• Title/Summary/Keyword: Singular perturbation theory

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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 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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Multi-Time Scale Separations and Optimal Control Problems of Multi-Parameter Singular Perturbation Systems (여러 매개상수 특이접동계에서의 여러 시간스케일 분리와 최적제어 문제)

  • Kim, Sam-Soo;Hong, Jae-Keun;Kim, Soo-Joong
    • 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.

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Design of Optimal Controller for the Congestion in ATM Networks (ATM망의 체증을 해결하기 위한 최적 제어기 설계)

  • Jung Woo-Chae;Kim Young-Joong;Lim Myo-Taeg
    • 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.

NUMERICAL METHOD FOR SINGULAR PERTURBATION PROBLEMS ARISING IN CHEMICAL REACTOR THEORY

  • Andargie, Awoke
    • Journal of applied mathematics & informatics
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    • v.28 no.1_2
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    • pp.411-423
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    • 2010
  • In this paper, a numerical method for singular perturbation problems arising in chemical reactor theory for general singularly perturbed two point boundary value problems with boundary layer at one end(left or right) of the underlying interval is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

Adaptive control of flexible joint manipulators based on the singular perturbation theory (특이 섭동 이론에 의한 유연성 관절 매니퓰레이터의 적응제어)

  • 김응석;양해원
    • 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.

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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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    • 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.

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Precise Braking Torque Control for Momentum Flywheels Based on a Singular Perturbation Analysis

  • Zhou, Xinxiu;Su, Dan
    • 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.

Robust Output Regulator with Frequency Adaptation Algorithm for Optical Disc Drives (광디스크를 위한 주파수 적응 알고리즘과 함께하는 강인 출력 제어기)

  • Kim, Sang-Hyun;Kim, Hyung-Jong;Shim, Hyung-Bo
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.48 no.4
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    • pp.17-24
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    • 2011
  • This paper presents a control scheme to cancel periodic disturbance with unknown frequency for optical disc drives. The control scheme consists of an output regulator and a frequency adaptive algorithm. Here, the frequency adaptive algorithm based on IMP plays a role in obtaining a frequency of periodic disturbance. The stability analysis of whole system and disturbance rejection performance are proven by the singular perturbation theory. The contribution of this paper are as follows. (1) There is no design constraints of the frequency range. (2) Ability for perfect disturbance rejection is preserved even with uncertain plant model.

Anti-Reset windup basd compensation method for state constrained control systems (리셋 와인드엎 방지법에 기초한 상태 제한이 존재하는 제어 시스템의 보상 방법)

  • Park, Jong-Koo
    • Journal of Institute of Control, Robotics and Systems
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    • v.5 no.5
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    • pp.511-520
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    • 1999
  • An anti-reset windup (ARW) based compensation method for state constrained control systems is studied. First, a linear controller is constructed to give a desirable nominal performance ignoring state-constraints of a plant. Then, an additional compensator is introduced to provide smooth performance degradation under state-constraints of the plant. This paper focuses on the effective design method of the additional compensator. By minimizing a reasonable performance index, the proposed compensator is expressed in terms of theplant and ocntroller parameters. The resulting dynamics of the compensated controller exhibits the dominant part of the linear closed-loop system which can be seen from the singular perturbation model reducton theory. THe proposed method guarantees total stability of overall resulting systems if linear controllers were constructed to meet certain condition.

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