National Instruments 370753C-01 Manual De Usuario

© National Instruments Corporation

As the gain varies, small 

✱

’s appear on the locus indicating the closed-loop 

pole location for that choice of gain. The locus shown in Figure 5-2 shows 
that for small gain values the closed-loop system is stable, with all of its 
roots in the left half of the complex plane.

The frequency response of a dynamic system is the output, or response, of 
a system given unit-amplitude, zero-phase sinusoidal input. A sinusoidal 
input with unit amplitude and zero phase, and frequency 

ω produces the 

following sinusoidal output: 

where A is the magnitude of the response as a function of 

ω, and φ is the 

phase. The magnitude and phase of the system output will vary depending 
on the values of the system poles, zeros, and gain. In many practical 
engineering applications, the system poles and zeros are not precisely 
known. Because the frequency response can be determined experimentally, 
undesirable parts of the system’s frequency response then can be improved 
by adding known compensation to the system.

H=freq(Sys,F,{Fmin,Fmax,npts,track,delta})

The 

freq( )

 function calculates the frequency response of a system in 

several different ways, depending on the system representation. For 
continuous-time transfer functions, the frequency response H(

ω) at a given 

frequency 

ω is obtained by substituting the complex frequency value jω for 

qin the following equation. For discrete-time transfer functions, the value 
e

, with T the system sampling interval, is substituted for q instead.

For continuous-time state-space systems, the basic method for finding 
frequency response is to substitute different frequency values, represented 
by 

ω, into the following equation:

ω

( )

ω

( )e

φ ω

( )

=

( )

1

+

(

)… q z

+

(

)

1

+

(

)… q p

+

(

)

---------------------------------------------

=

( )

–

(

)

1

–

+

=