Galil Motion Control CDS-3310 User Manual page 136

Encoder
ZOH
Compensation Filter
The next step is to combine all the system elements, with the exception of G(s), into one function, L(s).
Then the open loop transfer function, A(s), is
Now, determine the magnitude and phase of L(s) at the frequency ω c = 500.
This function has a magnitude of
and a phase
G(s) is selected so that A(s) has a crossover frequency of 500 rad/s and a phase margin of 45 degrees.
This requires that
However, since
then it follows that G(s) must have magnitude of
and a phase
In other words, we need to select a filter function G(s) of the form
so that at the frequency ω c =500, the function would have a magnitude of 160 and a phase lead of 59
degrees.
These requirements may be expressed as:
and
The solution of these equations leads to:
CDS-3310
K f = 4N/2π = 636
H(s) = 2000/(s+2000)
G(s) = P + sD
L(s) = M(s) K a K d K f H(s) =3.17∗10 6 /[s 2 (s+2000)]
A(s) = L(s) G(s)
L(j500) = 3.17∗10 6 /[(j500) 2 (j500+2000)]
|L(j500)| = 0.00625
Arg[L(j500)] = -180° - tan -1 (500/2000) = -194°
|A(j500)| = 1
Arg [A(j500)] = -135°
A(s) = L(s) G(s)
|G(j500)| = |A(j500)/L(j500)| = 160
arg [G(j500)] = arg [A(j500)] - arg [L(j500)] = -135° + 194° = 59°
G(s) = P + sD
|G(j500)| = |P + (j500D)| = 160
arg [G(j500)] = tan -1 [500D/P] = 59°
P = 160cos 59° = 82.4
Chapter 10 Theory of Operation
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