Galil DMC-2X00 - Manual (Page 197)

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, 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.
Next, we determine the phase of A(s) at the crossover frequency.
A(j200) = 390,000 (j200+51)/[(j200)2 . (j200 + 2000)]
α = Arg[A(j200)] = tan-1(200/51)-180° -tan-1(200/2000)
α = 76° - 180° - 6° = -110°
DMC-2X00 Chapter 10 Theory of Operation y 187