## 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
tfTransfer function model in polynomial form
zpkTransfer function model in zero-pole-gain (factorized) form
ssState-space model
frdFrequency response data model
pidParallel-form PID controller
pidstdStandard-form PID controller
pid2Parallel-form two-degree-of-freedom (2-DOF) PID controller
pidstd2Standard-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:

• Analyzing linear system dynamics using analysis commands such as bode, step, or impulse.

• Designing controllers for linear systems using the Control System Designer app or the PID Tuner GUI.

• Designing controllers using control design commands such as pidtune, rlocus, or lqr/lqg.

### Identified LTI Models

Identified LTI Models represent linear systems with coefficients that are identified using measured input/output data (requires System Identification Toolbox™ software). 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 (System Identification Toolbox)Transfer function model in polynomial form, with identifiable parameters
idss (System Identification Toolbox)State-space model, with identifiable parameters
idpoly (System Identification Toolbox)Polynomial input-output model, with identifiable parameters
idproc (System Identification Toolbox)Continuous-time process model, with identifiable parameters
idfrd (System Identification Toolbox)Frequency-response model, with identifiable parameters
idgrey (System Identification Toolbox)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 (requires System Identification Toolbox software). 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 (System Identification Toolbox)Nonlinear ARX model, with identifiable parameters
idnlgrey (System Identification Toolbox)Nonlinear ODE (grey-box) model, with identifiable parameters
idnlhw (System Identification Toolbox)Hammerstein-Wiener model, with identifiable parameters