Accelerating the pace of engineering and science

# pzmap

Pole-zero plot of dynamic system

## Syntax

pzmap(sys)
pzmap(sys1,sys2,...,sysN)
[p,z] = pzmap(sys)

## Description

pzmap(sys) creates a pole-zero plot of the continuous- or discrete-time dynamic system model sys. For SISO systems, pzmap plots the transfer function poles and zeros. For MIMO systems, it plots the system poles and transmission zeros. The poles are plotted as x's and the zeros are plotted as o's.

pzmap(sys1,sys2,...,sysN) creates the pole-zero plot of multiple models on a single figure. The models can have different numbers of inputs and outputs and can be a mix of continuous and discrete systems.

[p,z] = pzmap(sys) returns the system poles and (transmission) zeros in the column vectors p and z. No plot is drawn on the screen.

You can use the functions sgrid or zgrid to plot lines of constant damping ratio and natural frequency in the s- or z-plane.

## Examples

### Example 1

Pole-Zero Plot of Dynamic System

Plot the poles and zeros of the continuous-time system

$H\left(s\right)=\frac{2{s}^{2}+5s+1}{{s}^{2}+2s+3}$

```H = tf([2 5 1],[1 2 3]); sgrid
pzmap(H)
grid on```

### Example 2

Plot the pzmap for a 2-input-output discrete-time IDSS model.

```A = [0.1 0; 0.2 0.9]; B = [.1 .2; 0.1 .02]; C = [10 20; 2 -5]; D = [1 2; 0 1];
sys = idss(A,B,C,D, 'Ts', 0.1);```

expand all

### Tips

You can change the properties of your plot, for example the units. For information on the ways to change properties of your plots, see Ways to Customize Plots.

### Algorithms

pzmap uses a combination of pole and zero.