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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"

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

( )

1

4s

2

--------

2

2

ζ

0

ω

0

ω

0

2

+

ω

0

2

------------------------------------

2

ζ

1

ω

1

ω

1

2

+

ω

1

2

--------------------------------

+

-----------

⋅

⋅

2

2

ζ

2

ω

2

ω

2

2

+

ω

2

2

------------------------------------

2

2

ζ

3

ω

3

ω

3

2

+

ω

3

2

------------------------------------

2

2

ζ

4

ω

4

ω

4

2

+

ω

4

2

------------------------------------

⋅

⋅

---------------------------------------------------------------------------------------------------------------------

=