Access zero-pole-gain data
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Syntax
[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,'v')
Description
example
[z,p,k] = zpkdata(sys)
returns the zeros z
, poles p
, and gain(s) k
of the zero-pole-gain model sys
.
[z,p,k,Ts] = zpkdata(sys)
also returns the sample time Ts
.
example
[z,p,k,Ts,covz,covp,covk] = zpkdata(sys)
also returns the covariances of the zeros, poles and gain of the identified model sys
.
[z,p,k] = zpkdata(sys,
returns the zeros and poles directly as column vectors for SISO zero-pole-gain models.'v'
)
Examples
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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
collapse all
sys
— Zero-pole-gain model
zpk
model object
Zero-pole-gain model, specified as a zpk model object.
Output Arguments
collapse all
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
See Also
get | ssdata | tfdata | zpk
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