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Errors of elementary floating-point operations in control algorithms

Świder Z.

Archives of Control Sciences

2003

Vol. 13, no. 4

505-526

The paper presents analytical development of erroe variances for elementary floatinf-point operations, i.e. quantization, multiplication, and additin, based on expressions for probability density distributions. Guassian inputs are assumed and steps executed by the processor taken into account, particularly normalization of the mantissa to interval [1/2, 1). Uniform estimate (...) of the variance for the three elementary operations is obtained, where b denotes the number of mantissa bits. Error of Euler rectangular integrator (...), commonly used in digital controllers, is evaluated as well. For small sampling step the error depends primarily on precision of the addition executed by the integrator. Increase of the precision used in some small controllers is also considered. The results are verified for first-order transfer function subject to white noise, sinusoidal and constant-plus-noise inputs.