Galil DMC-2X00 user manual Magnitude 200 2000 Rad/s

V

Σ

FILTER

50+0.980s

ENCODER

318

ZOH

2000

S+2000

DAC

0.0003

AMP

4

MOTOR

500

S2

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.

Magnitude
4
1
50	200	2000	W (rad/s)
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. 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°

142 • Chapter 10 Theory of Operation DMC-2X00