National Instruments 370753C-01 Manual De Usuario

For discrete-time state-space systems with a sampling interval of T, the 
frequency response for each frequency point 

ω is shown in the following 

equation:

The algorithm, based on [Lau86], uses a Hessenberg decomposition to 
simplify the previous equations and is quite robust. It finds matrices P and 
H such that A = PHP', where PP' = P'P = I and H is a Hessenberg matrix, 
and substitutes for A. Because H is zero only below the first subdiagonal, 
the number of operations needed to evaluate the response expression is 
proportional to the square of the size of A. 

freq( )

 allows you to prespecify frequency ranges of interest, or it can 

generate a representative frequency range from minimum and maximum 
frequencies you specify. It then evaluates the complex frequency response 
over those frequencies, using specialized algorithms to do this efficiently. 

You can specify either a complete set of frequency points (the optional 
input 

F

) or a range of frequency points (the keyword pair 

Fmin

 and 

Fmax

) 

at which to evaluate the response. The 

track

 keyword indicates that phase 

tracking will be used to determine the values of the frequencies between 

Fmin

 and 

Fmax

. The number of intermediate frequency points produced 

using 

track

 varies depending on the system and the 

Fmin

 and 

Fmax

 you 

choose. Alternately, you can use the 

npts

 keyword to specify the exact 

number of logarithmically-spaced frequency points you want computed. 
Specifying 

track

 invokes an algorithm which tracks the phase of the 

frequency response to make sure that all peaks and valleys are included in 
the computed response. The 

delta

 keyword indicates the amount of phase 

change (measured in degrees) to which the response evaluation should be 
sensitive. If phase change between two adjacent frequency points exceeds 
this delta, closer frequencies are used until either the phase change is less 
than 

delta

 or a maximum number of iterations is reached. Evaluation is 

forced at key frequency points which include the poles and the points lying 
halfway between adjacent poles. 

freq( )

 returns a PDM having the frequency range as its domain. The 

dependent matrices of the frequency response PDM have as many rows as 
the system has outputs, and as many columns as the system has inputs. For 
MIMO systems, the (i,j) element of a dependent matrix is thus interpreted 
as the frequency response from input j to output i. This frequency response 
forms the core of the classical control design tools discussed in this chapter. 

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