文档介绍：Topic #5
Feedback Control Systems
Control Design using Bode Plots
• Performance Issues
• Synthesis
• Lead/Lag examples
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 5–1
Bode’s Gain Phase Relationship
• Control synthesis by classical means would be very hard if we had
to consider both the magnitude and phase plots of the loop, but
that is not the case.
• Theorem: For any stable, minimum phase system G(s), G(jω)
is uniquely related to |G(jω)|.
• The relationship is that, on a log-log plot, if the slope of the
magnitude plot is constant over a decade in frequency, with slope
n, then
G(jω) ≈ 90◦n
• So in the crossover region, where L(jω) ≈ 1 if the magnitude plot
is (locally):
s0 slope of 0, so no crossover possible
s−1 slope of -1, so about 90◦PM
s−2 slope of -2, so PM very small
• Basic rule of classical control design:
Select Gc(s) so that the LTF crosses over with a slope of -1.
September 13, 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 5–2
Performance Issues
• Step error response
1
ess =
1 + Gc(0)Gp(0)
and we can determine Gc(0)Gp(0) from the low frequency Bode
plot for a type 0 system.
• For a type 1 system, the DC gain is infinite, but define
Kv = lim sGc(s)Gp(s) ⇒ ess = 1/Kv
s→0
– So can easily determine this from the low frequency slope of
the Bode plot.
September 13, 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 5–3
Performance Issues II
• Classic question: how much p