Discrete State-Space

Implement discrete state-space system

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Libraries:
Simulink / Discrete
Simulink / Quick Insert / Discrete
HDL Coder / RCP and HIL

Description

Block Behavior for Non-Empty Matrices

The Discrete State-Space block implements the system described by

$$\begin{array}{c}x(n+1)=Ax(n)+Bu(n)\\ y(n)=Cx(n)+Du(n),\end{array}$$

where u is the input, x is the state, and y is the output. The matrix coefficients must have these characteristics, as illustrated in the following diagram:

• 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 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.

To specify a vector or matrix of zeros for A, B, C, D, or Initial conditions, use the zeros function.

Block Behavior for Empty Matrices

When the matrices A, B, and C are empty (for example, []), the functionality of the block becomes y(n) = Du(n). If the Initial conditions vector is also empty, the block uses an initial state vector of zeros.

Examples

Inverted Pendulum with Animation

Use Simulink® to model and animate an inverted pendulum system. An inverted pendulum has its center of mass above its pivot point. To stably maintain this position, the system implements control logic to move the pivot point below the center-of mass as the pendulum starts to fall. The inverted pendulum is a classic dynamics problem used to test control strategies.

• Open Model

Ports

Input

Port_1 — Input signal

scalar | vector

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

Tip

For integer and fixed-point input signals, use the Fixed-Point State-Space block.

Data Types: single | double

Output

Port_1 — Output vector

scalar | vector

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

Data Types: single | double

Parameters

Main

A — Matrix coefficient A

1 (default) | scalar | vector | matrix

Specify the matrix coefficient A, as a real-valued n-by-n matrix, 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: '1'

B — Matrix coefficient B

1 (default) | scalar | vector | matrix

Specify the matrix coefficient B, as a real-valued n-by-m matrix, 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'

C — Matrix coefficient, C

1 (default) | scalar | vector | matrix

Specify the matrix coefficient C, as a real-valued r-by-n matrix, 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: '1'

D — Matrix coefficient, D

1 (default) | scalar | vector | matrix

Specify the matrix coefficient D, as a real-valued r-by-m matrix, 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: '1'

Initial conditions — Initial state vector

0 (default) | scalar | vector

Specify the initial state vector as a scalar or vector. The initial state vector cannot include inf or NaN values.

Programmatic Use

Block Parameter: InitialCondition

Type: character vector

Values: scalar | vector

Default: '0'

Sample time (–1 for inherited) — Interval between samples

-1 (default) | scalar | vector

Specify the time interval between samples. See Specify Sample Time.

Programmatic Use

Block Parameter: SampleTime

Type: character vector

Values: scalar | vector

Default: '-1'

State Attributes

State name — Unique name for block state

'' (default) | alphanumeric string

Use this parameter to assign a unique name to the block state. The default is ' '. When this field is blank, no name is assigned. When using this parameter, remember these considerations:

• A valid identifier starts with an alphabetic or underscore character, followed by alphanumeric or underscore characters.

• The state name applies only to the selected block.

This parameter enables State name must resolve to Simulink signal object when you click Apply.

For more information, see C Data Code Interface Configuration for Model Interface Elements (Simulink Coder).

Programmatic Use

Block Parameter: StateName

Type: character vector

Values: unique name

Default: ''

State name must resolve to Simulink signal object — Require state name resolve to a signal object

off (default) | on

Select this check box to require that the state name resolves to a Simulink^® signal object.

Dependencies

To enable this parameter, specify a value for State name. This parameter appears only if you set the model configuration parameter Signal resolution to a value other than None.

Programmatic Use

Block Parameter: StateMustResolveToSignalObject

Type: character vector

Values: 'off' | 'on'

Default: 'off'

Block Characteristics

Data Types	double | single
Direct Feedthrough	yes
Multidimensional Signals	no
Variable-Size Signals	no
Zero-Crossing Detection	no

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

Generated code relies on memcpy or memset functions (string.h) under certain conditions.

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.

Native Floating Point
LatencyStrategy	Specify whether to map the blocks in your design to inherit, Max, Min, or Zero for the floating-point operator. The default is inherit. See also LatencyStrategy (HDL Coder).

PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.

Version History

Introduced before R2006a