Transfer function model

Use `tf`

to create real-valued or complex-valued transfer
function models, or to convert dynamic system
models to transfer function form.

Transfer functions are a frequency-domain representation of linear time-invariant
systems. For instance, consider a continuous-time SISO dynamic system represented by the
transfer function `sys(s) = N(s)/D(s)`

, where `s = jw`

and `N(s)`

and `D(s)`

are called the numerator and
denominator polynomials, respectively. The `tf`

model object can
represent SISO or MIMO transfer functions in continuous time or discrete time.

You can create a transfer function model object either by specifying its coefficients
directly, or by converting a model of another type (such as a state-space model
`ss`

) to transfer-function form. For more information, see Transfer Functions.

You can also use `tf`

to create generalized state-space (`genss`

) models or uncertain state-space (`uss`

) models.

creates a continuous-time transfer function model, setting the
`sys`

= tf(`numerator`

,`denominator`

)`Numerator`

and `Denominator`

properties. For instance, consider a continuous-time SISO dynamic system
represented by the transfer function `sys(s) = N(s)/D(s)`

,
the input arguments `numerator`

and
`denominator`

are the coefficients of
`N(s)`

and `D(s)`

,
respectively.

creates a discrete-time transfer function model, setting the
`sys`

= tf(`numerator`

,`denominator`

,`ts`

)`Numerator`

, `Denominator`

, and
`Ts`

properties. For instance, consider a
discrete-time SISO dynamic system represented by the transfer function
`sys(z) = N(z)/D(z)`

, the input arguments
`numerator`

and `denominator`

are
the coefficients of `N(z)`

and `D(z)`

,
respectively. To leave the sample time unspecified, set
`ts`

input argument to `-1`

.

creates a transfer function model with properties inherited from the dynamic
system model `sys`

= tf(`numerator`

,`denominator`

,`ltiSys`

)`ltiSys`

, including the sample time.

`s = tf('s')`

creates special variable
`s`

that you can use in a rational expression to create
a continuous-time transfer function model. Using a rational expression can
sometimes be easier and more intuitive than specifying polynomial
coefficients.

The following lists contain a representative subset of the functions you can use with
`tf`

models. In general, any function applicable to Dynamic System Models
is applicable to a `tf`

object.

Transfer function models are ill-suited for numerical computations. Once created, convert them to state-space form before combining them with other models or performing model transformations. You can then convert the resulting models back to transfer function form for inspection purposes

An identified nonlinear model cannot be directly converted into a transfer function model using

`tf`

. To obtain a transfer function model:Convert the nonlinear identified model to an identified LTI model using

`linapp`

,`idnlarx/linearize`

, or`idnlhw/linearize`

.Then, convert the resulting model to a transfer function model using

`tf`

.