zpkdata
Access zero-pole-gain data
Syntax
Description
Examples
Example 1
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
Example 2
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]); [z1, 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)
Input Arguments
sys
— Zero-pole-gain model
zpk
model object
Zero-pole-gain model, specified as a zpk
(Control System Toolbox) model object.
Output Arguments
z
— Zeros
cell array (default) | column vector
Zeros of the zero-pole-gain model, returned as a cell array with as many rows as
outputs and as many columns as inputs. The (i,j)
entry
z{i,j}
is the (column) vector of zeros of the transfer function
from input j
to output i
.
p
— Poles
cell array (default) | column vector
Poles of the zero-pole-gain model, returned as a cell array with as many rows as
outputs and as many columns as inputs. The (i,j)
entry
p{i,j}
is the (column) vector of zeros of the transfer function
from input j
to output i
.
k
— Gain
matrix
Gain of the zero-pole-gain model, returned as 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
.
Ts
— Sample time
scalar
Sample time, specified as a scalar.
covz
— Covariance of zeros
cell array
Covariance of zeros, returned as 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
— Covariance of poles
cell array
Covariance of poles, returned as a cell array such that
covp{ky,ku}
contains the covariance information about the poles in
the vector p{ky,ku}
. covp{ky,ku}
is a 3-D array of
dimension 2-by-2-by-Np, where Np
is the length of
p{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.
covk
— Covariance of gain
cell array
Covariance of zeros, returned as a cell array such that
covk{ky,ku}
contains the covariance information about the zeros in
the vector k{ky,ku}
. covk{ky,ku}
is a 3-D array of
dimension 2-by-2-by-Nk, where Nk
is the length of
k{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.
Version History
Introduced before R2006a
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