• Title/Summary/Keyword: Theorem Lyapunov

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Robust Adaptive Control for Nonlinear Systems Using Nonlinear Disturbance Observer (외란 관측기를 이용한 비선형 시스템의 강인 적응제어)

  • Hwang, Young-Ho;Han, Byung-Jo;Kim, Hong-Pil;Yang, Hai-Won
    • Proceedings of the KIEE Conference
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    • 2006.10c
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    • pp.327-329
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    • 2006
  • A controller is proposed for the robust adaptive backstepping control of a class of uncertain nonlinear systems using nonlinear disturbance observer (NDO). The NDO is applied to estimate the time-varying lumped disturbance in each step, but a disturbance observer error does not converge to zero since the derivative of lumped disturbance is not zero. Then the fuzzy neural network (FNN) is presented to estimate the disturbance observer error such that the outputs of the system are proved to converge to a small neighborhood of the desired trajectory. The proposed control scheme guarantees that all the signals in the closed-loop are semiglobally uniformly ultimately bounded on the basis of the Lyapunov theorem. Simulation results are presented to illustrate the effectiveness and the applicability of the approaches proposed.

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Stability and a scheduling method for network-based control systems (네트워크를 이용한 제어 시스템의 안정도 및 스케줄링에 관한 연구)

  • 김용호;권욱현;박홍성
    • 제어로봇시스템학회:학술대회논문집
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    • 1996.10b
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    • pp.1432-1435
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    • 1996
  • This paper obtains maximum allowable delay bounds for stability of network-based control systems and presents a network scheduling method which makes the network-induced delay be less than the maximum allowable delay bound. The maximum allowable delay bounds are obtained using the Lyapunov theorem. Using the network scheduling method, the bandwidth of a network can be allocated to each node and the sampling period of each sensor and controller can be determined. The presented method can handle three kinds of data (periodic, real-time asynchronous, and non real-time asynchronous data) and guarantee real-time transmissions of real-time synchronous data and periodic data, and possible transmissions of non real-time asynchronous data. The proposed method is shown to be useful by examples in two types of network protocols such as the token control and the central control.

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Sliding Mode Control of 5-link Biped Robot Using Wavelet Neural Network

  • Kim, Chul-Ha;Yu, Sung-Jin;Park, Jin-Bae;Choi, Yoon-Ho
    • 제어로봇시스템학회:학술대회논문집
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    • 2005.06a
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    • pp.2279-2284
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    • 2005
  • Generally, biped walking is difficult to control because it is a nonlinear system with various uncertainties. In this paper, we design a robust control system based on sliding-mode control (SMC) of 5-link biped robot using the wavelet neural network(WNN), in order to improve the efficiency of position tracking performance of biped locomotion. In our control system, the WNN is utilized to estimate uncertain and nonlinear system parameters, where the weights of WNN are trained by adaptive laws that are induced from the Lyapunov stability theorem. Finally, the effectiveness of the proposed control system is verified by computer simulations.

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Intelligent Gain and Boundary Layer Based Sliding Mode Control for Robotic Systems with Unknown Uncertainties

  • Yoo, Sung-Jin;Park, Jin-Bae;Choi, Yoon-Ho
    • 제어로봇시스템학회:학술대회논문집
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    • 2005.06a
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    • pp.2319-2324
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    • 2005
  • This paper proposes a intelligent gain and boundary layer based sliding mode control (SMC) method for robotic systems with unknown model uncertainties. For intelligent gain and boundary layer, we employ the self recurrent wavelet neural network (SRWNN) which has the properties such as a simple structure and fast convergence. In our control structure, the SRWNNs are used for estimating the width of boundary layer, uncertainty bound, and nonlinear terms of robotic systems. The adaptation laws for all parameters of SRWNNs and reconstruction error bounds are derived from the Lyapunov stability theorem, which are used for an on-line control of robotic systems with unknown uncertainties. Accordingly, the proposed method can overcome the chattering phenomena in the control effort and has the robustness regardless of unknown uncertainties. Finally, simulation results for the three-link manipulator, one of the robotic systems, are included to illustrate the effectiveness of the proposed method.

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Self-Recurrent Wavelet Neural Network Based Adaptive Backstepping Control for Steering Control of an Autonomous Underwater Vehicle (수중 자율 운동체의 방향 제어를 위한 자기회귀 웨이블릿 신경회로망 기반 적응 백스테핑 제어)

  • Seo, Kyoung-Cheol;Yoo, Sung-Jin;Park, Jin-Bae;Choi, Yoon-Ho
    • Journal of Institute of Control, Robotics and Systems
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    • v.13 no.5
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    • pp.406-413
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    • 2007
  • This paper proposes a self-recurrent wavelet neural network(SRWNN) based adaptive backstepping control technique for the robust steering control of autonomous underwater vehicles(AUVs) with unknown model uncertainties and external disturbance. The SRWNN, which has the properties such as fast convergence and simple structure, is used as the uncertainty observer of the steering model of AUV. The adaptation laws for the weights of SRWNN and reconstruction error compensator are induced from the Lyapunov stability theorem, which are used for the on-line control of AUV. Finally, simulation results for steering control of an AUV with unknown model uncertainties and external disturbance are included to illustrate the effectiveness of the proposed method.

A Novel Robust Adaptive Control Algorithm for Systems with Unknown Disturbances (미지의 외란을 가지는 시스템의 새로운 형태의 적응 제어 알고리즘)

  • Koo, Keun-Mo;Jeon, Jeong-Yeol;Kim, Jong-Hwan
    • Proceedings of the KIEE Conference
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    • 1992.07a
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    • pp.371-373
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    • 1992
  • This note proposes a novel robust adaptive control algorithm for systems with unknown disturbances by introducing an additional term in the control input. This additional term is easily implementable by estimating the upper bound of the unknown disturbances. By this term, the output error can be made to be uniformly ultimately bounded in a desired region via Lyapunov second stability theorem when the relative degree of system is one.

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Chattering-Free Sliding Mode Control with a Time-Varying Sliding Surface

  • Kyung, Tai-Hyun;Kim, Jong-Shik;Lee, Kyu-Joon
    • 제어로봇시스템학회:학술대회논문집
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    • 2001.10a
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    • pp.151.4-151
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    • 2001
  • Chattering-free sliding mode control is derived from the reaching law method and Lyapunov stability theorem. Its control input Is composed of continuous term and discontinuous term. By the combination of these terms, the robustness and tracking performance can be improved and the chattering can be avoided. But in the reaching mode, the sliding mode control is sensitive to the modeling uncertainties, parameter variations and disturbances, also it needs a large control input. These result in poor transient responses. In this paper, to overcome these problems in the reaching mode, a time-varying sliding surface is proposed. And it is applied to a 2-link SCARA robot manipulator, experimental results show that the transient response is improved and its ...

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Robust Adaptive Control of A HexaSlide Type Parallel Manipulator

  • Kim, Jong-Phil;Kim, Sung-Gaun;Ryu, Jeha
    • Transactions on Control, Automation and Systems Engineering
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    • v.3 no.4
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    • pp.262-267
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    • 2001
  • Jeha Ryu Department of Mechatronics, Kwangju Institute of Science and Technology This paper presents an application of a robust adaptive control strategy to HexaSlide type six degrees-of-freedom parallel manipulators. The HexaSlide type parallel manipulators are characterized as an architecture with constant link lengths that are attached to moving sliders on the ground and to a mobile platform. The proposed control law is developed based on a simplified second order system dynamic equation in joint space with uncertain mass, damper, spring, and Coulomb friction terms. These uncertain parameters are updated by an adaptation law that is derived by Lyapunov stability theorem. A robust adaptive control law by using the boundary layer is designed for the purpose of compensating for the neglected dynamic effects of the mobile platform and the six moving links that are modeled as a disturbance term. Experimental results show good and fast tracking performance.

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Position Control of Ball-Screw Systems with Compensation of Estimated Coulomb Friction (추정된 쿨롱 마찰을 보상한 볼-스크류 시스템의 위치제어)

  • Kim, Han-Me;Choi, Jeong-Ju;Lee, Young-Jin;Kim, Jong-Shik
    • Proceedings of the KSME Conference
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    • 2003.04a
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    • pp.893-898
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    • 2003
  • Coulomb friction is an important factor for precise position tracking control systems. The control systems with friction causes the steady state error because of being sensitive to the change of system condition and highly nonlinear characteristics. To overcome these problems, we use an estimation scheme of Coulomb friction to experiment for it's compensating. The estimated factor for Coulomb friction is used as a feed-forward compensator to improve the tracking performance of ball-screw systems. The tracking performance was improved by compensating the estimated friction torque in the feed-forward term. And, the sliding mode control which is derived from the Lyapunov stability theorem is applied for robust stability and reducing chattering. The experimental results show that the sliding mode controller with adaptive friction compensator has a good tracking performance compared with the friction uncompensated controller.

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PRACTICAL ${\phi}_0$-STABILITY FOR IMPULSIVE DYNAMIC SYSTEMS WITH TIME SCALES AND INITIAL TIME DIFFERENCE

  • Chen, Weisong;Han, Zhenlai;Sun, Shurong;Li, Tongxing
    • Journal of applied mathematics & informatics
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    • v.29 no.3_4
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    • pp.891-900
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    • 2011
  • In this paper, we study the impulsive dynamic systems on time scales with initial time difference. By employing cone-valued Lyapunov functions, some comparison theorems and several practical ${\phi}_0$-stability criteria for impulsive system on time scales with initial time difference are obtained.