Descriptor State-Space
Model linear implicit system
Libraries:
Simulink /
Continuous
Description
The Descriptor State-Space block allows you to model linear implicit systems described in the implicit form , where E is the mass matrix of the system. When E is nonsingular and therefore invertible, you can describe the system in the explicit form, , and model the system using the State-Space block.
When the mass matrix E is singular, the equations do not contain derivatives for one or more of the dependent variables in the system. Dependent variables in the system are also called algebraic variables, and differential equations that contain algebraic variables are called differential algebraic equations. The state-space representation of a system described by differential algebraic equations has this form:
where:
x is the state vector.
u is the input vector.
y is the output vector.
Examples
Model a Series RLC Circuit
Model a series RLC circuit while avoiding algebraic loops by using the Descriptor State Space block.
Ports
Input
Input 1 — Input signal
scalar | vector
Real-valued scalar or vector input signal of the implicit system. The
input signal data type must be double
. For vector
input signals, the signal width must match the number of columns in the
B and D matrices for the
system.
This port has direct feedthrough when:
You set the Direct Feedthrough parameter to
True
.You set the Direct Feedthrough parameter to
Auto
and the software determines that the block has direct feedthrough.
Data Types: double
Output
Output 1 — Output signal
scalar | vector
Output signal of implicit system.
Data Types: double
Parameters
E — Mass matrix E of implicit system
1
(default) | scalar | matrix
Specify the mass matrix E as a real-valued n-by-n matrix, where n is the number of states in the system. The mass matrix can be singular or nonsingular and must have the same dimensions as the A matrix.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
To get the block parameter value
programmatically, use the get_param
function.
Parameter: | E |
Values: | '1' (default) | scalar | matrix |
Data Types: | char | string |
Example: set_param("MyModel/Descriptor State-Space",E="[1 2;3
4]")
A — A matrix of implicit system
1
(default) | scalar | matrix
Specify the matrix A as a real-valued n-by-n matrix, where n is the number of states in the system. The matrix A must have the same dimensions as the mass matrix E.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
To get the block parameter value
programmatically, use the get_param
function.
Parameter: | A |
Values: | '1' (default) | scalar | matrix |
Data Types: | char | string |
Example: set_param("MyModel/Descriptor State-Space",A="[1 2;3
4]")
B — B matrix of implicit system
1
(default) | scalar | vector | matrix
Specify the matrix B as a real-valued n-by-m matrix, where n is the number of states in the system and m is the number of inputs.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
To get the block parameter value
programmatically, use the get_param
function.
Parameter: | B |
Values: | '1' (default) | scalar | vector | matrix |
Data Types: | char | string |
Example: set_param("MyModel/Descriptor State-Space",B="[1
2]")
C — C matrix of implicit system
1
(default) | scalar | vector | matrix
Specify the matrix C as a real-valued r-by-n matrix, where n is the number of states in the system and r is the number of outputs.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
To get the block parameter value
programmatically, use the get_param
function.
Parameter: | C |
Values: | '1' (default) | scalar | vector | matrix |
Data Types: | char | string |
Example: set_param("MyModel/Descriptor State-Space",C="[3
4]")
D — D matrix of implicit system
1
(default) | scalar | vector | matrix
Specify the matrix D as a real-valued r-by-m matrix, where r is the number of system outputs and m is the number of system inputs.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
To get the block parameter value
programmatically, use the get_param
function.
Parameter: | D |
Values: | '1' (default) | scalar | vector | matrix |
Data Types: | char | string |
Example: set_param("MyModel/Descriptor
State-Space",D="5")
Initial condition — Initial state values
0
(default) | scalar | vector | matrix
Specify the initial values for states of the implicit system. States
cannot have Inf
or NaN
values.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
To get the block parameter value
programmatically, use the get_param
function.
Parameter: | InitialCondition |
Values: | '0' (default) | scalar | vector | matrix |
Data Types: | char | string |
Example: set_param("MyModel/Descriptor State-Space",InitialCondition="[2
3]")
Direct feedthrough — Whether output signal value depends on input signal value
True
(default) | False
| Auto
Specify whether the implicit system has direct feedthrough. A block has direct feedthrough when the value of one or more output signals directly depends on the value of one or more input signals.
True
— The output signal value directly depends on the input signal value.False
— The output signal value does not directly depend on input signal value.Auto
— The software determines whether the output signal value directly depends on the input signal value based on the characteristics of the specified matrices.
When this block implements a system with more than 500 continuous states, specifying this
parameter as True
or
False
can speed up the simulation.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
To get the block parameter value
programmatically, use the get_param
function.
Parameter: | DirectFeedthrough |
Values: | 'True' (default) | 'False' | 'Auto' |
Data Types: | char | string |
Example: set_param("MyModel/Descriptor
State-Space",DirectFeedthrough="False")
Linearize to sparse model — Linearize states to sparse matrices
on
(default) | off
For Simulink® Control Design™ workflows, linearize the system represented by the Descriptor State-Space block to a sparse model during linearization.
Disable this parameter to linearize the system to a non-sparse explicit state-space model.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
To get the block parameter value
programmatically, use the get_param
function.
Parameter: | LinearizeToSparse |
Values: | 'off' (default) | 'on' |
Data Types: | char | string |
Example: set_param("MyModel/Descriptor
State-Space",LinearizeToSparse="on")
Absolute tolerance — Absolute tolerance for computing block states
auto
(default) | scalar | vector
Variable-step solvers use absolute and relative tolerances when choosing the step size to determine whether the error in state calculations is acceptable.
To inherit the absolute tolerance from the Absolute tolerance configuration parameter, specify this parameter
value as auto
or -1
.
To specify an absolute tolerance for this block that overrides the value specified for the Absolute tolerance configuration parameter:
Enter a real, positive scalar value to use to compute all block states.
Enter a real vector with dimensions that match the dimensions of the continuous states for the block.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
To get the block parameter value
programmatically, use the get_param
function.
Parameter: | AbsoluteTolerance |
Values: | 'auto' (default) | '-1' | positive real scalar number | vector of positive real scalar numbers |
Data Types: | char | string |
Example: set_param("MyModel/Descriptor
State-Space",AbsoluteTolerance="-1")
State Name (e.g., 'position') — Option to assign unique names to states
''
(default) | character vector | cell array of character vectors | MATLAB® variable | ...
Use this parameter to optionally assign names to the states of this block. The names you assign apply only to the states of this block.
To use default state names, leave this field blank (
''
).To assign a single name to a single state, enter the name between quotes. For example, to name a single state
position
, enter'position'
.To assign names to multiple states, specify this parameter value as a cell array of character vectors. Each name in the cell array must be unique. For example, to assign the names
a
,b
, andc
, enter{'a','b','c'}
.To specify the names using a MATLAB variable, enter the name of the variable without quotes. For example, to use the variable
names
to specify the state names, enternames
.
You can specify a number of names that is less than the number of states in the block. In this case, the state names are used for multiple states, and the number of states must divide evenly into the number of state names. For example, when you specify two names for a block that has four states, the first name is used for the first two states, and the second name is used for the last two states.
Programmatic Use
To set the block parameter value programmatically, use
the set_param
function.
To get the block parameter value
programmatically, use the get_param
function.
Parameter: | ContinuousStateAttributes |
Values: | '' (default) | valid MATLAB variable name |
Data Types: | char | string | cell |
Example: set_param("MyModel/Descriptor
State-Space",ContinuousStateAttributes={'position','velocity'})
Block Characteristics
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Not recommended for production code.
Before R2024b: The Descriptor State-Space block supports only C code generation and does not support C++ code generation.
Consider using the Model Discretizer to map continuous blocks such as the Descriptor State-Space block to discrete equivalents that support code generation. To open the Model Discretizer, in the Apps tab, under Control Systems, click Model Discretizer.
Version History
Introduced in R2018bR2024b: C++ code generation support
You can generate C++ code for implicit systems that have a mass matrix, such as those implemented using the Descriptor State-Space block. Use the Language (Simulink Coder) parameter to specify the language for code generation.
See Also
Blocks
Functions
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