User`s guide

Table Of Contents

2 LTI Models

2-12

while

E = tf

creates an empty transfer function.

Zero-Pole-Gain Models

This section explains how to specify continuous-time SISO and MIMO

zero-pole-gain models. The specification for discrete-time zero-pole-gain

models is a simple extension of the continuous-time case. See “Discrete-Time

Models” on page 2-20.

SISO Zero-Pole-Gain Models

Continuous-time SISO zero-pole-gain models are of the form

where is a real-valued scalar (the gain), and ,..., and ,..., are the

real or complex conjugate pairs of zeros and poles of the transfer function .

This model is closely related to the transfer function representation: the zeros

are simply the numerator roots, and the poles, the denominator roots.

There are two ways to specify SISO zero-pole-ga in models:

• Using the

zpk command

• As rational expressions in the Laplace variable s

The syntax to specify ZPK models directly using

zpk is

h = zpk(z,p,k)

where z and p are the vectors of zeros and poles, and k is the gain. This

produces a ZPK object

h that encapsulates the z, p,andkdata. For example,

typing

h = zpk(0, [1–i 1+i 2], –2)

hs() k

–()

... sz

–()

–()... sp

–()

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()