## Numeric Models

### Numeric Linear Time Invariant (LTI) Models

Numeric LTI models are the basic numeric representation of linear systems or components of linear systems. Use numeric LTI models for modeling dynamic components, such as transfer functions or state-space models, whose coefficients are fixed, numeric values. You can use numeric LTI models for linear analysis or control design tasks.

The following table summarizes the available types of numeric LTI models.

Model TypeDescription
`tf` (Control System Toolbox)Transfer function model in polynomial form
`zpk` (Control System Toolbox)Transfer function model in zero-pole-gain (factorized) form
`ss` (Control System Toolbox)State-space model
`frd` (Control System Toolbox)Frequency response data model
`pid` (Control System Toolbox)Parallel-form PID controller
`pidstd` (Control System Toolbox)Standard-form PID controller
`pid2` (Control System Toolbox)Parallel-form two-degree-of-freedom (2-DOF) PID controller
`pidstd2` (Control System Toolbox)Standard-form 2-DOF PID controller

#### Creating Numeric LTI Models

For information about creating numeric LTI models, see:

#### Applications of Numeric LTI Models

You can use Numeric LTI models to represent block diagram components such as plant or sensor dynamics. By connecting Numeric LTI models together, you can derive Numeric LTI models of block diagrams. Use Numeric LTI models for most modeling, analysis, and control design tasks, including:

### Identified LTI Models

Identified LTI Models represent linear systems with coefficients that are identified using measured input/output data. You can specify initial values and constraints for the estimation of the coefficients.

The following table summarizes the available types of identified LTI models.

Model TypeDescription
`idtf`Transfer function model in polynomial form, with identifiable parameters
`idss`State-space model, with identifiable parameters
`idpoly`Polynomial input-output model, with identifiable parameters
`idproc`Continuous-time process model, with identifiable parameters
`idfrd`Frequency-response model, with identifiable parameters
`idgrey`Linear ODE (grey-box) model, with identifiable parameters

### Identified Nonlinear Models

Identified Nonlinear Models represent nonlinear systems with coefficients that are identified using measured input/output data. You can specify initial values and constraints for the estimation of the coefficients.

The following table summarizes the available types of identified nonlinear models.

Model TypeDescription
`idnlarx`Nonlinear ARX model, with identifiable parameters
`idnlgrey`Nonlinear ODE (grey-box) model, with identifiable parameters
`idnlhw`Hammerstein-Wiener model, with identifiable parameters