# Basic 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

## Blocks

LTI System | Use linear time invariant system model object in Simulink |

LPV System | Simulate Linear Parameter-Varying (LPV) systems |

## Topics

### Getting Started

**Control System Modeling with Model Objects**

Model objects can represent components such as the plant, actuators, sensors, or controllers. You connect model objects to build aggregate models that represent the combined response of multiple elements.**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.