Civil Engineering Reference
In-Depth Information
Such frequency responses are often shown as Bode plots. The magnitude and phase for different
input signal frequencies are plotted separately. The magnitude is plotted on a logarithmic scale,
against the frequency, which is also plotted on a logarithmic scale. At the whim of the maker of the
plot, the frequency may be given in rad
sec, in Hertz, or sometimes in octaves. For the magnitude,
often a decibel (dB) scale is used. The relation between a magnification M and its equivalent in dB
m is:
/
m
¼
20
log
10
M
½
dB
:
(12
:
6)
Figure 12.5 shows the Bode plot for this system. One can see that for low frequencies the gain of
the system is 1 (0 dB). For high frequencies the gain decreases 20 dB per decade. The asymptotes for
the low and high frequency behavior cross at the corner frequency 1
/
t, in this case, with t
¼
10 sec,
at 0.1 rad
/
sec.
12.2.4 Control
12.2.4.1 Feed-Forward and Feedback
In a control system, a controlling element (controller) provides input to a system, often called a
plant, normally with the aim of producing outputs of the plant that are equal to given reference
values. Unknown disturbances may be acting on the plant, as for example, the turbulence acting
on an aircraft. The controller may be an automatic device, such as an autopilot, or it may be a
human.
In feed-forward control, or open-loop control, the controller measures the disturbances on the plant,
and based on the knowledge about the plant's dynamics, creates inputs that produce plant outputs as
close to the reference values as possible, see Figure 12.6a.
Amplitude Response
10
1
10
0
10
−1
corner frequency
10
−2
10
−2
10
−1
10
0
10
1
Phase Response
0
−20
−40
−60
corner frequency
−80
10
−2
10
−1
10
0
10
1
frequency, rad/sec
FIGURE 12.5 Bode plot for LTI system H(jv)
1
(1
þ
10jv). The circles show the system response for the four
¼
/
frequencies shown in Figure 12.4.
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