Galil Motion Control DMC-42 0 Series, User Manual

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System Design and Compensation
The closed-loop control system can be stabilized by a digital filter, which is pre-programmed in the DMC-42x0
controller. The filter parameters can be selected by the user for the best compensation. The following discussion
presents an analytical design method.
The Analytical Method
The analytical design method is aimed at closing the loop at a crossover frequency, ω
c
, with a phase margin PM.
The system parameters are assumed known. The design procedure is best illustrated by a design example.
Consider a system with the following parameters:
K
t
Nm/A Torque constant
J = 2 * 10
-4
kg.m
2 System moment of inertia
R = 2 Ω Motor resistance
K
a
= 2 Amp/Volt Current amplifier gain
N = 1000 Counts/rev Encoder line density
The DAC of the DMC-42x0 outputs ±10V for a 16-bit command of ±32768 counts.
The design objective is to select the filter parameters in order to close a position loop with a crossover frequency of
ωc = 500 rad/s and a phase margin of 45 degrees.
The first step is to develop a mathematical model of the system, as discussed in the previous system.
Motor
M(s) = P/I = Kt/Js
2
= 1000/s
2
Amp
K
a
= 2 [Amp/V]
DAC
K
d
= 10/32768 = .0003
Encoder
K
f
= 4N/2π = 636
ZOH
H(s) = 2000/(s+2000)
Compensation Filter
G(s) = P + sD
The next step is to combine all the system elements, with the exception of G(s), into one function, L(s).
L(s) = M(s) K
a
K
d
K
f
H(s) =3.17∙10
6
/[s
2
(s+2000)]
Then the open loop transfer function, A(s), is
A(s) = L(s) G(s)
Now, determine the magnitude and phase of L(s) at the frequency ωc = 500.
L(j500) = 3.17∙106/[(j500)2 (j500+2000)]
This function has a magnitude of
|L(j500)| = 0.00625
and a phase
Chapter 10 Theory of Operation ▫ 164 DMC-42x0 User Manual