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 Type	Description
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:

• Transfer Functions (Control System Toolbox)

• State-Space Models (Control System Toolbox)

• Frequency Response Data (FRD) Models (Control System Toolbox)

• Proportional-Integral-Derivative (PID) Controllers (Control System Toolbox)

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 (Control System Toolbox) app or the PID Tuner GUI (Control System Toolbox).

• Designing controllers using control design commands such as pidtune (Control System Toolbox), rlocus (Control System Toolbox), or lqr (Control System Toolbox)/lqg (Control System Toolbox).

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 Type	Description
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 Type	Description
idnlarx	Nonlinear ARX model, with identifiable parameters
idnlgrey	Nonlinear ODE (grey-box) model, with identifiable parameters
idnlhw	Hammerstein-Wiener model, with identifiable parameters