• Journal of the Korean Society for Precision Engineering
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• v.13 no.1
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• pp.62-68
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• 1996

Linear controllers, such as LQG/LTR controller, have been investigated to control flexible link manipulators. The performance and complexity of these depend largely on the linearized model upon which the controller is designed. In this study, singular perturbation model is tested in designing a LQG/LTR controller for a flexible link manipulator. The order of the resulting controller is much lower than the one based on a full model. Through numerical study, it is shown that the performance of the proposed controller reaches reasonably to the one based on the full model.

• Proceedings of the KIEE Conference
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• 1997.07b
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• pp.685-688
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• 1997

In this paper, we introduce a new adaptive controller for induction motor based on singular perturbation theory. The design of 5th induction motor was changed for the 3rd modeling using the singular perturbation method. The resulting boundary layer and quasi-steady-state systems are made exponentially stable. Therefore the statements of Tychonov's theorm are valid for an infinite time interval for induction motor, too.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.54 no.6
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• pp.359-365
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• 2005

This paper presents an reduced-order near-optimal controller for the congestion control of Available Bit Rate (ABR) service in Asynchronous Transfer Mode (ATM) networks. We introduce the model, of a class of ABR traffic, that can be controlled using a Explicit Rate feedback for congestion control in ATM networks. Since there are great computational complexities in the class of optimal control problem for the ABR model, the near-optimal controller via reduced-order technique is applied to this model. It is implemented by the help of weakly coupling and singular perturbation theory, and we use bilinear transformation because of its computational convenience. Since the bilinear transformation can convert discrete Riccati equation into continuous Riccati equation, the design problems of optimal congestion control can be reduced. Using weakly coupling and singular perturbation theory, the computation time of Riccati equations can be saved, moreover the real-time congestion control for ATM networks can be possible.

• Journal of Power Electronics
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• v.17 no.4
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• pp.953-962
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• 2017

Momentum flywheels are widely applied for the generation of small and precise torque for the attitude control and inertial stabilization of satellites and space stations. Due to its inherited system nonlinearity, the tracking performance of the flywheel torque/speed in dynamic/plug braking operations is limited when a conventional controller is employed. To take advantage of the well-separated two-time-scale quantities of a flywheel driving system, the singular perturbation technique is adopted to improve the torque tracking performance. In addition, the composite control law, which combines slow- and fast- dynamic portions, is derived for flywheel driving systems. Furthermore, a novel control strategy for plug braking dynamics, which considers couplings between the Buck converter and the three-phase inverter load, is designed with easy implementation. Finally, experimental results are presented to demonstrate the correctness of the analysis and the superiority of the proposed methods.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.165-177
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• 2013

In this paper, we apply Homotopy perturbation transform method (HPTM) for solving singular fourth order parabolic partial differential equations with variable coefficients. This method is the combination of the Laplace transform method and Homotopy perturbation method. The nonlinear terms can be easily handled by the use of He's polynomials. The aim of using the Laplace transform is to overcome the deficiency that is mainly caused by unsatisfied conditions in other semi-analytical methods such as Homotopy perturbation method (HPM), Variational iteration method (VIM) and Adomain Decomposition method (ADM). The proposed scheme finds the solutions without any discretization or restrictive assumptions and avoids the round-off errors. The comparison shows a precise agreement between the results and introduces this method as an applicable one which it needs fewer computations and is much easier and more convenient than others, so it can be widely used in engineering too.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• v.1
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• pp.133-138
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• 2006

Singular value decomposition (SDV) approach is applied to the observability analysis of GPS/INS in this paper. A measure of observability for a subspace is introduced. It indicates the minimum size of perturbation in the information matrix that makes the subspace unobservable. It is shown that the measure has direct connections with observability of systems, error covariance, and singular structure of the information matrix. The observability measure given in this paper is applicable to the multi-input/multi-output time-varying systems. An example on the observability analysis of GPS/INS is given. The measure of observability is confirmed to be less sensitive to system model perturbation. It is also shown that the estimation error for the vertical component of gyro bias can be considered unobservable for small initial error covariance for a constant velocity horizontal motion.

• Communications for Statistical Applications and Methods
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• v.23 no.1
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• pp.21-32
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• 2016

We study asymptotic expansion formulae for numerical computation of Greeks (i.e. sensitivity) in finance. Our approach is based on the integration-by-parts formula of the Malliavin calculus. We propose asymptotic expansion of Greeks for a stochastic volatility model using the Greeks formula of the Black-Scholes model. A singular perturbation method is applied to derive asymptotic Greeks formulae. We also provide numerical simulation of our method and compare it to the Monte Carlo finite difference approach.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.7-11
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• 1991

The adaptive control of flexible joint manipulator is the focus of this paper. The full order flexible joint manipulator dynamic system does not allow the determination of a feedback linearization control as for rigid manipulators. This drawback is overcome by a model order reduction based on a singular perturbation strategy. The full order flexible joint manipulator dynamic model is adopted for derivation of the adaptive control law to damp out the elastic oscillations at the joints. It is shown that the joint position error will converge to zero asymptotically and that other signals remain bounded without precise knowledge of parameters of the manipulator and its joint flexibility.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.317-329
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• 2006

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1279-1292
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• 2009

In this paper, a numerical method that uses standard finite difference scheme defined on Shishkin mesh for a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a discontinuous source term is presented. An error estimate is derived to show that the method is uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented to illustrate the theoretical results.