Galil DMC-13X8 user manual Ms = P/I = Kt/Js2 = 500/s2 rad/A Amp Ka = 4 Amp/V

M(s) = P/I = Kt/Js2 = 500/s2 [rad/A]

Amp

Ka = 4 [Amp/V]

DAC

Kd = 0.0003 [V/count]

Encoder

Kf = 4N/2π = 318 [count/rad]

ZOH

2000/(s+2000) Digital Filter

KP = 12.5, KD = 245, T = 0.001 Therefore,

D(z) = 1030 (z-0.95)/Z

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

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.

Chapter 10 Theory of Operation • 166 USER MANUAL