National Instruments 370760B-01

3.7. STRUCTURED SINGULAR VALUE(µ) ANALYSIS AND SYNTHESIS 113

Both the Dand D−1systems (Dsys and Dinvsys) are returned. The Dscale

(Dmagdata) comes from a µcalculation on a closed loop system. However, Dsys and

Dinvsys are required to multiply the open loop system. They must therefore contain the

identity matrices for theinputs a ndoutputs which correspond to the measurements and

controls. This information is not containedin blk and must be speciﬁed in the argument

list: nmeas is the number of measurements and ncntrl is the number of controls. The

user can specify a frequency domain weight for the ﬁtting. The variable sens, returned

from the mu function, is a good option.

There are several choices of rational ﬁtting functions available within musynfit.The

D-scale input variables are magnitude data. Phase data, corresponding to a

minimum-phase system is supplied with the Xµfunction mkphase. The user has a choice

of functions for the transfer function ﬁtting: the Xmath function tfid and the Xµ

function fitsys.Thefitsys function is discussed in more detail in Section 3.7.3 below.

For further information on tfid see the Xmath Basics Manual.

There are several choices of graphical display availableto help the user selectthe most

appropriate ﬁt. These are:

1. The D-scale magnitude data and the la sttwo transfer function ﬁts ar e displayed.

2. The D-scale magnitude data and the la sttwo transfer function ﬁts ar e displayed.

An additional plot shows the weighting function.

3. The D-scale magnitude data and the la sttwo transfer function ﬁts ar e displayed.

An additional plot compares the µupper bound (which uses the D-scale

magnitude data) to the bound which would be obtained from a frequency response

of the D-scale transfer function ﬁt.

In a problem with nperturbation blocks, there are n−1Dscales requiring ﬁtting. This

is because one can be chosen as the identity without loss of generality. The Dscale for

each block requires user interaction for the selection of the system order. The function

fitsys is called to ﬁt each Dscale block. This is available to the user and is described

in more detail below.

Transfer FunctionFitting Functions

The underlying functions used for the ﬁtting of each block of the Dscale are described

here as they may be of independent interest to the user. Other possible uses include