National Instruments 370753C-01 Manual De Usuario

plant is open-loop stable, then there should be no encirclements. 
If the plant has one open-loop unstable pole, there should be one negative 
(counter-clockwise) encirclement.

The stability criterion is most easily derived from the SISO 
transfer-function representation of a system. The Nyquist plot for a MIMO 
system consists of a set of plots, one for each output, each containing as 
many input frequency response curves as there are system inputs. You can 
derive any plot from a context menu. If you close a feedback loop around a 
SISO system in transfer function format, you obtain a closed-loop system 
as shown in Figure 5-6.

Figure 5-6.  Closed-Loop System Containing a Variable Gain K

You obtain the following closed-loop transfer function from Y(s) to U(s):

Thus, the closed-loop roots are the roots of the equation 1 + KH(s) = 0. 
The complex frequency response of KH(s), evaluated for s = j

ω in 

continuous time and e

ωT

 for discrete systems, will encircle (–1,0) in the 

complex plane if 1 + KH(s) encircles (0,0). If you are examining the 
Nyquist plot of H(s), you will notice that an encirclement of (–1/K,0) by 
H(s) is the same as an encirclement of (–1,0) by KH(s). This fact allows you 
to use one Nyquist plot to determine the stability of a system for any and 
all values of K.

H = nyquist(Sys,{F,keywords})

The 

nyquist( )

 function is structured very similarly to 

bode( )

 and 

nichols( )

 in that it is largely a wrapper on the 

freq( )

 function to 

obtain the system’s frequency response. The output 

H

 is just the output from 

the call to 

freq( )

. The main difference from the other two functions is 

that 

nyquist( )

 does not calculate the decibel gain and the phase of the 

system’s response. It generates the Nyquist plot by plotting the real part of 
each point of the response against the imaginary part.

U(s)

Y(s)

K

+

–

H(s) = 

num(s)

den(s)

( )

( )

-----------

( )

1 KH s

( )

+

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

=