• Title/Summary/Keyword: Lyapunov approach

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A new approach to robustness bounds using lyapunov stability concept

  • Jo, Jang-Hyen
    • 제어로봇시스템학회:학술대회논문집
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    • 1994.10a
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    • pp.543-547
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    • 1994
  • In this paper, the new approach and technique are introduced and derived from the original Lyapunov direct method which is used to decide the stability of system conveniently. This proposed technique modifies the formal concepts of the sufficient conditions of Lyapunov stability and is able to generate the methods for the robust design of control systems. Also, it applies to the dynamic systems with bounded perturbations and the results of the computer program using the new concept are compared with those of previous research papers and conventional Lyapunov direct method. It is possible to recognize the practical improvements of the estimation of robustness bounds of the systems.

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Control and Tracking Chaotic Liu Systems via Backstepping Design (백스테핑을 이용한 카오스 Liu 시스템의 제어)

  • Yoo, Sung-Hoon;Hyun, Chang-Ho;Park, Mig-Non
    • Proceedings of the KIEE Conference
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    • 2006.10c
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    • pp.324-326
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    • 2006
  • This paper present backstepping control approach for controling chaotic Liu system. The proposed method is a systematic design approach and consists in a recursive procedure that interlaces the choice of a Lyapunov Function. Based on Lyapunov stability theory, control laws are derived. We used the same technique to enable stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory to be achieved in a systematic way. Numerical solution are shown to verify the result.

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Robust control using the sliding mode observer in the presence of unmatched uncertainties (비정합조건 하의 슬라이딩 모드 관측기를 이용한 강인 제어)

  • 한상철;박인규;함운철
    • 제어로봇시스템학회:학술대회논문집
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    • 2000.10a
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    • pp.334-334
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    • 2000
  • In this paper, sliding mode observer design principles based on the equivalent control approach are discussed for the systems which may not satisfy the matching conditions. We propose a new approach for designing a sliding observer and the proof of the stability of the state reconstruction error system for time-invariant systems using the Lyapunov method. The reaching time to the sliding surface, the sliding dynamics of the system, the stability of the reconstruction error system via Lyapunov method, sufficient conditions for the existence of the sliding mode are studied.

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Control of Variable Reluctance Motors: A Comparison between Classical and Lyapunov-Based Fuzzy Schemes

  • Filizadeh, S.;Safavian, L.S.;Emadi, A.
    • Journal of Power Electronics
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    • v.2 no.4
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    • pp.305-311
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    • 2002
  • In this paper, two approaches for designing tracking controllers for a variable reluctance motor (VRM), namely the Lyapunov-based fuzzy approach and the classical approach, are compared. The nonlinear model of a VRM is first addressed. The two control schemes are introduced afterwards, and then applied to obtain tracking controllers. Simulation results of a sample case, to which the methods are applied, are also presented. Comparison of the methods based on the results obtained concludes the paper.

Three-axis Attitude Control for Flexible Spacecraft by Lyapunov Approach under Gravity Potential

  • Bang, Hyo-Choong;Lee, Kwang-Hyun;Lim, Hyung-Chul
    • International Journal of Aeronautical and Space Sciences
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    • v.4 no.1
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    • pp.99-109
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    • 2003
  • Attitude control law synthesis for the three-axis attitude maneuver of a flexible spacecraft model is presented in this study. The basic idea is motivated by previous works for the extension into a more general case. The new case includes gravitational gradient torque which has significant effect on a wide range of low earth orbit missions. As the first step, the fully nonlinear dynamic equations of motion are derived including gravitational gradient. The control law design based upon the Lyapunov approach is attempted. The Lyapunov function consists of a weighted combination of system kinetic and potential energy. Then, a set of stabilizing control law is derived from the basic Lyapunov stability theory. The new control law is therefore in a general form partially validating the previous work in some sense.

Robust control for mismatched uncertain system (불일치 시스템의 견실제어기 설계)

  • 김동환
    • 제어로봇시스템학회:학술대회논문집
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    • 1997.10a
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    • pp.117-119
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    • 1997
  • We consider the control design for nonlinear uncertain systems. The uncertainty is mismatched and possibly fast time-varying. Within the suitable range of the uncertainty the control is valid. No statistical information on uncertainty is imposed. Only the possible bound of the uncertain parameter is known and the control design is based on Lyapunov approach.

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A V-Shaped Lyapunov Function Approach to Model-Based Control of Flexible-Joint Robots

  • Lee, Ho-Hoon;Park, Seung-Gap
    • Journal of Mechanical Science and Technology
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    • v.14 no.11
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    • pp.1225-1231
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    • 2000
  • This paper proposes a V-shaped Lyapunov function approach for the model-based control of flexible-joint robots, in which a new model-based nonlinear control scheme is designed based on a V-shaped Lyapunov function. The proposed control guarantees global asymptotic stability for link trajectory control while keeping all internal signals bounded. Since joint flexibility is used as a control parameter, the proposed control is not restricted by the degree of joint flexibility and be applied to flexibility-joint, partly-flexibility, or rigid-joint robots without modification. the effectiveness of the proposed control has been by computer simulation.

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Derivation of a Group of Lyapunov Functions reflecting Damping Effects and its Application

  • Moon, Young-Hyun;Park, Byoung-Kon;Cho, Byoung-Hoon;Roh, Tae-Hoon
    • Journal of Electrical Engineering and information Science
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    • v.3 no.3
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    • pp.322-329
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    • 1998
  • Stability analysis of nonlinear systems is mostly based on the Lyapunov stability theory. The well-known Lyapunov function method provides precise and rigorous theoretical backgrounds. However, the conventional approach to direct stability analysis has been performed without taking account of damping effects, which is pointed as a minor but crucial drawback. For accurate has been performed without taking account of damping effects, which is pointed as a minor but crucial drawback. For accurate stability analysis of nonlinear systems, it is required to take the damping effects into account. This paper presents a new method to derive a group of Lyapunov functions to reflect the damping effects by considering the integral relationships of the system governing equations. A systematical approach is developed to convert a part of damping loss into some appropriate system energy terms. Examples show that the proposed method remarkably improves the estimation of the region of attraction compared considering damping effects. The proposed method can be utilized as a useful tol to determine the region of attraction.

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The Stable Adaptive Converter Control Method of Photovoltaic Power Systems using Lyapunov Redesign Approach (Lyapunov Redesign 기법을 이용한 태양광 발전 시스템의 안정한 적응형 컨버터 제어기법)

  • Cho, Hyun-Cheol;Park, Ji-Ho;Kim, Dong-Wan
    • The Transactions of the Korean Institute of Electrical Engineers P
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    • v.61 no.4
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    • pp.161-167
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    • 2012
  • Energy conversion systems such as power inverters and converters are basically significant in establishing photovoltaic power systems to enhance power effectiveness. This paper proposes a new converter control method by using the Lyapunov redesign approach. We construct the proposed control mechanism linearly composed of nominal control and auxiliary control laws. The former is generally designed through a well-known power electronic technology and the latter is implemented to compensate real-time control error due to uncertain natures of converter systems in practice. For realizing adaptive control capability in the proposed control mechanism, a control parameter vector is estimated by utilizing a steepest descent based optimization method. We carry out numerical simulation with Matlab(c) software to demonstrate reliability of the proposed converter control system and conduct a comparative study to prove its superiority by comparing with a generic converter control methodology.

Design of Lyapunov Theory based State Feedback Controller for Time-Delay Systems (시간지연 시스템을 위한 리아푸노브 이론 기반 상태 피드백 제어기 설계)

  • Cho, Hyun Cheol;Shin, Chan Bai
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.62 no.1
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    • pp.95-100
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    • 2013
  • This paper presents a new state feedback control approach for communication networks based control systems in which control input and output observation time-delay natures are generally occurred in practice. We first establish a generic state feedback control framework based on well-known linear system theory. A maximum time-delay value which allows critical stability of whole control system are defined to make a positive definite Lyapunov function which is mathematically composed of controlled system states. We analytically derive its control parameters by using a steepest descent optimization method in order to guarantee a stability condition through Lyapunov theory. Computer simulation is numerically carried out for demonstrating reliability of the proposed NCS algorithm and a comparative study is accomplished to prove its superiority for which the traditional control approach for NCS is made use of under same simulation scenarios.