• Title, Summary, Keyword: Singular Perturbation

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Adaptive controller design for nonlinear systems Using Singular perturbation Method (특이섭동방식을 이용한 비선형 적응제어에 관한 연구)

  • Kim, Do-Woo;Rhee, Hyung-Chan;Yang, Hai-Won
    • Proceedings of the KIEE Conference
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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.

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Design of an improved STT missile digital autopilot with respect to sampling time (샘플링 시간에 대해 개선된 Singular Perturbation 기반 STT missile 디지털 autopilot 설계)

  • 정선태
    • 제어로봇시스템학회:학술대회논문집
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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.

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Simplified Nonlinear Control for Planar Motor based on Singular Perturbation Theory (특이섭동이론을 기반으로한 평판모터의 비선형 제어)

  • Seo, HyungDuk;Shin, Donghoon;Lee, Youngwoo;Chung, Chung Choo
    • 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.

A Singular Perturbation-Like Approach to EDFA Gain Control Based on Observer Techniques

  • Song, Seong-Ho;Chang, Dong Eui;Lee, Kwang Y.;Kim, Ho-Chan
    • Journal of Electrical Engineering and Technology
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    • v.10 no.4
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    • pp.1864-1876
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    • 2015
  • In this paper, we propose a singular perturbation-like approach to EDFA gain controller design and analysis. Considering a three-level model of EDFA, a gain controller containing a state observer and a channel add/drop estimator is designed based on a singular perturbation - like concept. The proposed design methodology is shown to be effective and advantageous not only in theoretically verifying the asymptotic stability of systems with multi-time scales such as EDFA but also in designing an asymptotic estimator for channel add/drops which does not satisfy the matching condition.

Analysis and Improvement of Time Sampling effects on Singular Perturbation based Control Systems - Its Aplication to Design of Singular Pertubation based STT Missible Digital Autopilot (특이섭동 기법 기반 제어 시스템에 대한 샘플링 영향 분석 및 개선 - 특이섭동 기법 기반 STT 미사일 디지털 자동조정장치 설계에의 적용)

  • Jeong, Seon-Tae
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.37 no.3
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    • pp.33-43
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    • 2000
  • The guarantee of the fast dynamics stability is essential for successful application of singular Perturbation technique to control systems design. Even though the fast dynamics of the control systems is rendered stable by an analog controller, the fast dynamics stability of the control systems resulted from an digital implementation of the analog controller can be impaired severely. In this paper, we first investigate the time sampling effects on singular perturbation based control systems by centering on a design example of recently developed singular perturbation based STT missile autopilot with high performance. The investigation shows that the stability margin the fast dynamics of the STT misile autopilot system decreases rapidly as the sampling interval of discretizing the analog autopilot increases. Under this analysis, we propose a composite digital controller with compensation for the decreasing stability margin of the fast dynamics due to time sampling to achieve better performance with respect to sampling time. The improved performance of the proposed composite digital controller is verified by simulation. This result shows that one needs to investigate time sampling effects in the digital implementation of singular perturbation based controllder, and then can have benefit from the investigation.

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A FIFTH ORDER NUMERICAL METHOD FOR SINGULAR PERTURBATION PROBLEMS

  • Chakravarthy, P. Pramod;Phaneendra, K.;Reddy, Y.N.
    • 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.

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Robust Deterministic Control of Singularly Perturbed Uncertain Systems (특이섭동 불확실시스템의 견실확정제어)

  • 강철구
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.18 no.6
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    • pp.1542-1550
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    • 1994
  • For a class of singularly perturbed uncertain system, an output feedback control law is designed. The controller structure is designed based on the uncertain reduced-order system, and the controller parameters are determined by information on the reduced-order and full-order systems. It has been shown that the reduces-order system with the designed controller possesses a stability property(specifically, a global uniform attractivity). Furthermore, the stability property of this control scheme is robust with respect to singular perturbation ; i.e., the full-order system, subject to the same controller, possesses the global uniform attractivity, provided the singular perturbation parameter $\mu<\mu^{*}$, where a threshold value $\mu^{*}$ can be computed from the information available on the full-order system.

Optimal control of a flexible robot arm using singular perturbation model (유연 링크 로봇의 특이섭동모델 최적제어)

  • Han, Ki-Bong;Lee, Shi-Bok
    • 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.

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A Singular Perturbation-like Method to Compensate the Effect of Fin Actuator Dynamics in Nonlinear Missile Control (비선형 미사일 제어에서의 핀 구동기 동역학 영향을 보상하는 새로운 유사특이섭동기법)

  • Hong, Jin-Woo;Yeom, Joon-Hyung;Song, Seong-Ho;Ha, In-Joong
    • Proceedings of the KIEE Conference
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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.

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Robust ℋ Sampled-Data Control for Takagi-Sugeno Fuzzy Model with Singular Perturbation (특이섭동 타카기-수게노 퍼지모델의 강인 ℋ 샘플치 제어)

  • Kang, Hyoung Bin;Moon, Ji Hyun;Lee, Ho Jae
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.65 no.9
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    • pp.1524-1530
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    • 2016
  • This paper deals with a robust $H_{\infty}$ sampled-data controller design problem for nonlinear systems in Takagi-Sugeno fuzzy form with singular perturbation. The employed controller takes a state-feedback form. The design condition is represented in terms of linear matrix inequalities. A numerical examples is included to show the effectiveness of the theoretical development.