Analysis of quantization errors in digital control systems using floating‐point arithmetic—considering computational order in controller

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<jats:title>Abstract</jats:title><jats:p>The floating‐point representation is employed widely in the digital control system due to its features of large dynamic range and high accuracy. However, a sufficient study has not been made on the quantitative evaluation of the quantization error because of the difficulty of the analysis.</jats:p><jats:p>From such a viewpoint, this paper considers the general digital control system and discusses the evaluation method for the control error and the performance deterioration of the control system due to the quantization in the A‐D and D‐A converters, as well as the arithmetic operations in the controller. The difference equation for the error of the state of the digital control system is derived, and the quantitative evaluation of the error (i.e., the mean and the variance) is proposed based on the equation.</jats:p><jats:p>It is noted that there is a freedom in the order of computation in the control operation in the digital controller, and the computation error depends on the order of computation. Consequently, a matrix is newly defined to specify the order of computation, and a method is proposed for the analysis of the control error considering the order of computation.</jats:p><jats:p>In the proposed method, the error can be evaluated for the general digital control system without specifying the object of analysis. The usefulness is demonstrated by a numerical example.</jats:p>

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