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┃ ┃~el _ ┃
┃ ┃'0 a ┃
┣━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╋━━━━━┫
┃LI D -5 - -3 \I -- i t- zc -* ~- 2.5435 ┃ ┃
┃5'1278/. _j ┃ ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┻━━━━━┛
Fig. 536 Root-Iocii for the control system of Example 5.10-
~,:r
I
500 PERFORMANCE, STABILI-fY, DYNAMICS, AND CONTROL
Root-Locus of PD Compensated System
ReaIAxis
c)
Fig. 5.36 Root-Iocii for the control system of Example 5.lO,continued.
the closed-loop pole locations are -0.8299 + j1.9426 and -6.3402. Because the
third pole located at -6.3402 is farther from the second-order poles, we can use the
second-order approximation. With this assumption, the times for peak amplitude
for the basic system Tp and that for the compensated system Tpc are given by
7r
Tp = tOd
rr
= ~9~426 = 1.6172 s
Tp. = fj = 0.5391s
Then,
cocic = T
7r
= 0 539~
- 5.8278
LINEAR SYSTEMS, THEORY, AND DESIGN: A BRIEF REVIEW 501
Root-Locus of lead-lag compensated system.
Real Axis
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