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4.1. THE HIMAT EXAMPLE 141
The second thing to note is that the interconnection structure has the additional control
inputs and measurement outputs. The D and Dinv systems must be augmented with
identities corresponding to these additional inputs and outputs.
The musynfit function performs both of these operations. The syntax of musynfit is:
[Dsys,Dinvsys] = musynfit(D,blk,nmeas,nctrls,sens,oldDsys)
The variables D and sens come directly from the mu function. The block structure is
specified by blk and nmeas and nctrls are the number of measurements and controls
respectively.
The outputs are the dynamic systems which approximate D and Dinv. The new scaled
H
∞
problem can be set up with
new
ic = Dsys * old ic * Dinvsys.
D-K iteration involves iterating between calculating and fitting D-scales and designing
controllers, K.
If there are N blocks in the µ problem set up, then the D scale matrices have N − 1
different transfer functions that require fitting. The Nth transfer function is taken to be
unity.
We recommend choosing a 3rd order transfer function for the fit. This increases the
number of states in the interconnection structure by 3*(size of block)*2. A different
order can be chosen — which will lead to a slightly different controller in the subsequent
analysis.
Note that g1g is also passed to musynfit. This will provide the user with a comparison
between the calculated upperbound and that based on the rational fit. This comparison
is useful in deciding between fits of differing orders.
[D1sys,D1invsys] = musynfit(D1,blk,nmeas,nctrls,sens1,g1g,{Hertz})