Main Content

Pole-zero plot of dynamic system

`pzmap(`

creates a pole-zero plot
of the continuous or discrete-time dynamic
system model
`sys`

)`sys`

. `x`

and `o`

indicates the poles and zeros respectively, as shown in the following
figure.

From the figure above, an open-loop linear time-invariant system is stable if:

In continuous-time, all the poles on the complex s-plane must be in the left-half plane (blue region) to ensure stability. The system is marginally stable if distinct poles lie on the imaginary axis, that is, the real parts of the poles are zero.

In discrete-time, all the poles in the complex z-plane must lie inside the unit circle (blue region). The system is marginally stable if it has one or more poles lying on the unit circle.

`pzmap(`

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. For SISO systems, `sys`

1,`sys`

2,...,`sys`

N)`pzmap`

plots the system
poles and zeros. For MIMO systems, `pzmap`

plots the system
poles and transmission zeros.

Use the functions

`sgrid`

or`zgrid`

to plot lines of constant damping ratio and natural frequency in the*s*- or*z*-plane on the pole-zero plot.For MIMO models,

`pzmap`

displays all system poles and transmission zeros on a single plot. To map poles and zeros for individual I/O pairs, use`iopzmap`

.For additional options to customize the appearance of the pole-zero plot, use

`pzplot`

.

`damp`

| `iopzmap`

| `pole`

| `pzplot`

| `sgrid`

| `zero`

| `zgrid`

| `dsort`

(Control System Toolbox) | `esort`

(Control System Toolbox) | `rlocus`

(Control System Toolbox)