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State-Space - Implement linear state-space system

Library

Continuous

Description

The State-Space block implements a system whose behavior you define as

where x is the state vector, u is the input vector, and y is the output vector. The matrix coefficients must have these characteristics:

• A must be an n-by-n matrix, where n is the number of states.

• B must be an n-by-m matrix, where m is the number of inputs.

• C must be an r-by-n matrix, where r is the number of outputs.

• D must be an r-by-m matrix.

  

The block accepts one input and generates one output. The input vector width depends on the number of columns in the B and D matrices. The output vector width depends on the number of rows in the C and D matrices.

Simulink software converts a matrix containing zeros to a sparse matrix for efficient multiplication.

Data Type Support

A State-Space block accepts and outputs real signals of type double.

Parameters and Dialog Box

A

Specify the n-by-n matrix coefficient, where n is the number of states.

Settings

Default: 1

Command-Line Information

See Block-Specific Parameters for the command-line information.

B

Specify the n-by-m matrix coefficient, where n is the number of states and m is the number of inputs.

Settings

Default: 1

Command-Line Information

See Block-Specific Parameters for the command-line information.

C

Specify the r-by-n matrix coefficient, where r is the number of outputs and n is the number of states.

Settings

Default: 1

Command-Line Information

See Block-Specific Parameters for the command-line information.

D

Specify the r-by-m matrix coefficient, where r is the number of outputs and m is the number of inputs.

Settings

Default: 1

Command-Line Information

See Block-Specific Parameters for the command-line information.

Initial conditions

Specify the initial state vector.

Settings

Default: 0

The initial conditions of this block cannot be inf or NaN.

Command-Line Information

See Block-Specific Parameters for the command-line information.

Absolute tolerance

Specify the absolute tolerance for computing the block output.

Settings

Default: auto

• You can enter auto or a numeric value.

• If you enter auto, Simulink uses the absolute tolerance value in the Configuration Parameters dialog box (see Solver Pane) to compute the block output.

• If you enter a numeric value, that value overrides the absolute tolerance in the Configuration Parameters dialog box.

Command-Line Information

See Block-Specific Parameters for the command-line information.

State Name (e.g., 'position')

Assign a unique name to each state.

Settings

Default: ' '

If this field is blank, no name assignment occurs.

Tips

• To assign a name to a single state, enter the name between quotes, for example, 'velocity'.

• To assign names to multiple states, enter a comma-delimited list surrounded by braces, for example, {'a', 'b', 'c'}. Each name must be unique.

• The state names apply only to the selected block.

• The number of states must divide evenly among the number of state names.

• You can specify fewer names than states, but you cannot specify more names than states.

  For example, you can specify two names in a system with four states. The first name applies to the first two states and the second name to the last two states.

• To assign state names with a variable in the MATLAB workspace, enter the variable without quotes. A variable can be a string, cell array, or structure.

Command-Line Information

See Block-Specific Parameters for the command-line information.

Characteristics

Direct Feedthrough	Only if D ≠ 0
Sample Time	Continuous
Scalar Expansion	Yes, of the initial conditions
States	Depends on the size of A
Dimensionalized	Yes
Zero-Crossing Detection	No

See Also

Discrete State-Space

Squeeze

Step

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