• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.13 no.1
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• pp.119-127
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• 1999

In this paper, a robust direct adaptive contrdler is presented in a linear time-invariant. Continuous systems with unmodeded dynamics and bounded disturbance using a rmdified control law and the adaptive law to Compensate for the drawback of ${\sigma}$-modification algorithm. The proposed algorithm is awlied to a plant with unrmdeled dynamics represented as a singular perturbation. Boundness of all signals in overall system is guaranteed with mathematical analysis. simulation results are presented the effectiveness foc the first-order plant even in the presence of unmodelled dynamics or bounded disturbance simulatneousIy.eousIy.

• Proceedings of the KIEE Conference
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• 1984.07a
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• pp.107-110
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• 1984

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.407-412
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• 2004

This paper presents a new algorithm for the closed-loop $H_{\infty}$ composite control of singularly perturbed nonlinear systems with a exogenous disturbance, using the successive Galerkin approximation(SGA). The singularly perturbed nonlinear system is decomposed into two subsystems of a slow-time scale and a fast-time scale via singular perturbation theory, and two $H_{\infty}$ control laws are obtained to each subsystem by using the SGA method. The composite control law that consists of two $H_{\infty}$ control laws of each subsystem is designed. One of the purposes of this paper is to design the closed-loop $H_{\infty}$ composite control law for the singularly perturbed nonlinear systems via the SGA method. The other is to reduce the computational complexity when the SGA method is applied to the high order systems.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.10
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• pp.1066-1074
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• 1990

In this paper, we attempt to control induction motors with high power efficiency as well as high dynamic performance by utilizing the recently developed theories : singular perturbation technique and noninteracting feedback control. Our controller consists of three subcontrollers` a saturation current controller, a decoupling controller, and a well-known flux simulator. The decoupling controller decouples rotor speed (or motor torque) and rotor flux linearly. Our controller does not need the rotor resistance that varies widely with the machine temperature. To illuminate the practical significance of our results, we present simulation and experimental results as well as mathematical performance analysis.

• Journal of the Society of Naval Architects of Korea
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• v.45 no.5
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• pp.469-476
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• 2008

In this paper, it is shown that an input-output (I/O) feedback linearized controller can be designed rationally by utilizing the time-scale properties of heave and pitch for an underwater vehicle. It is assumed that the dynamics of the vehicle is restricted to the vertical plane. An output-feedback control is designed, which stabilizes steady cruising paths. It is shown that the vehicle dynamics with acceleration as output becomes minimum phase. The dynamics can be transformed into a reduced system through a kind of partial linearization and singular perturbation technique. The reduced system is not only minimum phase but also exactly I/O linearizable via feedback. The I/O dynamic characteristics of the heave and pitch modes can be made linear and decoupled. Furthermore it becomes independent of cruising condition such as vehicle velocity. This study may help for designing autopilot systems for underwater vehicles.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.32 no.7
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• pp.76-82
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• 2004

A method of designing a state feedback gam achieving a specified insensitivity of the closed-loop trajectory by the singularly perturbed unified system using the operators is proposed. The order of system is reduced by the singular perturbation technique by ignoring the fast mode in it. The proposed method takes care of the actual trajectory variations over the range of the singular perturbation parameter. Necessary conditions for optimality are also derived. The previous study was done in the continuous time system The present paper extends the previous study to the discrete system and the ${\delta}-operating$ system that unifies the continuous and discrete systems. Advantages of the proposed method are shown in the numerical example.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.49-65
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• 2006

A robust numerical method for a singularly perturbed second-order ordinary differential equation having two parameters with a discontinuous source term is presented in this article. Theoretical bounds are derived for the derivatives of the solution and its smooth and singular components. An appropriate piecewise uniform mesh is constructed, and classical upwind finite difference schemes are used on this mesh to obtain the discrete system of equations. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are provided to illustrate the convergence of the numerical approximations.

• Journal of the Korean Mathematical Society
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• v.51 no.4
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• pp.679-702
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• 2014

Investigation of the numerical solution of singularly perturbed turning point problems dates back to late 1970s. However, due to the presence of layers, not many high order schemes could be developed to solve such problems. On the other hand, one could think of applying the convergence acceleration technique to improve the performance of existing numerical methods. However, that itself posed some challenges. To this end, we design and analyze a novel fitted operator finite difference method (FOFDM) to solve this type of problems. Then we develop a fitted mesh finite difference method (FMFDM). Our detailed convergence analysis shows that this FMFDM is robust with respect to the singular perturbation parameter. Then we investigate the effect of Richardson extrapolation on both of these methods. We observe that, the accuracy is improved in both cases whereas the rate of convergence depends on the particular scheme being used.

• Journal of Power Electronics
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• v.13 no.5
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• pp.814-828
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• 2013

The LCL resonant inductive power transfer (IPT) system is increasingly used because of its harmonic filtering capabilities, high efficiency at light load, and unity power factor feature. However, the modeling and controller design of this system become extremely difficult because of parameter uncertainty, high-order property, and switching nonlinear property. This paper proposes a frequency and load uncertainty modeling method for the LCL resonant IPT system. By using the linear fractional transformation method, we detach the uncertain part from the system model. A robust control structure with weighting functions is introduced, and a control method using structured singular values is used to enhance the system performance of perturbation rejection and reference tracking. Analysis of the controller performance is provided. The simulation and experimental results verify the robust control method and analysis results. The control method not only guarantees system stability but also improves performance under perturbation.

• Communications of the Korean Mathematical Society
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• v.39 no.1
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• pp.149-160
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• 2024

In this paper, we give sufficient conditions for the generalized Ornstein-Uhlenbeck operators perturbed by regular potentials and inverse square potentials A_Φ,G,V,c=∆-∇Φ·∇+G·∇-V+c|x|^-2 with a suitable domain generates a quasi-contractive, positive and analytic C₀-semigroup in L^p(ℝ^N , e^-Φ(x)dx), 1 < p < ∞. The proofs are based on an L^p-weighted Hardy inequality and perturbation techniques. The results extend and improve the generation theorems established by Metoui [7] and Metoui-Mourou [8].