Galil Motion Control DMC-21 5 Series User Manual page 138

L(s) = M(s) K
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 ω c = 500.
L(j500) = 3.17· 10 6 /[(j500) 2 (j500+2000)]
This function has a magnitude of
|L(j500)| = 0.00625
and a phase
Arg[L(j500)] = -180° - tan
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
|A(j500)| = 1
Arg [A(j500)] = -135°
However, since
A(s) = L(s) G(s)
then it follows that G(s) must have magnitude of
|G(j500)| = |A(j500)/L(j500)| = 160
and a phase
arg [G(j500)] = arg [A(j500)] - arg [L(j500)] = -135° + 194° = 59°
In other words, a filter function G(s) needs to be selected of the form
G(s) = P + sD
so that at the frequency ω
These requirements may be expressed as:
|G(j500)| = |P + (j500D)| = 160
and
arg [G(j500)] = tan -1 [500D/P] = 59°
The solution of these equations leads to:
P = 160cos 59° = 82.4
500D = 160sin 59° = 137
Therefore,
D = 0.274
and
G = 82.4 + 0.274s
The function G is equivalent to a digital filter of the form:
D(z) = KP + KD(1-z -1 )
where
P = KP
Chapter 10 Theory of Operation ▫ 133
6 2
K K H(s) =3.17· 10 /[s (s+2000)]
a d f
-1 [500/2000] = -194°
=500, the function would have a magnitude of 160 and a phase lead of 59 degrees.
c
DMC-21x5 User Manual 1.0a1