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-40x0 controller and the following parameters:
K
t
= 0.1 Nm/A Torque constant
J = 2 * 10
-4
kg.m
2
System moment of inertia
R = 2 Ω 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
The transfer function of the system elements are:
Motor
M(s) = P/I = K
t
/Js
2
= 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) = 1030 (z-0.95)/Z
Accordingly, the coefficients of the continuous filter are:
P = 50
D = 0.98
The filter equation may be written in the continuous equivalent form:
Chapter 10 Theory of Operation ▫ 177 DMC-40x0 User Manual
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