Control System Toolbox Function Reference

zpkdata

Quick access to zero-pole-gain data

Syntax

[z,p,k] = zpkdata(sys)
[z,p,k] = zpkdata(sys,'v')
[z,p,k,Ts,Td] = zpkdata(sys)

Description

[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. See Table 11-15, "LTI Properties," on page 11-194 for more information on the format of state-space model data.

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,Td] = zpkdata(sys) also returns the sample time Ts and the input delay data Td. For continuous-time models, Td is a row vector with one entry per input channel (Td(j) indicates by how many seconds the jth input is delayed). For discrete-time models, Td is the empty matrix [] (see d2d for delays in discrete systems).

You can access the remaining LTI properties of sys with get or by direct referencing, for example,

sys.Ts
sys.inputname

Example

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...
         1
 #1:  -------
      (z-0.3)
 
           2 (z+0.5)
 #2:  -------------------
      (z^2 - 0.2z + 1.01)
 
Sampling 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

See Also
get         Get properties of LTI models

ssdata      Quick access to state-space data

tfdata      Quick access to transfer function data

zpk         Specify zero-pole-gain models

zpk