# ivx

ARX model estimation using instrumental variable method with arbitrary instruments

## Syntax

## Description

### Estimate ARX Polynomial Model

estimates an ARX polynomial model `sys`

= ivx(`tt`

,```
[na
nb nk]
```

,`x`

)`sys`

using the time-domain data in
the timetable `tt`

. `[na nb nk]`

specifies the ARX
structure orders of the *A* and *B* polynomials and the
input-to-output delay, expressed in the number of samples. `x`

specifies the instrument variable matrix.

The software estimates `sys`

using the instrumental variable method
with arbitrary instruments.

An ARX model is represented as:

$$A(q)y(t)=B(q)u(t-nk)+v(t)$$

For more details on the ARX model structure, see `arx`

.

uses the time-domain input and output signals in the comma-separated matrices
`sys`

= ivx(`u`

,`y`

,`[na nb nk]`

,`x`

)`u`

,`y`

. The software assumes that the data sample
time is one second. To change the sample time, set `Ts`

using
name-value syntax.

uses the time-domain or frequency-domain data in the data object
`sys`

= ivx(`data`

,`[na nb nk]`

,`x`

)`data`

. Use this syntax especially when you want to estimate a model
using frequency-domain or frequency-response data, or when you want to take advantage of
the additional information, such as data sample time or experiment labeling, that data
objects provide.

### Specify Additional Model Options

specifies additional options using one or more name-value arguments.`sys`

= ivx(___,`Name,Value`

)

### Return Estimated Initial Conditions

`[`

returns the estimated initial conditions as an `sys`

,`ic`

] = ivx(___)`initialCondition`

object. For more information on `ic`

, see the `ic`

argument description.

Use this syntax if you plan to simulate or predict the model response using the same estimation input data and then compare the response with the same estimation output data. Incorporating the initial conditions yields a better match during the first part of the simulation.

## Input Arguments

## Output Arguments

## Tips

Use

`iv4`

first for IV estimation to identify ARX polynomial models where the instruments`x`

are chosen automatically. Use`ivx`

for nonstandard situations. For example, use`ivx`

when there is feedback present in the data or when instruments other than those used in`iv4`

need to be tried. You can also use`ivx`

to automatically generate instruments from certain custom defined filters.

## References

[1] Ljung, Lennart. System Identification: Theory for the User, 2nd ed. Prentice Hall Information and System Sciences Series. Upper Saddle River, NJ: Prentice Hall PTR, 1999.

## Version History

**Introduced before R2006a**