Galil Motion Control DMC-18 2 Series User Manual page 175

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.
V
Σ
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)/[s 2 (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.
4
1
0.1
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.
164 ● Chapter 10 Theory of Operation
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FILTER
50+0.980s
ENCODER
318
Magnitude
50 200
ZOH DAC
2000
0.0003
S+2000
2000
AMP MOTOR
500
4
2
S
W (rad/s)
DMC-18x2