文档介绍：0066_frame_C27 Page 1 Wednesday, January 9, 2002 7:10 PM
27
Frequency Response
Methods
Introduction
Bode Plots
Polar Plots
Log-Magnitude Versus Phase plots
Experimental Determination
of Transfer Functions
Jyh-Jong Sheen The Nyquist Stability Criterion
National Taiwan Ocean University Relative Stability
Introduction
The analysis and design of industrial control systems are often plished utilizing frequency response
methods. By the term frequency response, we mean the steady-state response of a linear constant coefficient
system to a sinusoidal input test signal. We will see that the response of the system to a sinusoidal input
signal is also a sinusoidal output signal at the same frequency as the input. However, the magnitude and
phase of the output signal differ from those of the input signal, and the amount of difference is a function
of the input frequency. Thus, we will be investigating the relationship between the transfer function and
the frequency response of linear stable systems.
ω
Consider a stable linear constant coefficient system shown in Fig. . Using Euler’s formula, e j t =
cosωt + j sinωt, let us assume that the input sinusoidal signal is given by
()==jwt +
ut U0e U0 coswt jU0 sinwt ()
Taking the Laplace transform of u(t) gives
+
()==U0 sjw =U0s + U0w
Us ------------- U0 ---------------- ---------------- j---------------- ()
sj– w s2 + w2 s2 + w2 s2 + w2
ω
The first term in Eq. () is the Laplace transform of U0 cos t, while the second term, without the
ω
imaginary number j, is the Laplace transform of U0 sin t.
Suppose that the transfer function G(s) can be written as
() ()
()==ns ns
Gs ---------()- ------------------------------------------------------------()+ ()+ …()+ - ()
ds sp1 sp2 spn
©2002 CRC Press LLC
0066_frame_C27 Page 2 Wednesday, January 9, 2002 7:10 PM
FIGURE A stable linear constant coefficient