System Analysis - Galil Motion Control DMC-1000 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 DMC-1000 controller and the following parameters:
K t = 0.1
J = 2.10 -4
R = 2
K a = 4
KP = 12.5
KD = 245
KI = 0
N = 500
T = 1
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 = 0.0003 [V/count]
Encoder
K f = 4N/2π = 318 [count/rad]
ZOH
2000/(s+2000)
Digital Filter
KP = 12.5, KD = 245, T = 0.001
Therefore,
D(z) = 50 + 980 (1-z-1)
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
The system elements are shown in Fig. 10.7.
DMC-1000
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Nm/A
kg.m 2
Ω
Amp/Volt
Counts/rev
ms
Torque constant
System moment of inertia
Motor resistance
Current amplifier gain
Digital filter gain
Digital filter zero
No integrator
Encoder line density
Sample period
Chapter 10 Theory of Operation • 139