文档介绍：Topic #3
Feedback Control
Frequency response methods
• Analysis
• Synthesis
• Performance
• Stability
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 3–1
FR: Introduction
• Root locus methods have:
– Advantages:
Good indicator 0f transient response;
Explicitly shows location of all closed-loop poles;
Trade-offs in the design are fairly clear.
– Disadvantages:
Requires a transfer function model (poles and zeros);
Difficult to infer all performance metrics;
Hard to determine response to steady-state (sinusoids)
Hard to infer stability margins
• Frequency response methods are a plement to the root
locus techniques:
– Can infer performance and stability from the same plot
– Can use measured data rather than a transfer function model
– Design process can be independent of the system order
– Time delays are handled correctly
– Graphical techniques (analysis and synthesis) are quite simple.
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 3–2
Frequency Response Function
• Given a system with a transfer function G(s), we call the G(jω),
ω∈[0, ∞) the frequency response function (FRF)
G(jω) = |G(jω)|G(jω)
– The FRF can be used to find the steady-state response of a
system to a sinusoidal input since, if
e(t) → G(s) → y(t)
and e(t) = sin 2t, |G(2j)| = , G(2j) = 80◦, then the
steady-state output is
y(t) = sin(2t − 80◦)
⇒ The FRF clearly shows the magnitude (and phase) of the
response of a system to sinusoidal input
• A variety of ways to display this:
1. Polar (Nyquist) plot – Re vs. Im of G(jω) plex plane.
– Hard to visualize, not useful for