National Instruments 370760B-01 A.7 Structured Singular Value() Analysis and Synthesis

400 APPENDICES

Description µ-Tools function Xmath/Xµequivalent

H2norm calculation h2norm h2norm

H∞norm calculation hinfnorm hinfnorm

H2controller synthesis h2syn h2syn

H∞controller synthesis hinfsyn hinfsyn

The major syntactical diﬀerence is that the Xµfunctionsdo not return the closed loop

system. This is easily calculated by a subsequent call to starp. The reason for this is

that the D-Kiteration changes typically involve a diﬀerently weightedclosed loo p

system in subsequent operations. Having a separate calculation of the closed loop

reduces the potential for confusion.

The µ-Tools function hinffi has no Xmath/Xµequivalent. This function calculates the

full information H∞controller. hinfsyn solves the more general problem and is of more

practical use in controller applications.

A.7 Structured Singular Value(µ) Analysis and Synthesis

The issue of whether or not the frequency domain variable is radian/second or Hertz

arises here. Although this makes no diﬀerence to the calculation of µis aﬀects how the

Dscales and ∆ perturbations are interpolated. µ-Tools assumes that the frequency scale

is radians/second. In Xµthe default assumption is Hertz. The reason for this is that

Hertz is the default output of the frequency response calculation freq.Inallcases

where it makes a diﬀerence, the user can specify the keyword {!Hertz}to switch the

meaning of the domain.

Calculation of µ

There is a diﬀerence in the returned variable format for the Xµfunction mu.The

Matlab functionreturns the D-scale and perturbations in coded vector form. The Xµ

mu function returns both the Dscalea nd its inverse in matrix form. The relevant

functions are summarized below.