National Instruments 370753C-01 Manual De Usuario

© National Instruments Corporation

and define the zeros of S(

λ) as any values of λ for which the system matrix 

drops rank. For single-input single-output systems this is equivalent to the 
polynomial zeros of the transfer-function numerator. This definition is 
somewhat more complex for MIMO systems.

In terms of the dynamic response associated with the poles and zeros of a 
system, a pole is said to be stable if the response it contributes decays over 
time. If the response becomes larger over time, the pole is said to be 
unstable. If the response remains unchanged over time, you describe the 
pole that causes it as neutrally stable. All the closed-loop poles of a system 
must be stable to describe the system as stable.

p = poles(Sys)

The 

poles( )

 function returns a vector listing all the poles of a system. 

If the input system 

Sys

 is in transfer-function form, 

poles( )

 obtains the 

poles from the roots of the transfer function’s denominator (which are 
automatically stored if the system is in zero-pole format or if the roots have 
been previously calculated). If 

Sys

 is in state-space form, the poles are 

computed as the eigenvalues of the A matrix. To see how to use 

poles( )

 

with a system in transfer function form, refer to Example 4-1.

H = 0.5*polynomial([-0.36])/...

makepoly([1,2.79,2.74,1.11,0.16]);

poles(H)

ans (a column vector) =

-0.395 + 0.0630476 j

-0.395 - 0.0630476 j

-1

-1 

[z,k] = zeros(Sys)

The 

zeros( )

 function finds the invariant zeros, the values of

 λ at which 

R(

λ) = 0 and S(λ) lose rank, and gain is returned only for SISO systems 

(of a system 

Sys

). If 

Sys

 is in transfer function form, the zeros are obtained