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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 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 block determines the input vector width by the number of columns in the B and D matrices. Similarly, the block determines the output vector width 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 box 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 Attributes pane of the Fixed-Point State-Space block dialog box 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 data type setting against changes by the fixed-point tools

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 Fixed-Point Tool and Fixed-Point Advisor in the Simulink Fixed Point documentation.

Integer rounding mode

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. Otherwise, they wrap.

Characteristics

Direct Feedthrough	Yes
Scalar Expansion	Yes, of initial conditions

First-Order Hold

For Iterator

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