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The Model Reduction Module is particularly suitable for achieving low 
order controller design for a high order plant. This section explains some of 
the broad issues involved.

Most modern controller design methods, for example, LQG and H

∞

, yield 

controllers of order roughly comparable with that of the plant. It follows 
that, to obtain a low order controller using such methods, one must either 
follow a high order controller design by a controller reduction step, 
or reduce an initially given high order plant model, and then design a 
controller using the resulting low order plant, with the understanding that 
the controller will actually be used on the high order plant. Refer to 
Figure 1-2.

Figure 1-2.  Low Order Controller Design for a High Order Plant

Generally speaking, in any design procedure, it is better to postpone 
approximation to a late step of the procedure: if approximation is done 
early, the subsequent steps of the design procedure may have unpredictable 
effects on the approximation errors. Hence, the scheme based on high order 
controller design followed by reduction is generally to be preferred.

Controller reduction should aim to preserve closed-loop properties as far 
as possible. Hence the controller reduction procedures advocated in this 
module reflect the plant in some way. This leads to the frequency weighted 
reduction schemes of 

wtbalance( )

 and 

fracred( )

, as described in 

Chapter 4, 

. Plant reduction logically 

should also seek to preserve closed-loop properties, and thus should involve 
the controller. With the controller unknown however, this is impossible. 
Nevertheless, it can be argued, on the basis of the high loop gain property 
within the closed-loop bandwidth that is typical of many systems, that