National Instruments 370753C-01 poles( ), zeros( )

Chapter 4 System Analysis

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.

poles( )

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.

Example 4-1 Using poles( ) with a System in Transfer Function Form

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

zeros( )

[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