zpkdata

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

[z,p,k] = zpkdata(sys) returns the zeros z, poles p, and gain(s) k of the zero-pole-gain model sys.

example

[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.

example

[z,p,k] = zpkdata(sys,'v') returns the zeros and poles directly as column vectors for SISO zero-pole-gain models.

Examples

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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]);

[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

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Zero-pole-gain model, specified as a zpk model object.

Output Arguments

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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.

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.

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.

Sample time, specified as a scalar.

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.

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.

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

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