• Title/Summary/Keyword: Lyapunov's function

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Control Algorithm for Stabilization of Tilt Angle of Unmanned Electric Bicycle

  • Han, Sangchul;Han, Jongkil;Ham, Woonchul
    • Transactions on Control, Automation and Systems Engineering
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    • 제3권3호
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    • pp.176-180
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    • 2001
  • In this papers, we derive a simple kinematic and dynamic formulation of an unmanned electric bicycle. We also check the controllability of the stabilization problem of bicycle. We propose a new control algorithm for the self stabilization of unmanned bicycle with bounded wheel speed and steering angle by using nonlinear control based on the sliding patch and stuck phenomena which was introduced by W. Ham. We also propose a sort of optimal control strategy for steering angle and driving wheel speed that make the length of bicycle\`s path be the shortest. From the computer simulation results, we prove the validity of the proposed control algorithm.

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Robust H${\infty}$Fuzzy Control of Nonlinear Systems with Time-Varying Delay via Static Output Feedback

  • Kim, Taek-Ryong;Park, Jin-Bae;Joo, Young-Hoon
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 2005년도 ICCAS
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    • pp.1486-1491
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    • 2005
  • In this paper, a robust H${\infty}$ stabilization problem to a uncertain fuzzy systems with time-varying delay via static output feedback is investigated. The Takagi-Sugeno (T-S) fuzzy model is employed to represent uncertain nonlinear systems with time-varying delayed state, which is a continuous-time or discrete-time system. Using a single Lyapunov function, the globally asymptotic stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust H${\infty}$controllers are given in terms of linear matrix inequalities.

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Second order integral sliding mode observer and controller for a nuclear reactor

  • Surjagade, Piyush V.;Shimjith, S.R.;Tiwari, A.P.
    • Nuclear Engineering and Technology
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    • 제52권3호
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    • pp.552-559
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    • 2020
  • This paper presents an observer-based chattering free robust optimal control scheme to regulate the total power of a nuclear reactor. The non-linear model of nuclear reactor is linearized around a steady state operating point to obtain a linear model for which an optimal second order integral sliding mode controller is designed. A second order integral sliding mode observer is also designed to estimate the unmeasurable states. In order to avoid the chattering effect, the discontinuous input of both observer and controller are designed using the super-twisting algorithm. The proposed controller is realized by combining an optimal linear tracking controller with a second order integral sliding mode controller to ensure minimum control effort and robustness of the closed-loop system in the presence of uncertainties. The condition for the selection of gains of discontinuous control based on the super-twisting algorithm is derived using a strict Lyapunov function. Performance of the proposed observer based control scheme is demonstrated through non-linear simulation studies.

분기 모우드를 활용한 얇은 빔의 혼돈 역학에 관한 연구 (On the Chaotic Vibrations of Thin Beams by a Bifurcation Mode)

  • 이영섭;주재만;박철희
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 1995년도 춘계학술대회논문집; 전남대학교, 19 May 1995
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    • pp.121-128
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    • 1995
  • The results are summarized as what follows: 1) The modeling of thin beams, which is a continuous system, into a two DOF system yields satisfactory results for the chaotic vibrations. 2) The concept of "natural forcing function" derived from the eigenfunction of the bifurcation mode is very useful for the natural responses of the system. 3) Among the perturbation techniques, HBM is a good estimate for the response when the geometry of motion is known. 4) It is known that there exist periodic solutions of coupled mode response for somewhat large damping and forcing amplitude, as well as weak damping and forcing. 5) The route-to-chaos related with lateral instability in thin beams is composed of period-doubling and quasiperiodic process and finally follows discontinuous period-doubling process. 6) The chaotic vibrations are verified by using Poincare maps, FFT's, time responses, trajectories in the configuration space, and the very powerful technique Lyapunov characteristics exponents.exponents.

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정합조건이 만족되지 않는 불확실한 다변수 계통에 대한 슬라이딩 모드 제어기의 설계 (Design of sliding mode controller for uncertain multivariable systems in the absence of matching conditions)

  • 천희영;박귀태;김동식;임성준;공진수
    • 제어로봇시스템학회:학술대회논문집
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    • 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 26-27 Oct. 1990
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    • pp.439-445
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    • 1990
  • All models of dynamical systems invariably have some measure of uncertainties associated with some of their dynamics. The recent approaches to establish robustness of stabilizing feedback control against the possible uncertainties have a serious limitation, that is their applicability only to the systems that satisfy the matching conditions. Such conditions are rarely met in general applications. If a particular system satisfies the matching conditions, the addition of an actuator will destroy the satisfaction of such conditions. In this paper, we develop robust control algorithm for uncertain multivariable systems in which the matching conditions are not necessarily met. We empoly Lyapunov's second method to derive robust stabilizing controllers which guarantee asymptotic stability against prescribed uncertainties. The derivation consists of transforming the original uncertain system to controllable canonical form and constructing a constant switching surface by designing the closed-loop characteristics as a function of the uncertainties. Numerical examples are discussed as illustrations.

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시변 지연 이산 시간 비선형 시스템에 대한 정적 출력 궤환 $H\infty$ 퍼지 강인 제어기 설계 (Static Output Feedback Robust $H\infty$ Fuzzy Control of Discrete-Time Nonlinear Systems with Time-Varying Delay)

  • 김택룡;박진배;주영훈
    • 한국지능시스템학회:학술대회논문집
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    • 한국퍼지및지능시스템학회 2005년도 춘계학술대회 학술발표 논문집 제15권 제1호
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    • pp.149-152
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    • 2005
  • In this paper, a robust $H\infty$ stabilization problem to a uncertain discrete-time fuzzy systems with time-varying delay via static output feedback is investigated. The Takagi -Sugeno (T-S) fuzzy model is employed to represent an uncertain nonlinear systems with time-varying delayed state. Using a single Lyapunov function, the globally asymptotic stability and disturbance attenuation of the closed-loop fuzzy control system are discussed. Sufficient conditions for the existence of robust $H\infty$ controllers are given in terms of linear matrix inequalities.

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수직면 직선추종유도법칙 설계 (A Vertical Line Following Guidance Law Design)

  • 황익호;조성진
    • 전기학회논문지
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    • 제59권7호
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    • pp.1309-1313
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    • 2010
  • In this paper, we propose a novel guidance law for controlling an UAV(Unmanned Air-Vehicle) to follow a reference line in vertical plane. A kinematics model representing the relative motion of the UAV to the reference line is derived. And then LQR(Linear Quadratic Regulator) theory is applied to the model to derive the VLFG(Vertical Line Following Guidance) law. The resultant guidance law forms a gain-scheduling controller scheduled by a simple parameter $\sigma$ which is a function of the UAV's velocity, axial acceleration, gravity, and the slope of the reference line. Also derived is a stability condition for the $\sigma$ variation based on Lyapunov theory. Simulation results show that the proposed guidance law can be applied effectively to UAV guidance algorithm design.

단일관절 유연성 로보트 팔에 대한 비선형 관측기 (Nonlinear Observer for One-Link Flexible Robot Arm)

  • 임규만;안봉만
    • 융합신호처리학회 학술대회논문집
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    • 한국신호처리시스템학회 2003년도 하계학술대회 논문집
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    • pp.183-187
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    • 2003
  • When a flexible arm is rotated by a motor about an axis through the arm's fixed end, transverse vibration may occur. The motor torque should be controlled in such a way that the motor rotates by a specified angle, while simultaneously stabilizing vibration of the flexible arm so that it is arrested at the end of rotation. In this paper, we propose nonlinear observer for one-link flexible am. Then based on the error dynamic equation between the plant dynamic equation and the nonlinear observer dynamic equation of the flexible one-link am, Lyapunov candidate function is applied to achieve a stable deterministic nonlinear feedback controller for the regulation of joint angle.

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신경회로망을 이용한 유연성 단일 링크 로봇 매니퓰레이터의 진동제어 (Vibration Control a Flexible Single Link Robot Manipulator Using Neural Networks)

  • 탁한호;이상배
    • 한국항해학회지
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    • 제21권3호
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    • pp.55-66
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    • 1997
  • In this paper, applications of neural networks to vibration control of flexible single link robot manipulator are ocnsidered. The architecture of neural networks is a hidden layer, which is comprised of self-recurrent one. Tow neural networks are utilized in a control system ; one as an identifier is called neuro identifier and the othe ra s a controller is called neuro controller. The neural networks can be used to approximate any continuous function to any desired degree of accuracy and the weights are updated by dynamic error-backpropagation algorithm(DEA). To guarantee concegence and to get faster learning, an approach that uses adaptive learning rates is developed by introducing a Lyapunov function. When a flexible manipulator is ratated by a motor through the fixed end, transverse vibration may occur. The motor torque should be controlle dinsuch as way, that the motor is rotated by a specified angle. while simulataneously stabilizing vibration of the flexible manipulators so that it is arrested as soon as possible at the end of rotation. Accurate vibration control of lightweight manipulator during the large body motions, as well as the flexural vibrations. Therefore, dynamic models for a flexible single link manipulator is derived, and LQR controller and nerual networks controller are composed. The effectiveness of the proposed nerual networks control system is confirmed by experiments.

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부족구동 기계시스템을 위한 적분 슬라이딩 모드 제어기 설계 (Design of Integral Sliding Mode Control for Underactuated Mechanical Systems)

  • 유동상
    • 한국지능시스템학회논문지
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    • 제23권3호
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    • pp.208-213
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    • 2013
  • 부족구동시스템은 제어되어야 하는 자유도보다 더 적은 수의 구동부를 가진 시스템으로 특정질 수 있으며, 이런 시스템을 제어하기 위한 알고리즘을 찾는 문제에 대한 관심이 지속적으로 증대되고 있다. 가변구조시스템 이론을 기반으로 하는 슬라이딩 모드 제어기는 비선형 시스템을 제어하는데 있어 강건한 도구를 제공하고 있다. 본 논문에서는 부족구동시스템을 효과적으로 제어하기 위한 적분슬라이딩 함수를 이용한 슬라이딩 모드 제어기를 제안하고, Lyapunov 안정도 이론을 이용하여 점근적 안정성을 입증하였다. 제안된 제어기의 효용성을 검증하기 위해 대표적인 부족구동시스템인 아크로봇 (Acrobot)을 대상으로 시뮬레이션을 수행하였다. 아크로봇의 동적 모델은 Mathworks사의 Simscape을 이용하여 구현하였으며, 제어기 구성은 Simulink를 이용하여 구성하였다. 시뮬레이션 결과는 제안된 제어기의 유용성과 효과성을 입증하였다.