• Title/Summary/Keyword: Lyapunov Stability Theorem

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Hybrid Sliding Mode Control of 5-link Biped Robot in Single Support Phase Using a Wavelet Neural Network (웨이블릿 신경망을 이용한 한발지지상태에서의 5 링크 이족 로봇의 하이브리드 슬라이딩 모드 제어)

  • Kim, Chul-Ha;Yoo, Sung-Jin;Choi, Yoon-Ho;Park, Jin-Bae
    • Journal of Institute of Control, Robotics and Systems
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    • v.12 no.11
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    • pp.1081-1087
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    • 2006
  • Generally, biped walking is difficult to control because a biped robot is a nonlinear system with various uncertainties. In this paper, we propose a hybrid sliding-mode control method using a WNN uncertainty observer for stable walking of the 5-link biped robot with model uncertainties and the external disturbance. In our control system, the sliding mode control is used as main controller for the stable walking and a wavelet neural network(WNN) is used as an uncertainty observe. to estimate uncertainties of a biped robot model, and the error compensator is designed to compensate the reconstruction error of the WNN. The weights of WNN are trained by adaptation laws that are induced from the Lyapunov stability theorem. Finally, the effectiveness of the proposed control system is verified through computer simulations.

Robust Control of Planar Biped Robots in Single Support Phase Using Intelligent Adaptive Backstepping Technique

  • Yoo, Sung-Jin;Park, Jin-Rae;Choi, Yoon-Ho
    • International Journal of Control, Automation, and Systems
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    • v.5 no.3
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    • pp.269-282
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    • 2007
  • This paper presents a robust control method via the intelligent adaptive backstepping design technique for stable walking of nine-link biped robots with unknown model uncertainties and external disturbances. In our control structure, the self recurrent wavelet neural network(SRWNN) which has the information storage ability is used to observe the uncertainties of the biped robots. The adaptation laws for all weights of the SRWNN are induced from the Lyapunov stability theorem, which are used for on-line controlling biped robots. Also, we prove that all signals in the closed-loop adaptive system are uniformly ultimately bounded. Through computer simulations of a nine-link biped robot with model uncertainties and external disturbances, we illustrate the effectiveness of the proposed control system.

Adaptive Neural Dynamic Surface Control via $H_{\infty}$ Approach for Nonlinear Flight System (비선형 비행 시스템을 위한 $H_{\infty}$ 접근법 기반 적응 신경망 동적 표면 제어)

  • Yoo, Sung-Jin;Choi, Yoon-Ho;Park, Jin-Bae
    • Proceedings of the KIEE Conference
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    • 2007.07a
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    • pp.1728-1729
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    • 2007
  • This paper presents an adaptive neural dynamic surface control (DSC) approach with $H_{\infty}$ tracking performance for a full dynamics of a nonlinear flight system. It is assumed in this paper that model uncertainties such as structured and unstrutured uncertainties and external disturbances influence the nonlinear aircraft model. In our control system, self recurrent wavelet neural networks (SRWNNs) are used to compensate model uncertainties of the nonlinear flight system, and an adaptive DSC technique is extended for disturbance attenuation of the nonlinear flight system. From Lyapunov stability theorem, it is shown that $H_{\infty}$ performance from external disturbances can be obtained. Finally, we perform the simulation for the nonlinear six-degree-of-freedom F-16 aircraft model to confirm the effectiveness of the proposed control system.

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Observer-based Distributed Consensus Algorithm for Multi-agent Systems with Output Saturations

  • Lim, Young-Hun;Lee, Gwang-Seok
    • Journal of information and communication convergence engineering
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    • v.17 no.3
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    • pp.167-173
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    • 2019
  • This study investigates the problem of leader-following consensus for multi-agent systems with output saturations. This study assumes that the agents are described as a neutrally stable system, and the leader agent generates the bounded trajectory within the saturation level. Then, the objective of the leader-following consensus is to track the trajectory of the leader by exchanging information with neighbors. To solve this problem, we propose an observer-based distributed consensus algorithm. Then, we provide a consensus analysis by applying the Lyapunov stability theorem and LaSalle's invariance principle. The result shows that the agents achieve the leader-following consensus in a global sense. Moreover, we can achieve the consensus by choosing any positive control gain. Finally, we perform a numerical simulation to demonstrate the validity of the proposed algorithm.

Self-Recurrent Wavelet Neural Network Based Direct Adaptive Control for Stable Path Tracking of Mobile Robots

  • You, Sung-Jin;Oh, Joon-Seop;Park, Jin-Bae;Choi, Yoon-Ho
    • 제어로봇시스템학회:학술대회논문집
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    • 2004.08a
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    • pp.640-645
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    • 2004
  • This paper proposes a direct adaptive control method using self-recurrent wavelet neural network (SRWNN) for stable path tracking of mobile robots. The architecture of the SRWNN is a modified model of the wavelet neural network (WNN). Unlike the WNN, since a mother wavelet layer of the SRWNN is composed of self-feedback neurons, the SRWNN has the ability to store the past information of the wavelet. For this ability of the SRWNN, the SRWNN is used as a controller with simpler structure than the WNN in our on-line control process. The gradient-descent method with adaptive learning rates (ALR) is applied to train the parameters of the SRWNN. The ALR are derived from discrete Lyapunov stability theorem, which are used to guarantee the stable path tracking of mobile robots. Finally, through computer simulations, we demonstrate the effectiveness and stability of the proposed controller.

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A Study on Adaptive Load Torque Observer for Robust Precision Position Control of BLDC Motor (적응제어형 외란 관측기를 이요한 BLDC 전동기의 정밀위치제어에 대한 연구)

  • 고종선;윤성구
    • Proceedings of the KIPE Conference
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    • 1999.07a
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    • pp.4-9
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    • 1999
  • A new control method for precision robust position control of a brushless DC (BLDC) motor using asymptotically stable adaptive load torque observer is presented in the paper. Precision position control is obtained for the BLDC motor system approximately linearized using the field-orientation method Recently, many of these drive systems use BLDC motors to avoid backlashe. However, the disadvantages of the motor are high cost and complex control because of nonlinear characteristics. Also, the load torque disturbance directly affects the motor shaft. The application of the load torque observer is published in [1] using fixed gain. However, the motor flux linkage is not exactly known for a load torque observer. There is the problem of uncertainty to obtain very high precision position control. Therefore a model reference adaptive observer is considered to overcome the problem of unknown parameter and torque disturbance in this paper. The system stability analysis is carried out using Lyapunov stability theorem. As a result, asymptotically stable observe gain can be obtained without affecting the overall system response. The load disturbance detected by the asymptotically stable adaptive observer is compensated by feedforwarding the equivalent current which gives fast response. The experimenta results are presented in the paper.

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Stabilizing Control of DC/DC Buck Converters with Constant Power Loads in Continuous Conduction and Discontinuous Conduction Modes Using Digital Power Alignment Technique

  • Khaligh Alireza;Emadi Ali
    • Journal of Electrical Engineering and Technology
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    • v.1 no.1
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    • pp.63-72
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    • 2006
  • The purpose of this raper is to address the negative impedance instability in DC/DC converters. We present the negative impedance instability of PWM DC/DC converters loaded by constant power loads (CPLs). An approach to design digital controllers for DC/DC converters Is presented. The proposed method, called Power Alignment control technique, is applied to DC/DC step-down choppers operating in continuous conduction or discontinuous conduction modes with CPLs. This approach uses two predefined state variables instead of conventional pulse width modulation (PWM) to regulate the output voltage. A comparator compares actual output voltage with the reference and then switches between the appropriate states. It needs few logic gates and comparators to be implemented thus, making it extremely simple and easy to develop using a low-cost application specific integrated circuit (ASIC) for converters with CPLs. Furthermore, stability of the proposed controllers using the small signal analysis as well as the second theorem of Lyapunov is verified. Finally, simulation and analytical results are presented to describe and verify the proposed technique.

Nonlinear Attitude Control for Uncertain Quad-rotors Using a Global Approximation-Free Control Scheme (GAFC 비선형 제어기법을 적용한 쿼드로터의 자세 및 고도제어)

  • Kim, Young-Ouk;Park, Seong-Yong;Leeghim, Henzeh
    • Journal of Institute of Control, Robotics and Systems
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    • v.22 no.10
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    • pp.779-787
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    • 2016
  • A nonlinear control law for the quad-rotor of a low-complexity, global approximation-free from system uncertainties and external disturbances are described in this paper. The control law guarantees convergence to a small bounded error using a prescribed performance function. The stability of the proposed nonlinear control system is also proven by the Lyapunov stability theorem. The advantage of this technique is that it has a simpler form than any other nonlinear compensators and is applicable to any nonlinear systems without precise knowledge of the systems. In this paper, the proposed approach is applied to attitude/altitude control of a quad-rotor. Numerical simulations are performed to investigate the proposed nonlinear attitude control law by applying it to an uncertain quadcopter system with external disturbances.

Variable Speed Control of Wind Turbines Using Robust Fuzzy Algorithm (강인 퍼지 이론을 이용한 풍력 터빈의 가변 속도 제어)

  • Sung, Hwa-Chang;Park, Jin-Bae;Joo, Young-Hoon
    • Journal of the Korean Institute of Intelligent Systems
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    • v.18 no.1
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    • pp.1-6
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    • 2008
  • In this paper, we present the robust fuzzy algorithm for variable speed control of wind turbines. Generally, the plants of wind turbines are consisted of complex nonlinearities, and the parameters of variable speed of wind turbines are represented as uncertain terms. For solving these complexity, we propose the robust fuzzy algorithm. At first, the exact fuzzy modeling are performed for variable speed of wind turbines. Next, we design the fuzzy controller for reanalyzed T-S fuzzy model of the wind turbines, then, we prove the stability of the plant through the Lyapunov stability theorem. At last, an example is included for visualizing the efficiency of the proposed technique.

Experimental Results of Adaptive Load Torque Observer and Robust Precision Position Control of PMSM (PMSM의 정밀 Robust 위치 제어 및 적응형 외란 관측기 적용 연구)

  • Go, Jong-Seon;Yun, Seong-Gu
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • v.49 no.3
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    • pp.117-123
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    • 2000
  • A new control method for precision robust position control of a PMSM (Permanent Magnet Synchronous Motor) using asymptotically stable adaptive load torque observer is presented in the paper. Precision position control is obtained for the PMSM system approximately linearized using the field-orientation method. Recently, many of these drive systems use the PMSM to avoid backlashes. However, the disadvantages of the motor are high cost and complex control because of nonlinear characteristics. Also, the load torque disturbance directly affects the motor shaft. The application of the load torque observer is published in [1] using fixed gain. However, the motor flux linkage is not exactly known for a load torque observer. There is the problem of uncertainty to obtain very high precision position control. Therefore, a model reference adaptive observer is considered to overcome the problem of unknown parameter and torque disturbance in this paper. The system stability analysis is carried out using Lyapunov stability theorem. As a result, asymptotically stable observer gain can be obtained without affecting the overall system response. The load disturbance detected by the asymptotically stable adaptive observer is compensated by feedforwarding the equivalent current which gives fast response. The experimental results are presented in the paper using DSP TMS320c31.

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