Overview
When developing a dynamic system using floating-point arithmetic,
you generally don't have to worry about numerical limitations since
floating-point data types have high precision and range. Conversely,
when working with fixed-point arithmetic, you must consider these
factors when developing dynamic systems:
Overflow
Adding two sufficiently large negative or positive values can
produce a result that does not fit into the representation. This will
have an adverse effect on the control system.
Quantization
Fixed-point values are rounded. Therefore, the output signal
to the plant and the input signal to the control system do not have
the same characteristics as the ideal discrete-time signal.
Computational noise
The accumulated errors that result from the rounding of individual
terms within the realization introduce noise into the control signal.
Limit cycles
In the ideal system, the output of a stable transfer function
(digital filter) approaches some constant for a constant input. With
quantization, limit cycles occur where the output oscillates between
two values in steady state.
This chapter describes the limitations involved when arithmetic
operations are performed using encoded fixed-point variables. It also
provides recommendations for encoding fixed-point variables such that
simulations and generated code are reasonably efficient.
 | Arithmetic Operations | | Limitations on Precision |  |
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