固定小数点マイクロプロセッサに適した制御アルゴリズムの実装方法（第２報） : ― 修正変数変調法の提案 ―

概要

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This paper considers finite word length (FWL) effects when implementing discrete-time transfer functions in delta form. There are power/size and price/cost constraints in realizing embedded control mechatronic systems such as humanoid robots. To meet these specifications, fixed-point microprocessors with a short word-length are suitable for the control. Fixed-point controller implementation including those using a delta form may suffer from underflow and overflow in the numerical calculations. To solve this problem, a new numerical integration method for fixed-point microprocessors named Variable Modulation Method (VMM) was previously proposed. The present report shows that the basic principle on the improvement of the numerical accuracy relies on the bias modulation in the every sampling period and its mathematical proof is given. From this basic principle, the controller input/output modulation and the high-pass filter are not necessary. Furthermore, in order to improve the numerical accuracy, this simple methodology is extended. As an illustrative example, a fourth-order Butterworth filter is considered. The simulated results show that modified VMM can improve the numerical accuracy the same as VMM. Also, the implementation of modified VMM is very simple, and becomes almost the same as the conventional delta form.