Numeric Linear Time-Invariant Models

Common models of linear systems, such as transfer functions and state-space models

Numeric linear-time-invariant (LTI) models are the basic building blocks that you use to represent linear systems. Numeric LTI model objects let you store dynamic systems in commonly-used representations. For example, tf models represent transfer functions in terms of the coefficients of their numerator and denominator polynomials, and ss models represent LTI systems in terms of their state-space matrices. There are also LTI model types specialized for representing PID controllers in terms of their proportional, integral, and derivative coefficients.

Build up a more complex model of a control system by representing individual components as LTI models and connecting the components to model your control architecture. For an example, see Control System Modeling with Model Objects.

Functions

expand all

Basic Models

`tf`	Transfer function model
`zpk`	Zero-pole-gain model
`ss`	State-space model
`frd`	Frequency-response data model
`filt`	Specify discrete transfer functions in DSP format
`dss`	Create descriptor state-space models

PID Models

`pid`	PID controller in parallel form
`pidstd`	PID controller in standard form
`pid2`	2-DOF PID controller in parallel form
`pidstd2`	2-DOF PID controller in standard form

Generate Random Models

`rss`	Generate random continuous test model
`drss`	Generate random discrete test model

Blocks

LTI System

Use linear time invariant system model object in Simulink

Topics

Getting Started

Control System Modeling with Model Objects
Build models that represent your control system using model objects.
What Are Model Objects?
Model objects represent linear systems as specialized data containers that encapsulate model data and attributes in a structured way.
Using Model Objects
Ways to use model objects include linear analysis, compensator design, and control system tuning.

Continuous-Time Models

Creating Continuous-Time Models
This example shows how to create continuous-time linear models using the tf, zpk, ss, and frd commands.
Transfer Functions
Represent transfer functions in terms of numerator and denominator coefficients or zeros, poles, and gain.
State-Space Models
Represent state-space models in terms of the state-space matrices.
Frequency Response Data (FRD) Models
Represent dynamic systems in terms of the magnitude and phase of their responses at various frequencies.
Proportional-Integral-Derivative (PID) Controllers
Represent PID controllers in terms of controller gains or time constants.
Two-Degree-of-Freedom PID Controllers
2-DOF PID controllers can achieve faster disturbance rejection without significant increase of overshoot in setpoint tracking.
Using the Right Model Representation
This example shows some best practices for working with LTI models.

Discrete-Time Models

Creating Discrete-Time Models
This example shows how to create discrete-time linear models using the tf, zpk, ss, and frd commands.
Discrete-Time Numeric Models
Represent discrete-time numeric models by specifying a sample time when you create the model object.
Discrete-Time Proportional-Integral-Derivative (PID) Controllers
The integrator and filter terms in discrete-time PID controllers can be represented by several different formulas.

MIMO Models

MIMO Transfer Functions
Create MIMO transfer functions by concatenating SISO transfer functions or by specifying coefficient sets for each I/O channel.
MIMO State-Space Models
These examples show how to represent MIMO systems as state-space models.
MIMO Frequency Response Data Models
Use frequency-response data from multiple I/O pairs in a system to create a MIMO frequency response model.
Select Input/Output Pairs in MIMO Models
Extract particular I/O channels from a MIMO dynamic system model.

LTI Models in Simulink

Import LTI Model Objects into Simulink
Use the LTI System block to import linear system model objects into Simulink^®.

More About Model Objects

Types of Model Objects
Model object types include numeric models, for representing systems with fixed coefficients, and generalized models for systems with tunable or uncertain coefficients.
Dynamic System Models
Represent systems that have internal dynamics or memory of past states, such as integrators, delays, transfer functions, and state-space models.
Numeric Models
Numeric LTI Models represent dynamic elements, such as transfer functions or state-space models, with fixed coefficients.
Static Models
Represent static input/output relationships, including tunable or uncertain parameters and arrays.