Analysis of Floating-Point Quantization Errors in Digital Control Systems: Influence of The Order of Arithmetic Steps in Controller

In this paper we present a general approach to the analysis problem of quantization errors in digital control systems using floating point arithmetic. The closed form of the description of system errors due to quantization is derived for the general class of linear digital control systems. We consider almost all kinds of quantization errors which may occur in general digital control systems; truncation or roundoff quantization errors of A/D and D/A conversions, and truncation or roundoff errors in arithmetic operations. We also develop a method to estimate the influence of the order of the arithmetic steps of control algorithms implemented in digital controllers on quantization errors. A mathematical description of the order of arithmetic steps in digital controller is introduced. The validity of the proposed analysis is comfirmed through numerical experiments.