Galil Motion Control DMC-18 2 Series, Руководство пользователя

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164 ● Chapter 10 Theory of Operation DMC-18x2
Accordingly, the coefficients of the continuous filter are:
P = 50
D = 0.98
The filter equation may be written in the continuous equivalent form:
G(s) = 50 + 0.98s = .098 (s+51)
The system elements are shown in Fig. 10.7.
Σ
50+0.980s
318
V
ENCODER
500
S
2
FILTER
2000
S+2000
0.0003 4
ZOH DAC
AMP
MOTOR
Figure 10.7 - Mathematical model of the control system
The open loop transfer function, A(s), is the product of all the elements in the loop.
A = 390,000 (s+51)/[s2(s+2000)]
To analyze the system stability, determine the crossover frequency,
ω
c at which A(j
ω
c) equals one.
This can be done by the Bode plot of A(j
ω
c), as shown in Fig. 10.8.
1
4
0.1
50 200 2000 W (rad/s)
Magnitude
Figure 10.8 - Bode plot of the open loop transfer function
For the given example, the crossover frequency was computed numerically resulting in 200 rad/s.
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