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Chapter 3 Multiplicative Error Reduction
© National Instruments Corporation 3-11 Xmath Model Reduction Module
The values of G(s), as shown in Figure 3-2, along the jω-axis are
the same as the values of around a circle with diameter defined by
[a – j0, b
–1
+ j0] on the positive real axis.
Figure 3-2. Bilinear Mapping from G(s) to (Case 1)
Also, the values of , as shown in Figure 3-3, along the jω-axis are
the same as the values of G(s) around a circle with diameter defined by
[–b
–1
+ j0, –a + j0].
Figure 3-3. Bilinear Mapping from G(s) to (Case 2)
We can implement an arbitrary bilinear transform using the subsys( )
function, which substitutes a given transfer function for the s- or z-domain
operator.
To implement use:
gtildesys=subsys(gsys,makep([-b,1]/makep([1,-a])
To implement use:
gsys=subsys(gtildesys,makep([b,1]/makep([1,a])
Note
The systems substituted in the previous calls to subsys invert the function
specification because these functions use backward polynomial rotation.
G
˜
s()
G
˜
s()
Gs()
valuesvalues
a
b
1–
G
˜
s()
G
˜
s()
G
˜
s()
Gs()
valuesvalues
-a
b
1–
G
˜
s()
G
˜
s() G
sa–
bs– 1+
-------------------
=
Gs() G
˜
sa+
s 1+
-----------
=