Fixed-Point Blockset

State-Space Realization

This section presents a fixed-point state-space realization. The difference equation, block parameters, and model design are discussed.

The FixPt State-Space Realization block is a masked subsystem that implements the system described by

where k is the current time step, k + 1 is the next time step, u(k) is the current input, x(k) is the current state, x(k + 1) is the state from the next time step, y(k) is the current output, and A, B, C, and D are all coefficient matrices. The realization is shown below.

Parameters and Dialog Box

The dialog box and parameter descriptions for the state-space realization are given below.

A

B

C

D

Initial conditions

Sample time

Base data type

Accumulator data type

The advantage of using the state-space realization is that you can build high order systems quickly. The disadvantage is that you can't individually scale the elements on vector signal lines. For example, even if the i-th state, x_i, is large and the j-th state, x_j, is small, you must use the same scaling for both. Matrix gain coefficients can be individually scaled but this may not suffice.

The solution to this problem is to use a new realization with more blocks and fewer elements on each signal line. For maximum control of scaling, you should use a diagram that has only scalars on each line.

Model Design Review

A brief review of the model design is given below. The design criteria reflect the rules presented in Design Rules.

• The matrix gains involve a multiplication which is a size-growing operation. In most cases, it is desirable for gains and inputs to use the word size given by the Base data type or smaller. The output can be left at the Accumulator data type for extra precision in subsequent operations. Alternatively, if the output were stored in RAM, or used by a size-growing operation, it could be reduced to the Base data type.
• The FixPt Sum blocks converts inputs to the output data type before performing the actual addition. Given this order of operation, using the Accumulator data type often gives better precision.
• The FixPt Conversion blocks force the output to the Base data type before storage in RAM (before input to the unit delay). Converting the output in the feed forward part of the realization prevents subsequent operations from being burdened with a large data type.

Lead Filter or Lag Filter Realization

Reference