• 제목/요약/키워드: Lyapunov Theory

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Indirect Adaptive Fuzzy Observer Design

  • Yang, Jong-Kun;Hyun, Chang-Ho;Kim, Jae-Hun;Kim, Eun-Tai;Park, Mignon
    • 한국지능시스템학회논문지
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    • 제14권7호
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    • pp.927-933
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    • 2004
  • This paper proposes an alternative observation scheme, T-S fuzzy model based indirect adaptive fuzzy observer. Nonlinear systems are represented by fuzzy models since fuzzy logic systems are universal approximators. In order to estimate the unmeasurable states of a given nonlinear system, T-S fuzzy modeling method is applied to get the dynamics of an observation system. T-S fuzzy system uses the linear combination of the input state variables and the modeling applications of them to various kinds of nonlinear systems can be found. The adaptive fuzzy scheme estimates the parameters comprising the fuzzy model representing the observation system. The proposed indirect adaptive fuzzy observer based on T-S fuzzy model can cope with not only unknown states but also unknown parameters. In the process of deriving adaptive law, the Lyapunov theory and Lipchitz condition are used. To show the performance of the proposed observation method, it is applied to an inverted pendulum on a cart.

비압축성 유동장내 2차원 익형의 혼돈거동 (Chaotic Behavior of 2-Dimensional Airfoil in Incompressible Flow)

  • 정성원;이동기;이상환
    • 대한기계학회논문집
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    • 제19권2호
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    • pp.495-508
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    • 1995
  • The self-excited vibrations of airfoil is related to the classical flutter problems, and it has been studied as a system with linear stiffness and small damping. However, since the actual aircraft wing and the many mechanical elements of airfoil type have various design variables and parameters, some of these could have strong nonlinearities, and the nonlinearities could be unexpectedly strong as the parameters vary. This abrupt chaotic behavior undergoes ordered routes, and the behaviors after these routes are uncontrollable and unexpectable since it is extremely sensitive to initial conditions. In order to study the chaotic behavior of the system, three parameters are considered, i.e., free-stream velocity, elastic distance and zero-lift angle. If the chaotic parameter region can be identified from the mathematically modeled nonlinear differential equation system, the designs which avoid chaotic regions could be suggested. In this study, by using recently developed dynamically system methods, and chaotic regions on the parameter plane will be found and the safe design variables will be suggested.

신경회로망 기반의 적응제어기를 이용한 AUV의 운동 제어 (Motion Control of an AUV Using a Neural-Net Based Adaptive Controller)

  • 이계홍;이판묵;이상정
    • 한국해양공학회지
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    • 제16권1호
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    • pp.8-15
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    • 2002
  • This paper presents a neural net based nonlinear adaptive controller for an autonomous underwater vehicle (AUV). AUV's dynamics are highly nonlinear and their hydrodynamic coefficients vary with different operational conditions, so it is necessary for the high performance control system of an AUV to have the capacities of learning and adapting to the change of the AUV's dynamics. In this paper a linearly parameterized neural network is used to approximate the uncertainties of the AUV's dynamic, and the basis function vector of network is constructed according to th AUV's physical properties. A sliding mode control scheme is introduced to attenuate the effect of the neural network's reconstruction errors and the disturbances in AUV's dynamics. Using Lyapunov theory, the stability of the presented control system is guaranteed as well as the uniformly boundedness of tracking errors and neural network's weights estimation errors. Finally, numerical simulations for motion control of an AUV are performed to illustrate the effectiveness of the proposed techniques.

불확실한 비선형 시스템에 대한 강인 유한 시간 안정화 (Robust Finite-Time Stabilization for an Uncertain Nonlinear System)

  • 서상보;심형보;서진헌
    • 전자공학회논문지SC
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    • 제46권2호
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    • pp.7-14
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    • 2009
  • 본 논문에서는 불확실성을 가지는 비선형 시스템에 대한 강인 유한 시간 안정화 문제를 고려한다. 불확실성은 시변 외란 혹은 이미 알고 있는 옹골 집합에 포함된 파라미터들이다. 제안된 설계기법은 역진기법(backstepping)과 추가된 다이나믹스를 이용한 다이나믹 지수 보정법(dynamic exponent scaling)에 기반을 두고 있으며, 이로부터 다이나믹 스무스 궤환 제어기(dynamic smooth feedback controller)가 유도된다. 페루프 시스템의 유한 시간 안정과 제어기의 유한함은 각각 유한 시간 안정에 관한 리아푸노프 안정 이론과 새로운 개념인 '차수 지표자(degree indicator)'를 이용하여 증명된다.

Design of T-S Fuzzy Model based Adaptive Fuzzy Observer and Controller

  • Ahn, Chang-Hwan
    • 조명전기설비학회논문지
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    • 제23권11호
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    • pp.9-21
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    • 2009
  • This paper proposes the alternative observer and controller design scheme based on T-S fuzzy model. Nonlinear systems are represented by fuzzy models since fuzzy logic systems are universal approximators. In order to estimate the unmeasurable states of a given unknown nonlinear system, T-S fuzzy modeling method is applied to get the dynamics of an observation system. T-S fuzzy system uses the linear combination of the input state variables and the modeling applications of them to various kinds of nonlinear systems can be found. The proposed indirect adaptive fuzzy observer based on T-S fuzzy model can cope with not only unknown states but also unknown parameters. The proposed controller is based on a simple output feedback method. Therefore, it solves the singularity problem, without any additional algorithm, which occurs in the inverse dynamics based on the feedback linearization method. The adaptive fuzzy scheme estimates the parameters and the feedback gain comprising the fuzzy model representing the observation system. In the process of deriving adaptive law, the Lyapunov theory and Lipchitz condition are used. To show the performance of the proposed observer and controller, they are applied to an inverted pendulum on a cart.

Disturbance observer based adaptive sliding mode control for power tracking of PWRs

  • Hui, Jiuwu;Yuan, Jingqi
    • Nuclear Engineering and Technology
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    • 제52권11호
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    • pp.2522-2534
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    • 2020
  • It is well known that the model of nuclear reactors features natural nonlinearity, and variable parameters during power tracking operation. In this paper, a disturbance observer-based adaptive sliding mode control (DOB-ASMC) strategy is proposed for power tracking of the pressurized-water reactor (PWR) in the presence of lumped disturbances. The nuclear reactor model is firstly established based on point-reactor kinetics equations with six delayed neutron groups. Then, a new sliding mode disturbance observer is designed to estimate the lumped disturbance, and its stability is discussed. On the basis of the developed DOB, an adaptive sliding mode control scheme is proposed, which is a combination of backstepping technique and integral sliding mode control approach. In addition, an adaptive law is introduced to enhance the robustness of a PWR with disturbances. The asymptotic stability of the overall control system is verified by Lyapunov stability theory. Simulation results are provided to demonstrate that the proposed DOB-ASMC strategy has better power tracking performance than conventional sliding mode controller and PID control method as well as conventional backstepping controller.

불확실성을 가지는 전기 구동 논홀로노믹 이동 로봇의 궤적 추종을 위한 강인 적응 퍼지 백스테핑 제어 (Robust Adaptive Fuzzy Backstepping Control for Trajectory Tracking of an Electrically Driven Nonholonomic Mobile Robot with Uncertainties)

  • 신진호
    • 제어로봇시스템학회논문지
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    • 제18권10호
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    • pp.902-911
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    • 2012
  • This paper proposes a robust adaptive fuzzy backstepping control scheme for trajectory tracking of an electrically driven nonholonomic mobile robot with uncertainties and actuator dynamics. A complete model of an electrically driven nonholonomic mobile robot described in this work includes all models of the uncertain robot kinematics with a nonholonomic constraint, the uncertain robot body dynamics with uncertain frictions and unmodeled disturbances, and the uncertain actuator dynamics with disturbances. The proposed control scheme uses the backstepping control approach through a kinematic controller and a robust adaptive fuzzy velocity tracking controller. The presented control scheme has a voltage control input with an auxiliary current control input rather than a torque control input. It has two FBFNs(Fuzzy Basis Function Networks) to approximate two unknown nonlinear robot dynamic functions and a robust adaptive control input with the proposed adaptive laws to overcome the uncertainties such as parameter uncertainties and external disturbances. The proposed control scheme does not a priori require the accurate knowledge of all parameters in the robot kinematics, robot dynamics and actuator dynamics. It can also alleviate the chattering of the control input. Using the Lyapunov stability theory, the stability of the closed-loop robot control system is guaranteed. Simulation results show the validity and robustness of the proposed control scheme.

T-S Fuzzy Model Based Indirect Adaptive Fuzzy Observer Design

  • Hyun Chang-Ho;Kim You-Keun;Kim Euntai;Park Mignon
    • 대한전자공학회:학술대회논문집
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    • 대한전자공학회 2004년도 ICEIC The International Conference on Electronics Informations and Communications
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    • pp.348-353
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    • 2004
  • This paper proposes an alternative observation scheme, T-S fuzzy model based indirect adaptive fuzzy observer. Nonlinear systems arc represented by fuzzy models since fuzzy logic systems arc universal approximators. In order to estimate the unmeasurable states of a given nonlinear system, T-S fuzzy modeling method is applied to get the dynamics of an observation system. T-S fuzzy system uses the linear combination of the input state variables and the modeling applications of them to various kinds of nonlinear systems can be found. The adaptive fuzzy scheme estimates the parameters comprising the fuzzy model representing the observation system. The proposed indirect adaptive fuzzy observer based on T-S fuzzy model can cope with not only unknown states but also unknown parameters. In the process of deriving adaptive law, the Lyapunov theory and Lipchitz condition are used. To show the performance of the proposed observation method, it is applied to an inverted pendulum on a cart.

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A Study on an Adaptive Robust Fuzzy Controller with GAs for Path Tracking of a Wheeled Mobile Robot

  • Nguyen, Hoang-Giap;Kim, Won-Ho;Shin, Jin-Ho
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제10권1호
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    • pp.12-18
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    • 2010
  • This paper proposes an adaptive robust fuzzy control scheme for path tracking of a wheeled mobile robot with uncertainties. The robot dynamics including the actuator dynamics is considered in this work. The presented controller is composed of a fuzzy basis function network (FBFN) to approximate an unknown nonlinear function of the robot complete dynamics, an adaptive robust input to overcome the uncertainties, and a stabilizing control input. Genetic algorithms are employed to optimize the fuzzy rules of FBFN. The stability and the convergence of the tracking errors are guaranteed using the Lyapunov stability theory. When the controller is designed, the different parameters for two actuator models in the dynamic equation are taken into account. The proposed control scheme does not require the accurate parameter values for the actuator parameters as well as the robot parameters. The validity and robustness of the proposed control scheme are demonstrated through computer simulations.

Accurate Voltage Parameter Estimation for Grid Synchronization in Single-Phase Power Systems

  • Dai, Zhiyong;Lin, Hui;Tian, Yanjun;Yao, Wenli;Yin, Hang
    • Journal of Power Electronics
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    • 제16권3호
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    • pp.1067-1075
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    • 2016
  • This paper presents an adaptive observer-based approach to estimate voltage parameters, including frequency, amplitude, and phase angle, for single-phase power systems. In contrast to most existing estimation methods of grid voltage parameters, in this study, grid voltage is treated as a dynamic system related to an unknown grid frequency. Based on adaptive observer theory, a full-order adaptive observer is proposed to estimate voltage parameters. A Lyapunov function-based argument is employed to ensure that the proposed estimation method of voltage parameters has zero steady-state error, even when frequency varies or phase angle jumps significantly. Meanwhile, a reduced-order adaptive observer is designed as the simplified version of the proposed full-order observer. Compared with the frequency-adaptive virtual flux estimation, the proposed adaptive observers exhibit better dynamic response to track the actual grid voltage frequency, amplitude, and phase angle. Simulations and experiments have been conducted to validate the effectiveness of the proposed observers.