ディジタル制御アルゴリズムの実装に関する研究 : デルタ形式と多項式形式の比較

概要

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This paper considers finite word length (FWL) effects when implementing the discrete-time transfer functions inthe delta form. A new numerical integration method for fixed-point microprocessors named Variable Modulation Method(VMM) was previously proposed. In this series of research, the effectiveness of VMM was verified on a digital filter anda controller via simulations and experiments. A general procedure for applying VMM to a digital controller by usingMatlab/Simulink is also reported. Furthermore, a simple methodology that is mathematically equivalent to VMM wasproposed. Since this modified VMM(MVMM) offers good finite word-length performance, and becomes the same formbased on the conventional delta operator, MVMM will be useful in the industrial applications. Concerning the deltaform, the polynomial form that generalizes the delta form is proposed and the optimization of the polynomial form is alsoreported. In these papers, the optimum implementation method is proposed, when a control algorithm with the transferfunction or the state-space description is given. On the other hand, MVMM improves the operational accuracy, whena control algorithm is given as a delta form in fixed-point arithmetic. This paper presents the effectiveness of MVMM,comparing the polynomial form to MVMM on a forth-order low-pass Butterworth digital filter.