters for lateral channel . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.3 Parameters for longitudinal channel . . . . . . . . . . . . . . . . . . . . . . 36
4.4 List of complete parameters(2007-08-02) . . . . . . . . . . . . . . . . . . . 37
4.5 List of complete parameters(2008-10-13) . . . . . . . . . . . . . . . . . . . 37
5.1 Characteristics of R-90 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.2 Unknown Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

List of Figures
2.1 Thunder Tiger Raptor-90 mini-helicopter . . . . . . . . . . . . . . . . . . . 4
2.2 The Axis System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Thunder Tip-path-plane rotor representation . . . . . . . . . . . . . . . . . 11
2.4 Thunder Tip-roll-plane rotor representation . . . . . . . . . . . . . . . . . 11
2.5 Definition of Rotor Parameters . . . . . . . . . . . . . . . . . . . . . . . . 12
4.1 The Roll Sine Input (2007-08-02) . . . . . . . . . . . . . . . . . . . . . . . 25
4.2 The Pitch Sine Input (2007-08-02) . . . . . . . . . . . . . . . . . . . . . . . 25
4.3 Output Signal (2007-08-02) . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.4 The Bode plot of p/δlat from ARX (2007-08-02) . . . . . . . . . . . . . . . 28
4.5 The Bode plot of q/δlon from ARX (2007-08-02) . . . . . . . . . . . . . . . 28
4.6 The Bode plot of p/δlat from ARX (2008-10-13) . . . . . . . . . . . . . . . 30
4.7 The Bode plot of q/δlon from ARX (2008-10-13) . . . . . . . . . . . . . . . 30
4.8 The Bode magnitude plot of p/δlat from CIFER . . . . . . . . . . . . . . . 32
4.9 The Bode phase plot of p/δlat from CIFER . . . . . . . . . . . . . . . . . . 32
4.10 The Bode magnitude plot of q/δlon from CIFER . . . . . . . . . . . . . . . 33
4.11 The Bode phase plot of q/δlon from CIFER . . . . . . . . . . . . . . . . . . 33
4.12 The Coherence plot of p/δlat . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.13 The Coherence plot of q/δlon . . . . . . . . . . . . . . . . . . . . . . . . . . 34

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