Yaskawa LEGEND-MC - Manual (Page 38)

28
LEGEND-MC User’s Manual
The transfer function of the system elements are:
Motor:
M(s) = P/I = Kt/Js2 = 500/s
2
[rad/A]
Amp:
K
a
= 4 [Amp/V]
DAC:
K
d
= 0.0012 [V/count]
Encoder:
K
f
= 4N/2
π = 318 [count/rad]
ZOH:
2000/(s+2000)
Digital Filter:
KP = 12.5, KD = 245, T = 0.001
Therefore,:
D(z) = 12.5 + 245 (1-z-1)
Accordingly, the coefficients of the continuous filter are:
P = 12.5
D = 0.245
The filter equation may be written in the continuous equivalent form:
G(s) = 12.5 + 0.245s = 0.245(s+51)
The system elements are shown in the following illustration:
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)]
N = 500 Counts/rev Encoder line density
T = 1 ms Sample period
Σ
0.245(S+51)
318
ENCODER
500
S 2
FILTER
2000
S+2000
0.0012 4
ZOH DAC AMP MOTOR