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.
tf models represent transfer functions
in terms of the coefficients of their numerator and denominator polynomials,
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.
- 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.
- Creating Continuous-Time Models
This example shows how to create continuous-time linear models using the
- 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.
- Creating Discrete-Time Models
This example shows how to create discrete-time linear models using the
- 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 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.