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《A Mathematical Perspective on Flight Dynamics and Control》
在飞行动力学与控制的数学观点
作者：
Andrea L’Afflitto
School of Aerospace and Mechanical
Engineering
The University of Oklahoma
出版社：Springer
出版时间：2017年
《A Mathematical Perspective on Flight Dynamics and Control》
《A Mathematical Perspective on Flight Dynamics and Control》
《A Mathematical Perspective on Flight Dynamics and Control》
《A Mathematical Perspective on Flight Dynamics and Control》
目录
1 Fundamentals of Rigid Body Dynamics . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Vectors and Vector Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 The First Derivative of a Vector with Respect to Time . . . . . . . . 5
1.4 Tait–Bryan Angles and Rotations . . . . . . . . . . . . . . . . . . . . . . . 10
1.4.1 Tait–Bryan Angles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4.2 Rotations of Reference Frames and Vectors. . . . . . . . . . . 12
1.4.3 Properties of the Tait–Bryan Angles
and Rotation Matrices. . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.5 Euler Parameters, Quaternions, and Rotations . . . . . . . . . . . . . . 19
1.5.1 Quaternions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.5.2 Quaternions and Rotations . . . . . . . . . . . . . . . . . . . . . . 23
1.5.3 Euler Parameters and Angular Velocity. . . . . . . . . . . . . . 26
1.6 The Second Derivative of a Vector with Respect to Time . . . . . . 28
1.7 Equations of Motion of a Rigid Body. . . . . . . . . . . . . . . . . . . . 30
2 Equations of Motion of an Aircraft . . . . . . . . . . . . . . . . . . . . . . . . 35
2.1 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.1.1 Body and Inertial Reference Frames . . . . . . . . . . . . . . . . 35
2.1.2 The Aircraft State Vector . . . . . . . . . . . . . . . . . . . . . . . 37
2.1.3 The Aircraft Control Vector . . . . . . . . . . . . . . . . . . . . . 37
2.1.4 Aerodynamic Angles . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.2 Forces and Moments Acting on an Aircraft . . . . . . . . . . . . . . . . 41
2.3 Equations of Motion of an Aircraft. . . . . . . . . . . . . . . . . . . . . . 42
2.4 Flight at Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.5 Linearization of the Aircraft Equations of Motion. . . . . . . . . . . . 46
2.6 Decoupling of the Linearized Equations of Motion. . . . . . . . . . . 48
2.7 Analysis of the Longitudinal Dynamics of an Aircraft. . . . . . . . . 54
2.8 Analysis of the Lateral-Directional Dynamics of an Aircraft . . . . 59
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3 Aircraft Automatic Control. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.2 Transfer Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.3 Proportional-Integral-Derivative Control . . . . . . . . . . . . . . . . . . 67
3.4 The Linear-Quadratic Gaussian Control. . . . . . . . . . . . . . . . . . . 75
3.5 Optimal State-Feedback H1 control . . . . . . . . . . . . . . . . . . . . . 81
3.6 Model Reference Adaptive Control. . . . . . . . . . . . . . . . . . . . . . 84
4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Appendix A: Fundamentals of Dynamical Systems Theory . . . . . . . . . 91
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
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