LTI System
Use linear time invariant system model object in Simulink
Libraries:
Control System Toolbox
Description
The LTI System block imports linear system model objects into the
Simulink® environment. You specify the LTI model to import in the LTI
system variable parameter. You can import any type of proper linear
time-invariant dynamic system model. If the imported system is a state-space (ss
) model, you can specify initial state values in the Initial
states parameter.
Examples
Simulate LTI Model in Simulink
The LTISystemBlockSimulation
model shows how to use an LTI System block to simulate the response of a SISO transfer function to a step input.
Import MIMO LTI Model into Simulink
How to use an LTI System block to represent a MIMO linear system in Simulink®.
Ports
Input
Port_1(In1) — Input signal
scalar | vector
For a single-input LTI system, the input signal is a scalar. For multiple-input systems, combine the system inputs into a vector signal, using blocks such as:
Mux (Simulink)
Vector Concatenate (Simulink)
Bus Creator (Simulink)
Output
Port_1(Out1) — Output signal
scalar | vector
For a single-output LTI system, the output signal is a scalar. For multiple-output systems, the output signal is a vector. To split system outputs into scalar signals, use blocks such as:
Demux (Simulink)
Bus Selector (Simulink)
Parameters
LTI system variable — Linear system
dynamic system model
Specify the linear system for the block as a MATLAB® expression or a variable in the MATLAB workspace, the model workspace, or a data dictionary. The model can be SISO or MIMO.
Most linear time-invariant dynamic system models are supported, except:
Frequency-response data models, such as
frd
andgenfrd
models.Nonlinear identified models, such as
idnlarx
.Models with unmodeled dynamics, such as
udyn
.
The specified model must be proper (see isproper
).
The model can be either continuous time or discrete time. When the LTI system block is in a Simulink model with synchronous state control (see the State Control (HDL Coder) block), you must specify a discrete-time model.
Simulink converts the model to its state-space equivalent prior to initializing the simulation.
Initial states (state-space only) — Initial state values for state-space model
[]
(default) | vector | scalar
If the linear system is in state-space form, specify the initial state
values as a vector with as many entries as the system has states. If you
specify a scalar value, the block applies that value to each state in the
system. The default value, []
, initializes all states to
zero.
The concept of initial state is not well-defined for linear systems that are not in state-space form, such as transfer functions or zero-pole-gain models. For such models, the initial state depends on the choice of state coordinates used by the realization algorithm. As a result, the block ignores this parameter for such models.
Pade order (for linearization) — Order of Pade approximation
0
(default) | positive integer | vector
Set the order of the Pade approximation for linearization routines.
The default value is
0
, which results in a unity gain with no dynamic states.Setting the order to a positive integer
n
addsn
states to your model, but results in a more accurate linear model of the delay.
Use a vector of positive integers to specify a different order for each input channel.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Version History
Introduced before R2006aR2024a: Simulate state-space models with offsets
You can now simulate a state-space model with offsets using the LTI
System block. Use the LTI system variable parameter
to specify a state-space variable containing model offsets in the
Offsets
property. Offsets usually arise when linearizing
nonlinear dynamics at some operating conditions. For more information about how to
store offsets, see ss
.
R2024a: Support for LTI models with complex coefficients
You can now simulate LTI models with complex coefficients using the LTI System block.
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