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)/[s
2
(s+2000)]
To analyze the system stability, determine the crossover frequency, ωc at which A(j ωc) equals one. This can be
done by the Bode plot of A(j ωc), 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.
DMC-40x0 User Manual Chapter 10 Theory of Operation • 192
To Next Page
Loading...
