National Instruments NI MATRIXx Xmath - Manual (Page 96)

© National Instruments Corporation 6-1 Xmath Model Reduction Module
6
Tutorial
This chapter illustrates a number of the MRM functions and their
underlying ideas. A plant and full-order controller are defined, and then
the effects of various reduction algorithms are examined. The data for this
example is stored in the file
mr_disc.xmd in the Xmath demos directory.
To follow the example, start Xmath, and then select File»Load from the
Xmath Commands menu, or enter the
load command with the file
specification appropriate to your operating system from the Xmath
Commands area. For example:
load "$XMATH/demos/mr_disc"
Plant and Full-Order Controller
The plant in question comprises four spinning disks, connected by a
flexible shaft. A motor applies torque to the third disk, and the output
variable of interest is the angular displacement of the first disk. The plant
transfer function, which is nonminimum phase and has a double pole at the
origin, is as follows:
with:
ζ
0
=0.02
ω
0
=1
ζ
1
=-0.4
ω
1
=5.65
ζ
2
=0.02
ω
2
=0.765
ζ
3
=0.02
ω
3
=1.41
ζ
4
=0.02
ω
4
=1.85
a=4.84
G s ( )
1
4s
2
--------
s
2
2 ζ
0
ω
0
s ω
0
2
+
ω
0
2
------------------------------------
s
2
ζ
1
ω
1
s ω
1
2
+
ω
1
2
--------------------------------
s a +
a
----------- ⋅ ⋅
s
2
2 ζ
2
ω
2
s ω
2
2
+
ω
2
2
------------------------------------
s
2
2 ζ
3
ω
3
s ω
3
2
+
ω
3
2
------------------------------------
s
2
2 ζ
4
ω
4
s ω
4
2
+
ω
4
2
------------------------------------
⋅ ⋅
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