本論文在探討無人直昇機自主停懸之控制器設計。之前我們已經利用系統鑑別的方法找出小型無人直昇機”翔蛉”(H-Ling，為雷虎翼手龍90級)的動力參數。在此基礎之上，我們設計了PID控制器來穩定它停懸時的姿態。僅管直昇機的動力學是非常複雜且常互相偶合，但在停懸時，通常只需考慮四個主要動態的控制：週期性側向輸入對滾轉率輸出、週期性縱向輸入對俯仰率輸出、尾懸翼輸入對偏航率輸出、以及集體槳矩輸入對垂直位置輸出。在我們的研究中，亦考量了來自環境的擾動，諸如陣風等，並將之用高斯分佈的隨機變數來模擬。本文採用Ziegler-Nichols Tuning Method 來選擇每個控制器的參數，並提供數值模擬結果。另外，我們也常是將外迴圈的控制器改成相位領先補償器，再跟原先的PID控制來做比較，選出結果較好的控制器。最後再將模擬結果來跟真實飛行的資料做比較，證明我們的設計是有效的。

The autonomous hover of unmanned helicopters and design of controllers are presented in this thesis. A Thunder Tiger Raptor-90 helicopter (renamed as H-Ling) is selected to
investigate. Starting from the identi ed model of H-Ling we design proportional-integralderivative (PID) controllers to stabilize its attitude in hover. Although the general dynamics of a helicopter is highly coupled and nonlinear, for the purpose of implementation we here only discuss control of dynamics of four main channels, cyclic lateral input to rolling rate, cyclic longitudinal input to pitching rate, pedal input to yawing rate, and collective pitch input to vertical motions, in the neighborhood of hovering state. Environment disturbances such as wind gusts, modeled as Gaussian random variables, are also
included in the analysis and the Ziegler-Nichols Tuning Method is selected to determine control gains. In addition, we also try to control the outer loop using a lead compensator, which later on is compared with the formor PID controllers. The better one is then selected for implementing candidate. Finally, numerical simulations and comparisons with flight test data are provide to shown the e ectiveness of our design.

Contents
Chinses Abstract i
Abstract ii
Acknowledgement iii
Nomenclature iv
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Research Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Dynamics Model 4
2.1 Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Coupling Dynamics of Fuselage and Rotor . . . . . . . . . . . . . . . . . . 7
2.3 Yaw Dynamics and Flybar Dynamics . . . . . . . . . . . . . . . . . . . . . 11
2.4 Overall model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Transfer Functions in Hover . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Autonomous Flight 24
3.1 Flight Test Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Design Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.1 Speci cations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.2 Constraints form Hardware . . . . . . . . . . . . . . . . . . . . . . 28
3.2.3 Disturbances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2.4 Hierarchical Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3 Ziegler-Nichols Tuning Method . . . . . . . . . . . . . . . . . . . . . . . . 30
3.4 PID Controller Gain Tuning (Design of Time Domain Method) . . . . . . . 31
3.5 Phase Lead Compensator Gain Tuning Method) . . . . . . . . . . . . . . . 33
3.5.1 Phase Lead Compensator . . . . . . . . . . . . . . . . . . . . . . . 33
3.5.2 Design Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.6 Design Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4 Numerical Simulations 36
4.1 Root Locus Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
4.2 Bode Polt Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 System Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.4 Simulation Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5 Comparison with Flight Data 54
6 Conclusions and Future Works 58
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Bibliography 61

List of Tables
2.1 A table listing the characteristic parameters of a Thunder Tiger Raptor 90
helicopter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.1 Performance of Crossbow AHRS400CC-100 . . . . . . . . . . . . . . . . . . 27
3.2 Parameter selection rules by Ziegler-Nichols Tuning Method . . . . . . . . 31
3.3 Selected parameters to stabilize the attitude in hover . . . . . . . . . . . . 35
3.4 The transfer function of phase-lead compensator for attitude control in hover 35

List of Figures
2.1 The Flowchart of Research Method . . . . . . . . . . . . . . . . . . . . . . 4
2.2 The Axis System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Definition of Rotor Parameters . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Definition of Rotor Parameters . . . . . . . . . . . . . . . . . . . . . . . . 8
2.5 Definition of Rotor Parameters . . . . . . . . . . . . . . . . . . . . . . . . 9
2.6 Flybar Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.7 Pole-Zero Map for Lateral Tranfer Function . . . . . . . . . . . . . . . . . 16
2.8 Pole-Zero Map for Longitudinal Tranfer Function . . . . . . . . . . . . . . 17
2.9 Pole-Zero Map for Yawing Tranfer Function . . . . . . . . . . . . . . . . . 18
2.10 Pole-Zero Map for Vertical Motion . . . . . . . . . . . . . . . . . . . . . . 19
2.11 Bode Diagram for Lateral Tranfer Function . . . . . . . . . . . . . . . . . . 20
2.12 Bode Diagram for Longitudinal Tranfer Function . . . . . . . . . . . . . . 21
2.13 Bode Diagram for Yawing Tranfer Function . . . . . . . . . . . . . . . . . 22
2.14 Bode Diagram for Vertical Motion . . . . . . . . . . . . . . . . . . . . . . . 23
3.1 Detailed scheme for the control system (obtain from NCKU) . . . . . . . . 25
3.2 The on-board computer kit . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 The R-90 helicopter equipped with the OBC kit . . . . . . . . . . . . . . . 26
3.4 Finished products for PWM Decoder circuit . . . . . . . . . . . . . . . . . 27
3.5 Detailed scheme for PID control . . . . . . . . . . . . . . . . . . . . . . . . 30
4.1 root locus analysis for lateral control . . . . . . . . . . . . . . . . . . . . . 37
4.2 root locus analysis for longitudinal control . . . . . . . . . . . . . . . . . . 38
4.3 root locus analysis for pedal control . . . . . . . . . . . . . . . . . . . . . . 39
4.4 root locus analysis for collective control . . . . . . . . . . . . . . . . . . . . 40
4.5 root locus analysis for lateral control . . . . . . . . . . . . . . . . . . . . . 41
4.6 root locus analysis for longitudinal control . . . . . . . . . . . . . . . . . . 42
4.7 root locus analysis for pedal control . . . . . . . . . . . . . . . . . . . . . . 43
4.8 root locus analysis for collective control . . . . . . . . . . . . . . . . . . . . 44
4.9 Block-diagram of roll angle control . . . . . . . . . . . . . . . . . . . . . . 46
4.10 Block-diagram of pitch angle control . . . . . . . . . . . . . . . . . . . . . 47
4.11 Block-diagram of yaw angle control . . . . . . . . . . . . . . . . . . . . . . 47
4.12 Block-diagram of vertical motion control . . . . . . . . . . . . . . . . . . . 47
4.13 Compare with PD Controller and Lead-Compensated result of roll angle
control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.14 Compare with PD Controller and Lead-Compensated result of pitch angle
control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.15 Compare with PD Controller and Lead-Compensated result of yaw angle
control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.16 PD Controller result of vertical motion control . . . . . . . . . . . . . . . . 51
4.17 Rate in terms of roll, pitch, yaw angles and vertical motion during a numerical
simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.18 Angle in terms of roll, pitch, yaw angles and vertical motion during a
numerical simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1 PWM signal with 
flight test (obtain from NCKU) . . . . . . . . . . . . . . 55
5.2 Compare PD algorithm with 
flight data for rolling control . . . . . . . . . 56
5.3 Compare PD algorithm with 
flight data for pitching control . . . . . . . . 57

[1] B. Mettler, M. Tischler, and T. Kanade, System identi cation of a model-scale
helicopter," Robotics Institute, Carnegie Mellon University, Pittsburgh, PA, Tech.
Rep. CMU-RI-TR-00-03, January 2000.
[2] B. Mettler, C. Dever, and E. Feron, Identi cation modeling, 
ying qualities, and
dynamic scaling of miniature rotorcraft," International Conference on Microelec-
tromechanical Systems (MEMS). 15th. Held in Las Vegas, pp. 511{515, 2002.
[3] B. Mettler, Identi cation modeling and characteristics of miniature rotorcraft.
Boston: Kluwer Academic Publishers, 2003.
[4] M. B. Tischler and M. G. Gau man, Frequency-response method for rotorcraft
system identi cation: Flight application to bo-105 coupled rotor/fuslage dynamics,"
the American Helicopter Society, Journal 37(3):3-17, 1992.
[5] S. K. Kim and D. M. Tilbury, Mathematical modeling and experimental identi -
cation of an unmanned helicopter robot with 
ybar dynamics," Journal of Robotic
Systems, vol. 21, pp. 95{116, 2004.
[6] I. P. A. Yue and G. Pad eld, h1 design and the improvement of helicopter handing
qualities," Vertica, Tech. Rep., 1989.
[7] M. W. Weilenmann, Robust mehrgrossen-regelung eines helicopters," Swiss Federal
Instititute of Technology, Zurich, Switzerland, PhD thesis, 1994.
[8] U. c. M. W. Weilenmann and H.-P. Geering, Robust helicopter posistion control at
hover," the 1994 American Control Conference, 1994.
61
[9] M. W. Weilenmann and H.-P. Geering, A test bench for the rotorcraft hover control,"
Monterey, CA, AIAA Guidance Navigation and Control Conference, 1993.
[10] H. K. Tatsuya Sakamoto and A. Ichikawa, Attitude control of a helicopter model by
robust pid controllers," International Symposium on Intelligent Control, pp. 1971{
1976, 2006.
[11] E. N. Sanchez, H. M. Becerra, and C. M. Velez, Combining fuzzy, pid and regulation
control for an autonomous mini-helicopter," Information Sciences, vol. 177, pp.
1999{2022, May 2007.
[12] ||, Combining fuzzy, pid and regulation control for an autonomous minihelicopter,"
Wseas Transactions On Systems, vol. 5, pp. 2250{2256, 2006.
[13] ||, Combining fuzzy and pid control for an unmanned helicopter," IEEE, vol. v
2005, pp. 235{240, 2005.
[14] C. M. Velez and A. Agudelo, Multirate control of an unmanned aerial vehicle,"
WSEAS Transactions on Circuits and Systems, vol. 4, no. 11, pp. 1628{1634, 2005.
[15] J. H. Tseng, System identi cation of unmanned helicopter: Applications to r-90,"
Tamkang University, Master's Thesis, 2007.
[16] R. Chen, E ects of primary rotor parameters on 
apping dynamics," NASA, Technical
Report TP 1431, 1980.
[17] G. D. Pad eld, Helicopter 
ight dynamics : the theory and application of 
ying
qualities and simulation modelling. Oxford: Blackwell Science, 1996.
[18] J. Valerio and J. S. da Costa, Tuning of fractional pid controllers with zieglernichols-
type rules," Proceedings of ASME, vol. 86, pp. 2771{2784, Octorber 2006.
[19] C. C. Yu, Autotuning of PID Controllers, 2nd ed. London: Springer-Verlag, 2006.
[20] L. Ljung, System Identi cation Toolbox 7 User's Guide, The Mathworks Inc., 2007.