ElmoMC SimplIQ Digital Servo Drives-Bell Command Reference - Manual (Page 285)

7.1.1 Link Parameterization
The basic continuous-time second-order element is a filter with a unity DC gain:
D Cs Es
B As Es
B
D
2
2
+ +
+ +
⋅
Note that this element is very general: It can be used, for example, as a notch filter, a
low-pass complex pole filter, a double-lead element or a single pole.
The equivalent discrete form is:
2 1
2
2 1
2
0
a z a z
b z b z b
+ +
+ +
Order Parameter Description Comment
1 k
1
b
0
+ b
1
+ b
2
Float, represented by a long value
2 k
2
-(b
1
+ b
2
) Float, represented by a long value
3 k
3
-b
2
Float, represented by a long value
4 k
4
a
2
Float, represented by a long value
Table 7-6: Fixed Link Parameters
The parameter a
1
is obtained explicitly by a
1
= b
1
+ b
1
+ b
1
- a
1
- 1.
7.2. Examples of Filter Implementation
The following examples illustrate how the more common filter links can be
implemented. Each example calculates the parameters b
0
, b
1
, b
2
, a
1
and a
2
.
Note that the frequency response of a discrete-time filter depends on the sampling
time. In the following examples, you should use sampling time T=2
×TT[1].
7.2.1 Low-pass (Complex Pole) Element
(Represented by Second-order Block)
The basic continuous-time complex pole element is:
2 2
2
2
ω ω
ω
+ ⋅ ⋅ ⋅ +
s d s
where:
f
⋅ = π ω 2
is the angular frequency.
f [Hz] is the pole frequency.
SimplIQ for Steppers Application Note Filters
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