• IEMEK Journal of Embedded Systems and Applications
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• v.9 no.5
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• pp.285-292
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• 2014

The commonly used Newton-Raphson's floating-point number divider algorithm performs two multiplications in one iteration. In this paper, a tentative K'th Newton-Raphson's floating-point number divider algorithm which performs K times multiplications in one iteration is proposed. Since the number of multiplications performed by the proposed algorithm is dependent on the input values, the average number of multiplications per an operation in single precision and double precision divider is derived from many reciprocal tables with varying sizes. In addition, an error correction algorithm, which consists of one multiplication and a decision, to get exact result in divider is proposed. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a floating point number divider unit. Also, it can be used to construct optimized approximate reciprocal tables.

• Journal of Power Electronics
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• v.14 no.3
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• pp.488-498
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• 2014

This paper presents an implementation of selective harmonic elimination (SHE) modulation for a single-phase 13-level transistor-clamped H-bridge (TCHB) based cascaded multilevel inverter. To determine the optimum switching angle of the SHE equations, the Newton-Raphson method is used in solving the transcendental equation describing the fundamental and harmonic components. The proposed SHE scheme used the relationship between the angles and a sinusoidal reference waveform based on voltage-angle equal criteria. The proposed SHE scheme is evaluated through simulation and experimental results. The digital modulator based-SHE scheme using a field-programmable gate array (FPGA) is described and has been implemented on an Altera DE2 board. The proposed SHE is efficient in eliminating the $3^{rd}$, $5^{th}$, $7^{th}$, $9^{th}$ and $11^{th}$ order harmonics, which validates the analytical results. From the results, it can be seen that the adopted 13-level inverter produces a higher quality with a better harmonic profile and sinusoidal shape of the stepped output waveform.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.9
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• pp.1384-1390
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• 2001

This paper deals with the forward kinematics of the 6-6 Stewart platform of planar base and moving platform using one extra linear sensor. Based on algebraic elimination method, it first derives an 8th-degree univariate equation and then finds tentative solution sets out of which the actual solution is to be selected. In order to provide more exact solution despite the error between measured sensor value and the theoretic alone, a correction method is also used in this paper. The overall procedure requires so little computation time that it can be efficiently used for real-time applications. In addition, unlike the iterative scheme e.g. Newton-Raphson, the algorithm does not require initial estimates of solution and is free of the problems that it does not converge to actual solution within limited time. The presented method has been implemented in C language and a numerical example is given to confirm the effectiveness and accuracy of the developed algorithm.