Fixed-Point State-Space

Implement discrete-time state space

• 

Libraries:
Simulink / Additional Math & Discrete / Additional Discrete

Description

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

$$y(n)=\text{C}x(n)+\text{D}u(n)$$

$$x(n+1)=\text{A}x(n)+\text{B}u(n)$$

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

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.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | Boolean | fixed point
Complex Number Support: Yes

Output

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.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | Boolean | fixed point

Parameters

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: 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 (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	Booleana | 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 Verilog and VHDL 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

If you use the block in matrix multiplication mode, you can specify the DotProductStrategy. This setting determines whether you want to implement the matrix multiplication by using a tree of adders and multipliers, or use the Multiply-Accumulate block implementation. The default is Fully Parallel.

Note

The DotProductStrategy must be set to Fully Parallel when you use the Native Floating Point mode.

For more information, see DotProductStrategy (HDL Coder).

General
ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is 0. For more details, see ConstrainedOutputPipeline (HDL Coder).
DSPStyle	Synthesis attributes for multiplier mapping. The default is none. See also DSPStyle (HDL Coder).
InputPipeline	Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see InputPipeline (HDL Coder).
OutputPipeline	Number of output pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see OutputPipeline (HDL Coder).

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

Version History

Introduced before R2006a