Descriptor State-Space

Model linear implicit system

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Libraries:
Simulink / Continuous

Description

The Descriptor State-Space block allows you to model linear implicit systems described in the implicit form $$E\dot{x}=Ax+Bu$$, 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, $$\dot{x}=E^{-1}Ax+E^{-1}Bu$$, 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:

$$\begin{array}{c}E\dot{x}=Ax+Bu\\ y=Cx+Du\end{array}$$

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.

• Open Model

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, and c, 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, enter names.

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

Data Types	double
Direct Feedthrough	noa
Multidimensional Signals	no
Variable-Size Signals	no
Zero-Crossing Detection	no
a Direct feedthrough characteristics for this block depend on block parameter values.

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 R2018b

R2024b: 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.