DMC-18x2
Chapter 10 Theory of Operation • 163
ZOH
The ZOH, or zero-order-hold, represents the effect of the sampling process, where the motor command
is updated once per sampling period. The effect of the ZOH can be modeled by the transfer function
H(s)
=
1/(1+sT/2)
If the sampling period is T = 0.001, for example, H(s) becomes:
H(s)
=
2000/(s+2000)
However, in most applications, H(s) may be approximated as one.
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-18x2 controller and the following parameters:
Kt = 0.1
Nm/A
Torque constant
J = 2.10-4 kg.m2
System moment of inertia
R = 2
Ω
Motor resistance
Ka = 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
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/2
π
= 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
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Содержание DMC-18 2 Series
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