文档介绍：Topic #2
Feedback Control Systems
Basic Root Locus
• Basic aircraft control concepts
• Basic control approaches
Cite as: Jonathan How, course materials for Feedback Control Systems, Fall 2007. MIT OpenCourseWare
(), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Fall 2007 2–1
Aircraft Longitudinal Control
• Consider the short period approximate model of an 747 aircraft.
x˙ sp = Aspxsp + Bspδe
where δe is the elevator input, and
w Zw/m U0
xsp = , Asp = −1 −1
q Iyy (Mw + Mw˙ Zw/m) Iyy (Mq + Mw˙ U0)
Zδe/m
Bsp = −1
Iyy (Mδe + Mw˙ Zδe/m)
• Add that θ˙= q, so sθ= q
• Take the output as θ, input is δe, then form the transfer function
θ(s) 1 q(s) 1 −1
= = 0 1 (sI − Asp) Bsp
δe(s) s δe(s) s
• For the 747 (40Kft, M = ) this reduces to:
θ(s) +
= − 2 ≡ Gθδe(s)
δe(s) s(s + + )
so that the dominant roots have a frequency of approximately 1
rad/sec and damping of about
Pole−Zero Map
1
1
0
Imaginary Axis
−
−
−
−
−1
−1 − − − − − − − − − 10
Real Axis
Figure 1: Pole-zero map for Gqδe
September 2, 2007
Cite as: Jonathan How, course materials for Feedback Control Systems, Fall 2007. MIT OpenCourseWare
(), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
Fall 2007 2–2
• Basic problem is that there are vast quantities of empirical data to
show that pilots do not like the flying qualities of an aircraft with
bination of frequency and damping
– What is preferred?
7
6
rad/sec
s
ω 5
POOR
ACCEPTABLE
4
3 SATISFACTORY
2
EPTABLE
1
Undamped natural frequency
0
1 2 4
Damping ratio ςs
Figure by MIT OpenCourseWa