Simulink®

Fixed-Point State-Space - Implement discrete-time state space

Library

Additional Math & Discrete / Additional Discrete

Description

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

y(n)  = Cx(n) + Du(n)

x(n+1) = Ax(n) + Bu(n)

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

The matrices A, B, C and D have the following 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.

In addition:

• The state x must be a n-by-1 vector

• The input u must be a m-by-1 vector

• The output y must be a r-by-1 vector

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

Data Type Support

The Fixed-Point State-Space block accepts signals of any numeric data type supported by Simulink software, including fixed-point data types.

Parameters and Dialog Box

The Main pane of the Fixed-Point State-Space block dialog appears as follows:

State Matrix A

Specify the matrix of states.

Input Matrix B

Specify the column vector of inputs.

Output Matrix C

Specify the column vector of outputs.

Direct Feedthrough Matrix D

Specify the matrix for direct feedthrough.

Initial condition for state

Specify the initial condition for the state.

The Signal Data Types pane of the Fixed-Point State-Space block dialog appears as follows:

Data type for internal calculations

Specify the data type for internal calculations.

Scaling for State Equation AX+BU

Specify the scaling for state equations.

Scaling for Output Equation CX+DU

Specify the scaling for output equations.

Lock output scaling against changes by the autoscaling tool

If you select this check box, the output scaling is locked.

Round toward

Select the rounding mode for fixed-point operations. For more information, see Rounding in the Simulink Fixed Point User's Guide.

Saturate to max or min when overflows occur

If selected, fixed-point overflows saturate.

Characteristics

First-Order Hold

For Iterator