• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.2
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• pp.289-296
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• 2015

In this paper, we propose the nonlinear control based on singular perturbation theory for position tracking and yaw regulation of planar motor. Singular perturbation theory is characterized by the existence of slow and fast transients in the system dynamics. The proposed method consists of auxiliary control to decouple error dynamics. We develop model reduction with control input. Also, we derIve decoupled error dynamics with auxiliary input. The controller is designed in order to guarantee the desired position and yaw regulation without current feedback or estimation. Simulation results validate the effect of proposed method.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.1
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• pp.20-27
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• 1987

The hierarchical approach method is proposed to sperate each different time scale sub-systems from linear time invariant multi-parameter singular perturbation systems. By means of this proposal, the original multi-parameter singular perturbation systems is completely separated into independent subsystems with each different time scale. It is also investigated that the controllability of the system is invariant. And this paper applies singular perturbation methods to the minimum control effort problem for linear time invariant systems with constrained controls. Also near-optimum control theory, which is based on dividing the total time interval with the time scales respectively, is proposed. As a result, the time scale separation method is show to be particularly useful in a near optimum design which can be otained through a decentralized control structure.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.468-471
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• 1997

In this paper, we investigate the time-sampling effects on the digital implementation of singular perturbation based STT autopilot with excellent performance and propose a compensation method for the time-sampling effects. In digitization of analog STT autopilot, it is found that the stability margin of the fast dynamics is mostly affected to lead to rapid decrease. Under the this analysis, a composite digital controller with additional compensator for fast dynamics is proposed to improve the time-sampling effect and a simulation verifies the result.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.689-706
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• 2008

In this paper, a fifth order numerical method is presented for solving singularly perturbed two point boundary value problems with a boundary layer at one end point. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two point boundary value problem is obtained from the theory of singular perturbations. It is used in the fifth order compact difference scheme to get a two term recurrence relation and is solved. Several linear and non-linear singular perturbation problems have been solved and the numerical results are presented to support the theory. It is observed that the present method approximates the exact solution very well.

• 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 KIEE Conference
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• 2006.04a
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• pp.219-221
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• 2006

The recently developed autopilot controller can make the input-output (I/O) dynamic characteristics of the nonlinear missile dynamics linear and independent of flight conditions. However, significant fin actuator dynamics can degenerate the I/O dynamic performance of the overall system. In this paper, we propose a singular perturbation-like method to compensate the effect of significant fin actuator dynamics in nonlinear missile control. The proposed compensation method does not require the time derivatives of fin angles but can maintain the linear I/O dynamic characteristics provided by the recently developed autopilot controller.

• 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.

• 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.

• 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.

• 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.