Fixed-Point State-Space

Implement discrete-time state space

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Library:
Simulink / Additional Math & Discrete / Additional Discrete

Description

The Fixed-Point State-Space block implements the system described by

$y (n) = C x (n) + D u (n)$

$x (n + 1) = A x (n) + B u (n)$

where u is the input, x is the state, and y is the output. Both equations have the same data type.

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.

In addition:

The state x must be an n-by-1 vector.
The input u must be an m-by-1 vector.
The output y must be an r-by-1 vector.

The block accepts one input and generates one output. The width of the input vector is the number of columns in the B and D matrices. The width of the output vector is the number of rows in the C and D matrices. To define the initial state vector, use the Initial conditions parameter.

Ports

Input

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`Port_1` — Input signal
scalar | vector | matrix

Input vector, where the width equals the number of columns in the B and D matrices. For more information, see Description.

Output

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`Port_1` — Output signal
scalar | vector | matrix

Output signal, with width equal to the number of rows in the C and D matrices. For more information, see Description.

Parameters

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Main

`State Matrix A` — Matrix of states
`[2.6020 -2.2793 0.6708; 1 0 0; 0 1 0]` (default) | scalar | vector | matrix

Specify the matrix of states as an n-by-n matrix of real or complex values, where n is the number of states. For more information on the matrix coefficients, see Description.

Programmatic Use

Block Parameter: A

Type: character vector

Values: scalar | vector | matrix

Default:

'[2.6020 -2.2793 0.6708; 1 0 0; 0 1
									0]'

`Input Matrix B` — Column vector of inputs
`[ 1; 0; 0]` (default) | scalar | vector | matrix

Specify the column vector of inputs as an n-by-m matrix of real or complex values, where n is the number of states, and m is the number of inputs. For more information on the matrix coefficients, see Description.

Programmatic Use

Block Parameter: B

Type: character vector

Values: scalar | vector | matrix

Default: '[ 1; 0; 0]'

`Output Matrix C` — Column vector of outputs
`[0.0184 0.0024 0.0055]` (default) | scalar | vector | matrix

Specify the column vector of outputs as an r-by-n matrix of real or complex values, where r is the number of outputs, and n is the number of states. For more information on the matrix coefficients, see Description.

Programmatic Use

Block Parameter: C

Type: character vector

Values: scalar | vector | matrix

Default: '[0.0184 0.0024 0.0055]'

`Direct Feedthrough Matrix D` — Matrix for direct feedthrough
`[0.0033]` (default) | scalar | vector | matrix

Specify the matrix for direct feedthrough as an r-by-m matrix of real or complex values, where r is the number of outputs, and m is the number of inputs. For more information on the matrix coefficients, see Description.

Programmatic Use

Block Parameter: D

Type: character vector

Values: scalar | vector | matrix

Default: '[0.0033]'

`Initial condition for state` — Initial state vector
`0.0` (default) | scalar | vector | matrix

Specify the initial condition for the state.

Limitations

The initial state cannot be inf or NaN.

Programmatic Use

Block Parameter: X0

Type: character vector

Values: scalar | vector | matrix

Default: '0.0'

Signal Attributes

`Data type for internal calculations` — Data type for internal calculations
`fixdt('double')` (default) | data type string

Specify the data type the block uses for internal calculations.

Programmatic Use

Block Parameter: InternalDataType

Type: character vector

Values: data type string

Default: 'fixdt('double')'

`Scaling for State Equation AX+BU` — Scaling for state equations
`2^0` (default) | scalar

Specify the scaling for the state equation AX+BU.

Programmatic Use

Block Parameter: StateEqScaling

Type: character vector

Values: scalar

Default: '2^0'

`Scaling for Output Equation CX+DU` — Scaling for output equations
`2^0` (default) | scalar

Specify the scaling for the output equation CX+DU.

Programmatic Use

Block Parameter: InternalDataType

Type: character vector

Values: scalar

Default: '2^0'

`Lock output data type setting against changes by the fixed-point tools` — Prevent fixed-point tools from overriding data types
`off` (default) | `on`

Select to lock the output data type setting of this block against changes by the Fixed-Point Tool and the Fixed-Point Advisor. For more information, see Use Lock Output Data Type Setting (Fixed-Point Designer).

Programmatic Use

Block Parameter: LockScale

Type: character vector

Values: 'off' | 'on'

Default: 'off'

`Integer rounding mode` — Rounding mode for fixed-point operations
`Floor` (default) | `Ceiling` | `Convergent` | `Nearest` | `Round` | `Simplest` | `Zero`

Specify the rounding mode for fixed-point operations. For more information, see Rounding (Fixed-Point Designer).

Programmatic Use

Block Parameter: RndMeth

Type: character vector

Values:

'Ceiling' | 'Convergent' | 'Floor' |
                                                  'Nearest' | 'Round' | 'Simplest' |
                                                  'Zero'

Default: 'Floor'

`Saturate to max or min when overflows occur` — Method of overflow action
`off` (default) | `on`

When you select this check box, overflows saturate to the maximum or minimum value that the data type can represent. Otherwise, overflows wrap.

When you select this check box, saturation applies to every internal operation on the block, not just the output or result. In general, the code generation process can detect when overflow is not possible. In this case, the code generator does not produce saturation code.

Programmatic Use

Block Parameter: DoSatur

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Model Examples