Yaskawa SMC–4000 - Manual (Page 34)

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SMC–4000 User Manual
System Analysis
To analyze the system, we start with a block diagram model of the system elements. The analysis
procedure is illustrated in terms of the following example.
Consider a position control system with the SMC–4000 controller and the following parameters:
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)
K
t
= 0.1 Nm/A Torque constant
J = 2.10 -4 kg.m 2 System moment of inertia
R = 2 W Motor resistance
K
a
= 4 Amp/Volt Current amplifier gain
KP = 12.5 Digital filter gain
KD = 245 Digital filter zero
KI = 0 No integrator
N = 500 Counts/rev Encoder line density
T = 1 ms Sample period