User`s guide

nyquist
11-157
When i nvoked with left-hand arguments
[re,im,w] = nyquist(sys)
[re,im] = nyquist(sys,w)
return the re al and imaginary parts of the frequ ency response at the
frequencies
w (in rad/sec). re and im are 3-D arrays with the frequency as last
dimension (see “Arguments” below for details).
Remark If sys is an FRD model, nyquist(sys,w), w can o nly include frequencies in
sys.frequency.
Arguments The output arguments re and im are 3-D arrays with dimensions
For SISO systems, the scalars
re(1,1,k) and im(1,1,k) are the real and
imaginary parts of the response at the frequency .
For MIMO systems with transfer function ,
re(:,:,k) and im(:,:,k)
give the real and imaginary parts of (both arrays with as many rows
as outputs and as many columns as inputs). Thus,
where is the transfer function from input to output .
Example Plot the Nyquist response of the system
number of outputs
()
number of i nputs
()×
length of
w()×
ω
k
w(k)=
re(1,1,k) Re hjω
k
()()=
im(1,1,k) Im hjω
k
()()=
Hs
()
Hj
ω
k
()
re(i,j,k) Re h
ij
jω
k
()()=
im(i,j,k) Im h
ij
jω
k
()()=
h
ij
j
i