Access zero-pole-gain data
[z,p,k] = zpkdata(sys)
[z,p,k,Ts] = zpkdata(sys)
[z,p,k,Ts,covz,covp,covk] = zpkdata(sys)
[z,p,k] = zpkdata(sys)
returns the zeros z, poles p,
and gain(s) k of the zero-pole-gain model sys.
The outputs z and p are cell
arrays with the following characteristics:
z and p have
as many rows as outputs and as many columns as inputs.
The (i,j) entries z{i,j} and p{i,j} are
the (column) vectors of zeros and poles of the transfer function from
input j to output i.
The output k is a matrix with as many rows
as outputs and as many columns as inputs such that k(i,j) is
the gain of the transfer function from input j to
output i. If sys is a transfer
function or state-space model, it is first converted to zero-pole-gain
form using zpk.
For SISO zero-pole-gain models, the syntax
[z,p,k] = zpkdata(sys,'v')
forces zpkdata to return the zeros and poles
directly as column vectors rather than as cell arrays (see example
below).
[z,p,k,Ts] = zpkdata(sys)
also returns the sample time Ts.
[z,p,k,Ts,covz,covp,covk] = zpkdata(sys)
also returns the covariances of the zeros, poles and gain of the identified
model sys. covz is a cell array
such that covz{ky,ku} contains the covariance information
about the zeros in the vector z{ky,ku}. covz{ky,ku} is
a 3-D array of dimension 2-by-2-by-Nz, where Nz is
the length of z{ky,ku}, so that the (1,1) element
is the variance of the real part, the (2,2) element
is the variance of the imaginary part, and the (1,2) and (2,1) elements
contain the covariance between the real and imaginary parts. covp has
a similar relationship to p.covk is a matrix containing
the variances of the elements of k.
You can access the remaining LTI properties of sys with get or
by direct referencing, for example,
sys.Ts sys.inputname
Given a zero-pole-gain model with two outputs and one input
H = zpk({[0];[-0.5]},{[0.3];[0.1+i 0.1-i]},[1;2],-1)
Zero/pole/gain from input to output...
z
#1: -------
(z-0.3)
2 (z+0.5)
#2: -------------------
(z^2 - 0.2z + 1.01)
Sample time: unspecified
you can extract the zero/pole/gain data embedded in H with
[z,p,k] = zpkdata(H)
z =
[ 0]
[-0.5000]
p =
[ 0.3000]
[2x1 double]
k =
1
2
To access the zeros and poles of the second output channel of H,
get the content of the second cell in z and p by
typing
z{2,1}
ans =
-0.5000
p{2,1}
ans =
0.1000+ 1.0000i
0.1000- 1.0000i
Extract the ZPK matrices and their standard deviations for a 2-input, 1 output identified transfer function.
load iddata7
transfer function model
sys1 = tfest(z7, 2, 1, 'InputDelay',[1 0]);
an equivalent process model
sys2 = procest(z7, {'P2UZ', 'P2UZ'}, 'InputDelay',[1 0]);
1, p1, k1, ~, dz1, dp1, dk1] = zpkdata(sys1);
[z2, p2, k2, ~, dz2, dp2, dk2] = zpkdata(sys2);Use iopzplot to visualize the pole-zero locations
and their covariances
h = iopzplot(sys1, sys2); showConfidence(h)