• Journal of applied mathematics & informatics
• /
• 제32권1_2호
• /
• pp.39-53
• /
• 2014

In this paper, a non-asymptotic method is presented for solving singularly perturbed delay differential equations whose solution exhibits a boundary layer behavior. The second order singularly perturbed delay differential equation is replaced by an asymptotically equivalent first order neutral type delay differential equation. Then, Simpson's integration formula and linear interpolation are employed to get three term recurrence relation which is solved easily by Discrete Invariant Imbedding Algorithm. Some numerical examples are given to validate the computational efficiency of the proposed numerical scheme for various values of the delay and perturbation parameters.

• Journal of Astronomy and Space Sciences
• /
• 제6권2호
• /
• pp.91-100
• /
• 1989

정지 위성 궤도의 평균 궤도 요소를 비 특이점 궤도 요소 항으로 연구하였다. 실제 위성의 위치는 평균 궤도로부터 단주기 섭동 만큼 위성 위치가 진동하는데, 그 진동의 진폭은 1800m 이하이다. $e_c$ 와 $e_s$의 평균값도 얻었다.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1999년도 하계학술대회 논문집 B
• /
• pp.643-645
• /
• 1999

In between of linear and nonlinear systems lies a large class of bilinear systems. The major importance of bilinear systems lies in the applications to the real world systems such as many physical processes, many biological process, some economic process. Despite vast application of bilinear systems they have not been studied extensively in the domain of singularly perturbations except for a few minor results. In this paper we will utilize singular peturbations theory to obtain the closed-loop optimal solution for discrete-time bilinear systems.

• 한국정밀공학회지
• /
• 제12권1호
• /
• pp.78-86
• /
• 1995

$H_{\infty}$ Controller of seeker scan-loop is designed using LSDP proposed by McFarlane. The performance and robustness of $H_{\infty}$ controller are analyzed using robustness theorems by Lehtomaki and compared with those of the LQG/LTR controller. Especially, structured singular value .mu. -test of Doyle is used to evaluate robust performance of seeker scan-loop. It is demonstated that seeker scan-loop by $H_{\infty}$ controller is very robust to model uncertainties described by additive and multiplicative perturbations.

• 대기
• /
• 제20권4호
• /
• pp.399-414
• /
• 2010

Sand and dust storm in East Asia, so called Asian dust, is a seasonal meteorological phenomenon. Mostly in spring, dust particles blown into atmosphere in the arid area over northern China desert and Manchuria are transported to East Asia by prevailing flows. An Asian dust event occurred on 6-8 May 2007 is chosen to investigate how sensitive the Asian dust transport forecast to the initial condition uncertainties and to interpret the characteristics of sensitivity structures from the viewpoint of dynamics and predictability. To investigate the forecast sensitivities to the initial condition, adjoint sensitivities that calculate gradient of the forecast aspect (i.e., response function) with respect to the initial condition are used. The forecast aspects relevant to Asian dust transports are dry energy forecast error and lower tropospheric pressure forecast error. The results show that the sensitive regions for the dry energy forecast error and the lower tropospheric pressure forecast error are initially located in the vicinity of the trough and then propagate eastward as the surface low system moves eastward. The vertical structures of the adjoint sensitivities for the dry energy forecast error are upshear tilted structures, which are typical adjoint sensitivity structures for extratropical cyclones. Energy distribution of singular vectors also show very similar structures with the adjoint sensitivities for the dry energy forecast error. The adjoint sensitivities of the lower tropospheric pressure forecast error with respect to the relative vorticity show that the accurate forecast of the trough (or relative vorticity) location and intensity is essential to have better forecasts of the Asian dust event. Forecast error for the atmospheric circulation during the dust event is reduced 62.8% by extracting properly weighted adjoint sensitivity perturbations from the initial state. Linearity assumption holds generally well for this case. Dynamics of the Asian dust transport is closely associated with predictability of it, and the improvement in the overall forecast by the adjoint sensitivity perturbations implies that adjoint sensitivities would be beneficial in improving the forecast of Asian dust events.

• Journal of Astronomy and Space Sciences
• /
• 제5권2호
• /
• pp.111-122
• /
• 1988

지구의 비대칭 중력장 $J_2$와 $J_3$가 원궤도에 가까운 인공위성의 궤도요소에 미치는 장, 단주기 섭동과 영년섭동을 해석적 방법으로 구하였다. 이 때 궤도의 이심률이 작은 경우에 섭동방정식에서 발생하는 특이점은 Taff(1985)가 제시한 방법중 궤도요소 e, $\omega$, M을 $e_s$=$esin\omega$, $e_c=e\;cos\;\omega$, $\ell=\omega+M$으로 치환하는 방법을 사용하여 제거시켰다. Walter(1967)의 방법을 이용하여 기상위성 NOAA-10호의 평균궤도요소를 결정하였고 이를 NASA의 Brouwer 평균 궤도요소와 비교하였다. 평균 궤도요소 a, i, $\Omega$는 TBUS의 결과와 거의 일치하나 평균 궤도요소 e, $\omega$, M은 약간의 차이를 보였다. 그리고 특이점을 제거하기 위한 Taff의 방법 중 e, $\omega$, M 대신에 $e_s=e\;sin(\Omega+\omega)$, $e_c=e\;cos(\Omega+\omega)$, $L=\Omega+\omega+M$으로 치환하는 방법이 극궤도위성에는 부적합한 것으로 나타났다.

• 천문학회지
• /
• 제33권2호
• /
• pp.111-121
• /
• 2000

Many models of globular cluster formation assume the presence of cold dense clouds in early universe. Here we re-examine the Fall & Rees (1985) model for formation of proto-globular cluster clouds (PGCCs) via thermal instabilities in a protogalactic halo. We first argue, based on the previous study of two-dimensional numerical simulations of thermally unstable clouds in a stratified halo of galaxy clusters by Real et al. (1991), that under the protogalactic environments only nonlinear (${\delta}{\ge}1$) density inhomogeneities can condense into PGCCs without being disrupted by the buoyancy-driven dynamical instabilities. We then carry out numerical simulations of the collapse of overdense douds in one-dimensional spherical geometry, including self-gravity and radiative cooling down to T = $10^4$ K. Since imprinting of Jeans mass at $10^4$ K is essential to this model, here we focus on the cases where external UV background radiation prevents the formation of $H_2$ molecules and so prevent the cloud from cooling below $10^4$ K. The quantitative results from these simulations can be summarized as follows: 1) Perturbations smaller than $M_{min}\~(10^{5.6}\;M{\bigodot})(nh/0.05cm^{-3})^{-2}$ cool isobarically, where nh is the unperturbed halo density, while perturbations larger than $M_{min}\~(10^8\;M{\bigodot})(nh/0.05cm^{-3})^{-2}$ cool isochorically and thermal instabilities do not operate. On the other hand, intermediate size perturbations ($M_{min} < M_{pgcc} < M_{max}$) are compressed supersonically, accompanied by strong accretion shocks. 2) For supersonically collapsing clouds, the density compression factor after they cool to $T_c = 10^4$ K range $10^{2.5} - 10^6$, while the isobaric compression factor is only $10^{2.5}$. 3) Isobarically collapsed clouds ($M < M_{min}$) are too small to be gravitationally bound. For supersonically collapsing clouds, however, the Jeans mass can be reduced to as small as $10^{5.5}\;M_{\bigodot}(nh/0.05cm^{-3})^{-1/2}$ at the maximum compression owing to the increased density compression. 4) The density profile of simulated PGCCs can be approximated by a constant core with a halo of $p{\infty} r^{-2}$ rather than a singular isothermal sphere.

• 제어로봇시스템학회논문지
• /
• 제8권7호
• /
• pp.539-546
• /
• 2002

This paper presents a new direct seek control scheme that provides fast data access capability and robust performance for high-speed rotational optical disk drives (ODD). When a disk is rotating at a high speed to obtain fast data transfer in ODD, the magnitude and frequency of velocity disturbance caused by eccentric rotation of the disk increase in proportion to the rotational speed of the disk. Such disturbances make it almost impossible for the conventional seek control scheme to achieve stable and satisfactory seek performance. We analyze the problems that may arise when the conventional seek control scheme is applied to the high-speed rotational ODD and propose a new direct seek control scheme that will solve such problems. In the proposed scheme, a seek control system is designed such that its performance is guaranteed for a set of plants with parameter perturbations. The performance of the proposed seek control scheme is shown by experiments using a high-speed rotational ODD.