Fixed-Point State-Space

Implement discrete-time state space

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Libraries:
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: InitialCondition

Type: character vector

Values: scalar | vector | matrix

Default: '0.0'

Alternatively, use X0.

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: OutputEqScaling

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 Modes (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'

Block Characteristics

Data Types	`Boolean^a` \| `double` \| `fixed point` \| `integer` \| `single`
Direct Feedthrough	`no`
Multidimensional Signals	`no`
Variable-Size Signals	`yes`
Zero-Crossing Detection	`no`
^a This block is not recommended for use with Boolean signals.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.

HDL Architecture

This block has one default HDL architecture.

HDL Block Properties

By default, the following HDL block property is available.

General
SharingFactor	Use SharingFactor to specify the number of functionally equivalent resources to map to a single shared resource. The default is 0. See Resource Sharing (HDL Coder).

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced before R2006a

Fixed-Point State-Space

Description

Ports

Input

Port_1 — Input signal scalar | vector | matrix

Output

Port_1 — Output signal scalar | vector | matrix

Parameters

Main

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Limitations

Programmatic Use

Signal Attributes

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

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

Programmatic Use

Block Characteristics

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using Simulink® Coder™.

HDL Code Generation Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

Fixed-Point Conversion Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

See Also

Topics

Port_1 — Input signal
scalar | vector | matrix

Port_1 — Output signal
scalar | vector | matrix

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

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

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

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

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

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

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

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

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

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

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

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation
Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.