• Journal of Astronomy and Space Sciences
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• v.15 no.1
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• pp.235-244
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• 1998

The solutions of orbital maneuver problem using the sliding mode control in the presence of the erath gravitational perturbations is obtained. Especially, the optimization of consuming fuel for maneuver is performed. The impulsive solution to Lambert's problem using the combined equation method to minimize total ${\Delta}V is used for the desired orbit and the maneuver times. Two-step sliding mode control method is introduced for satisfying the boundary conditions of finite-thrust rendezvous problem at the end of maneuver time. Using the new approach to the orbit maneuver problem, two-step sliding mode control, orbit maneuvers are processed. The solutions to a rendezvous using the optimal control are obtained, and they are compared to the results by two-step sliding control.According to the new approach for orbit maneuver, the thrust-coast-thrust type controller is obtained to make satellite to track desired Lambert's orbit, and the total ${\Delta}V$ required for maneuver is resonable in comparison with the impulsive solution to Lambert's problem. The final state variables, also are close to the boundary conditions at the end of maneuver times.

• 한국태양에너지학회:학술대회논문집
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• 2011.11a
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• pp.278-281
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• 2011

This system can predict the maximum output about all illumination levels so that the PV system designer can design the system having the best efficiency. For the output prediction exact about the solar cell, that is the device the basis most in the PV system, the basis has to be in order to try this way. The solution based on Lambert W-function are presented to express the transcendental current-voltage characteristic containing parasitic power consuming parameters like series and shunt resistances. A simple and efficient method for the extraction of a single current-voltage (I-V) curve under the constant illumination level is proposed. With the help of the Lambert W function, the explicit analytic expression for I is obtained. And the explicit analytic expression for V is obtained. This analytic expression is directly used to fit the experimental data and extract the device parameters. The I-V curve of the solar cell was expressed through the modeling using Lambert W-function and the numerical formula where there is the difficulty could be logarithmically expressed This method expresses with the I-V curve through the modeling using Lambert W-function which adds other loss ingredients to the equation2 as to the research afterward. And the solar cell goes as small and this I-V curve can predict the power penalty in the system unit.

• Journal of Aerospace System Engineering
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• v.18 no.1
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• pp.72-78
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• 2024

It is essential to coincide with moving target planet at future arrival changing point during space flight time in an interplanetary orbit design. Transition orbit elements can be obtained from traditional Lambert solutions by adjusting initial and final positions include flight time. Two-point boundary values of orbits can be selected in the design process. From this point of view, interplanetary orbits are infinite if they can be acquired from departure velocity without limit. However, appropriate and optimized procedures are needed to obtain an optimum interplanetary orbit to meet given conditions. The departure velocity is highly dependent on space launch vehicle's ability up to now. In this paper, algorithms of professor Howard Curtis at Embry-Riddle Aeronautical University were applied to obtain Lambert solution and orbit elements.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.480-485
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• 1993

A method for obtaining optimal orbital maneuvers of a space vehicle has been developed by combining feedback linearization method with the elegance of the Lambert's theorem. To obtain solutions to nonlinear orbital maneuver problems. The full nonlinear equations of motion for space vehicle in polar coordinate system are transformed exactly into a controllable linear set in Brunovsky canonical form by using feedback linearization by choosing position vector as fully observable output vector. These equations are used to pose a linear optimal tracking problem with a solutions to Lambert's problem and a linear analytical solution of continuous low thrust problem as reference trajectories.

• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.238-243
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• 1999

Minimum-fuel and -time orbit transfer are two major goals of the satellite trajectory optimization. In this paper, we consider satellites in two coplanar elliptic orbits when the apsidal lines coincide, and analytically find the conditions for the two-impulse minimum-time transfer orbit using Lambert's theorem. The transfer time is a decreasing function of a variable related to the transfer orbit's semimajor axis in the minimum-time case. In the minimum-time case, there is no unique minimum-time solution, but there is a limiting solution. However, there exists a unique solution in the case of minimum-fuel transfer, fur which we find analytically the necessary and sufficient conditions. As a special case, we consider when the transfer angle is one hundred and eighty degrees. In this case, we show that we obtain the classical fuel-optimal Hohmann transfer orbit. We also derive the Hohmann transfer rime and delta-velocity equations from more general equations, which are obtained using Lambert's theorem. We note the tradeoff between minimum-time and - fuel transfer. An optimal coplanar orbit maneuver algorithm to trade off the minimum-time goal against the minimum-fuel goal is proposed. Finally, the numerical simulation results are given to demonstrate the derived theory and the algorithm.

• Journal of the Institute of Electronics and Information Engineers
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• v.52 no.3
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• pp.19-24
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• 2015

We introduce an optimization of the number of base station antennas in massive multiple-input multiple-output (MIMO) wireless powered communication network (WPCN). We use channel hardening property of massive MIMO system to approximate channel gain in terms of the number of base station antennas. Then, we find an optimal solution by partial differential and obtain a closed form solution by using Lambert-W function. The simulation results show that the approximation and the method of solving the optimization problem are reasonable, and the optimal solution of proposed scheme is almost identical to the optimal number of base station antennas by the exhaustive search method.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.6A
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• pp.524-532
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• 2002

This paper reports that the Lambert W function applies to a non-iterative design of minimum mean square-error scalar quantizers for a Laplacian source. Specifically, it considers a non-iterative design algorithm for optimum quantizers for a Laplacian source; it finds that the solution of the recursive nonlinear equation in the non-iterative design is elegantly expressed in term of the principal branch of the Lambert W function in a closed form; and it proves that the non-iterative algorithm applies only to exponential or Laplacian sources. The contribution of the paper is in the reduction of the time needed for the design and the increased accuracy in resulting quantization points and thresholds, because the algorithm is non-iterative and the Lambert W function can be evaluated as accurately as desired. Also, numerical results show how optimal quantization distortion converges monotonically to the Panter-Dite constant and help derive an approximation formula for the key parameters of optimum quantizers.

• Journal of Life Science
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• v.29 no.5
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• pp.509-513
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• 2019

The Beer-Lambert law states that absorbance is proportional to the concentration of a solute in a solution at a given wavelength. This linearity works for an ideal or a 'sufficiently diluted' solution, so this linearity is often used as a criterion for the fidelity of the absorbance value measured. In this study, we used a chlorophyll (Chl) solution, isolated from rice leaves with 80% acetone to test the use of the Chl a/b ratio as an additional criterion for checking the fidelity of measured values using four different absorption spectrophotometers: Cary4E, UV-1650PC, Versamax (a microplate reader), and NanoDrop 1,000(which can handle a $4{\mu}l$ aliquot). We used Chl solutions of varying concentrations from $0.2{\mu}g/ml$ to $200{\mu}g/ml$ to measure absorbance values at 645 nm and 663 nm and checked the linearity first. The results indicated that the range of Chl concentrations that we can rely on based on the linearity was similar to the range in which the calculated Chl concentrations based on the measured absorbance values agreed with the known concentrations. However, some border cases or cases with very low Chl concentrations inside the fidelity range of Chl concentrations did not agree with the criterion that the Chl a/b ratio should not change after dilution of the Chl in the solution. These results suggest that the Chl a/b ratio is a better criterion for the reliability of the absorbance values measured for the determination of chlorophyll concentration than the criterion based on the linearity suggested by the Beer-Lambert law.

• Journal of the Korean Society of Tobacco Science
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• v.3 no.2
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• pp.77-81
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• 1981

A flew spectroscopic method was developed to determine microquantities of nicotine with cyanogen chloride and pyrazolon. Absorption maximum of tile derivative solution appeared at 520nm. The color formed in the proposed method was stable for at least 30 min. at pH 7.5, and followed the Lambert-Beer's law between tile limits of 1 and 5 micrograms of nicotine. The relative errors in burley and flue-cured tobacco leaves were $\pm5%$ in comparison with the Griffith method.

• YAKHAK HOEJI
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• v.31 no.2
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• pp.45-51
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• 1987

Methyl orange(MO) and cetyltrimethylammonium bromide(CTA) were mixed and added to 10ml of the buffer solution and then the solution was shaken for 5 minutes. The maximum absorption wavelength of the reaction product was 419nm. Dichloromethane was the best extracting solvent among the several organic solvents and the most suitable pH range was 2~8. When the CTA-MO calibration curve was made in the best experimental condition, the Lambert-Beer's law was obeyed in the range of CTA concentration of $1.5\times$$10^{-5}$~1.0$\times$$10^{-4}M$ by UV spectrophotometer. This method was possible to determine quaternary ammonium salts in the pharmaceutical preparations.