Download Manual

This completes the modeling of the system elements. Next, we discuss the system analysis.
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-1500 controller and the following parameters:
Kt = 0.1
J = 2.10-4
Nm/A
kg.m2
Torque constant
R=2
Ω
Motor resistance
Ka = 4
KP = 12.5
Amp/Volt
Current amplifier gain
System moment of inertia
Digital filter gain
KD = 245
Digital filter zero
KI = 0
No integrator
N = 500
Counts/rev
Encoder line density
T=1
ms
Sample period
The transfer function of the system elements are:
Motor
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) = 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.
User Manual DMC-1500
Theory of Operation • 10 - 145