先进航天器动力学与控制：第二版

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"《Space Vehicle Dynamics and Control》第二版由Bong Wie撰写，他是Iowa State University的教授。这本书在第一版的基础上增加了260多页的新内容，涵盖了近年来在敏捷成像卫星、控制力矩陀螺、太阳帆以及空间太阳能电站等先进航天器动态建模和控制方面的最新进展。这些新内容基于作者在过去10年中在《Journal of Guidance, Control, and Dynamics》期刊上发表或在各类技术会议上展示的技术论文。第一版中的少量排版错误在第二版中得到了修正，除了参考文献外，第一版的所有内容都得以保留。" 《Space Vehicle Dynamics and Control》是航空航天教育系列的一部分，由Joseph A. Schetz担任系列主编。该书由美国航空航天学会(American Institute of Aeronautics and Astronautics)出版，并在封面上注明了MATLAB商标归The MathWorks, Inc.所有。书号和版权信息显示，这本书于2008年首次发行，具有详细的参考文献和索引。本书详细探讨了空间车辆的动力学与控制，不仅涵盖基础理论，还关注了现代航天技术的最新发展。新增内容主要集中在以下几个方面： 1. **敏捷成像卫星**：这些卫星通常需要快速精确地调整姿态，以便对地面目标进行高分辨率成像。控制力矩陀螺（CMG）是这类卫星常用的一种姿态控制系统，它利用旋转质量产生控制力矩，能实现高效率和高精度的航天器姿态控制。 2. **太阳帆**：太阳帆是一种利用太阳光压驱动航天器前进的创新技术。书中可能详细讨论了太阳帆的设计、动力学模型以及如何利用微弱的太阳光压力进行轨道控制和姿态稳定。 3. **空间太阳能电站**：这类电站设想在地球静止轨道上建立大规模的太阳能收集装置，然后将能量无线传输到地球。控制和动力学问题在这个领域变得极其复杂，涉及大型结构的稳定性、轨道维持以及与地面的通信和能量传输。书中可能还涵盖了以下核心知识点： - **航天器动力学模型**：包括基本的牛顿运动定律，以及考虑地球重力、太阳引力、大气阻力等因素的完整动力学模型。 - **控制系统设计**：使用经典控制理论如PID控制，现代控制理论如状态反馈、滑模控制，以及针对非线性系统和不确定性问题的自适应控制策略。 - **姿态确定和导航**：介绍了姿态估计算法，如卡尔曼滤波，以及利用星敏感器、地球图像或其他传感器的数据进行导航的方法。 - **轨道动力学**：涵盖开普勒定律，近圆轨道和椭圆轨道的特性，以及轨道转移和维持策略。 - **实验与仿真**：可能包含实验平台的描述，以及使用MATLAB等工具进行航天器动力学和控制的数值仿真方法。《Space Vehicle Dynamics and Control》第二版是一部全面且深入的教材，适合航空航天工程的学生、研究人员以及行业从业者学习和参考，它将理论知识与实际应用相结合，展示了空间探索与利用领域的最新技术进展。

“Chapter02” — 2008/7/18 — 20:01 — page 128 — #8

128 SPACE VEHICLE DYNAMICS AND CONTROL

where |G( jω)| and φ(ω) denote, respectively, the magnitude and phase of G( jω)

deﬁned as

|G( jω)|=



{Re[G( jω)]}

+{Im[G( jω)]}

φ(ω) = tan

−1

Im[G( jω)]

Re[G( jω)]

For a given value of ω, G( jω) is a complex number. Thus, the frequency-

response function G( jω) is a complex function of ω. Mathematically, the fre-

quency-response function is a mapping from the s plane to the G( jω) plane. The

upper-half of the jω axis, which is a straight line, is mapped into the complex plane

via mapping G( jω).

One common method of displaying the frequency-response function is a polar

plot (also called a Nyquist plot) where the magnitude and phase angle of G( jω),

or its real and imaginary parts, are plotted in a plane as the frequency ω is varied.

Another form of displaying G( jω) is to plot the magnitude of G( jω) vs ω and to

plot the phase angle of G( jω) vs ω.InaBode plot, the magnitude and phase angle

are plotted with frequency on a logarithmic scale. Also, we often plot the magnitude

of the frequency-response function in decibels; that is, we plot 20 log |G( jω)|.A

plot of the logarithmic magnitude in decibels vs the phase angle for a frequency

range of interest is called a Nichols plot.

For a feedback control system, as shown in Fig. 2.1, the loop transfer function

K(s)G(s) evaluated at s = jω is used extensively in the analysis and design of the

system using frequency-response methods. The closed-loop frequency response

functions deﬁned as

y( jω)

d( jω)

= S( jω) =

1 + K( jω)G( jω)

(2.20)

y( jω)

r( jω)

= T ( jω) =

K( jω)G( jω)

1 + K( jω)G( jω)

(2.21)

are also used in classical frequency-domain control systems design.

Among the most important measures of the relative stability of a feedback

control system are the gain and phase margins as deﬁned as follows.

2.2.2.1 Gain Margin Given the loop transfer function K(s )G(s) of a feed-

back control system, the gain margin is deﬁned as the reciprocal of the magnitude

|K( jω)G( jω)| at the phase-crossover frequency at which the phase angle φ(ω) is

−180 deg; that is, the gain margin, denoted by g

, is deﬁned as

|K( jω

)G( jω

(2.22)

=−20 log |K( jω

)G( jω

)| dB (2.23)

where ω

is the phase-crossover frequency. For a stable minimum-phase system,

the gain margin indicates how much the gain can be increased before the closed-

loop system becomes unstable.

“Chapter02” — 2008/7/18 — 20:01 — page 131 — #11

DYNAMIC SYSTEMS CONTROL 131

where k and c are controller gains to be determined. The closed-loop system

illustrated by Fig. 2.4b is then described by

m¨y(t) + c˙y(t) + ky(t) = w(t)

which is, in fact, a mathematical representation of a mass–spring–damper system

forced by an external disturbance w(t), as illustrated in Fig. 2.4c.

The closed-loop characteristic equation of the system shown in Fig. 2.4 is

+ cs + k = 0

The control design task is to tune the active damper and active spring to meet given

performance/stability speciﬁcations of the closed-loop system. Let ω

and ζ be

the desired natural frequency and damping ratio of the closed-loop poles. Then the

desired closed-loop characteristic equation becomes

+ 2ζω

s + ω

= 0

and the controller gains c and k can be determined as

c = 2mζω

(2.27a)

k = mω

(2.27b)

The damping ratio ζ is often selected as 0.5 ≤ ζ ≤ 0.707, and the natural frequency

is then considered the bandwidth of the proportional-derivative (PD) controller

of a system with a rigid-body mode. For a unit-step disturbance, this closed-loop

system with the PD controller results in a nonzero steady-state output y(∞) = 1/k.

The steady-state output error y(∞) can be made small, however, by designing a

high-bandwidth control system.

To keep the cart at the desired position y = 0 at steady state in the presence of

a constant disturbance, consider a PID controller of the form

u(t) =−K

y(t) − K

y(t) dt − K

˙y(t) (2.28)

u(s) =−



+ K



y(s)

In practical analog circuit implementation of a PID controller when ˙y is not

directly measured, differentiation is always preceded by a low-pass ﬁlter to reduce

noise effects. It can be shown that for a constant disturbance, the closed-loop

system with the PID controller, in fact, results in a zero steady-state output

y(∞) = 0.

The closed-loop characteristic equation of the cart with the PID controller can

be found as

+ K

s + K

= 0

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先进航天器动力学与控制：第二版

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