• Title/Summary/Keyword: Lyapunov Method

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Design of Sliding Mode Observer for Solar Array Current Estimation in the Grid-Connected Photovoltaic System (계통연계형 태양광 발전시스템의 태양전지 전류 추정을 위한 슬라이딩 모드 관측기 설계)

  • Kim IL-Song;Baik In-Cheol;Youn Myung-Joong
    • The Transactions of the Korean Institute of Power Electronics
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    • v.10 no.4
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    • pp.411-419
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    • 2005
  • In this paper, a sliding mode observer for solar array current estimation in the photovoltaic power generation system is presented. The solar array current estimation Information is obtained from the sliding mode observer and fed into the maximum power point tracker to update the reference voltage. The parameter values such as inverter dc link capacitances cm be changed up to 50$\%$ from their nominal values and the linear observer can't estimate the correct state values under the parameter variations and noisy environments. The configuration of sliding mode observer is simple, but it shows the robust tracking performance against parameter variations and modeling uncertainties. In this paper, the method for constructing the sliding mode observer using equivalent control input is presented and the convergence of the proposed observer is verified by the Lyapunov method. The mathematical modeling and the experimental results verify the validity of the proposed method.

A Preliminary Study for Nonlinear Dynamic Analysis of EEG in Patients with Dementia of Alzheimer's Type Using Lyapunov Exponent (리아프노프 지수를 이용한 알쯔하이머형 치매 환자 뇌파의 비선형 역동 분석을 위한 예비연구)

  • Chae, Jeong-Ho;Kim, Dai-Jin;Choi, Sung-Bin;Bahk, Won-Myong;Lee, Chung Tai;Kim, Kwang-Soo;Jeong, Jaeseung;Kim, Soo-Yong
    • Korean Journal of Biological Psychiatry
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    • v.5 no.1
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    • pp.95-101
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    • 1998
  • The changes of electroencephalogram(EEG) in patients with dementia of Alzheimer's type are most commonly studied by analyzing power or magnitude in traditionally defined frequency bands. However because of the absence of an identified metric which quantifies the complex amount of information, there are many limitations in using such a linear method. According to the chaos theory, irregular signals of EEG can be also resulted from low dimensional deterministic chaos. Chaotic nonlinear dynamics in the EEG can be studied by calculating the largest Lyapunov exponent($L_1$). The authors have analyzed EEG epochs from three patients with dementia of Alzheimer's type and three matched control subjects. The largest $L_1$ is calculated from EEG epochs consisting of 16,384 data points per channel in 15 channels. The results showed that patients with dementia of Alzheimer's type had significantly lower $L_1$ than non-demented controls on 8 channels. Topographic analysis showed that the $L_1$ were significantly lower in patients with Alzheimer's disease on all the frontal, temporal, central, and occipital head regions. These results show that brains of patients with dementia of Alzheimer's type have a decreased chaotic quality of electrophysiological behavior. We conclude that the nonlinear analysis such as calculating the $L_1$ can be a promising tool for detecting relative changes in the complexity of brain dynamics.

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Effects of Muscle Activation Pattern and Stability of the Lower Extremity's Joint on Falls in the Elderly Walking -Retrospective Approach- (노인 보행 시 하지 근 활동 양상과 관절의 안정성이 낙상에 미치는 영향 -후향성 연구-)

  • Ryu, Jiseon
    • 한국체육학회지인문사회과학편
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    • v.57 no.3
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    • pp.345-356
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    • 2018
  • Objective: The purpose of this study was to investigate the local stability of the lower extremity joints and muscle activation patterns of the lower extremity during walking between falling and non-falling group in the elderly women. Method: Forty women, heel strikers, were recruited for this study. Twenty subjects (age:72.55±5.42yrs; height:154.40±4.26cm; mass:57.40±6.21kg; preference walking speed:0.52±0.17m/s; fall frequency=1.70±1.26 times) had a history falls(fall group) within two years and Twenty subjects (71.90±2..90yrs; height:155.28±4.73cm; mass:56.70±5.241kg; preference walking speed: 0.56±0.13m/s) had no history falls(non-fall group). While they were walking on a instrumented treadmill at their preference speed for a long while, kinematic and EMG signals were obtained using 3-D motion capture and wireless EMG electrodes, respectively. Local stability of the ankle and knee joint were calculated using Lyapunov Exponent (LyE) and muscles activation and their co-contraction index were also quantified. Hypotheses were tested using one-way ANOVA and Mann-Whitey. Spearman rank was also used to determine the correlation coefficients between variables. Level of significance was set at p<.05. Results: Local stability in the knee joint adduction-abduction was significantly greater in fall group than non-fall group(p<.05). Activation of anterior tibials that acts on the foot segment dorsal flexion was greater in non-fall group than fall group(p<.05). CI between gastrocnemius and anterior tibials was found to be significantly different between two groups(p<.05). In addition, there was significant correlation between CI of the leg and LyE of the ankle joint flexion-extention in the fall group(p<.05). Conclusion: In conclusion, muscles that act on the knee joint abduction-adduction as well as gastrocnemius and anterior tibials that act on the ankle joint flexion-extention need to be strengthened to prevent from potential fall during walking.

A Nonlinear Sliding Mode Controller for IPMSM Drives with an Adaptive Gain Tuning Rule

  • Jung, Jin-Woo;Dang, Dong Quang;Vu, Nga Thi-Thuy;Justo, Jackson John;Do, Ton Duc;Choi, Han Ho;Kim, Tae Heoung
    • Journal of Power Electronics
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    • v.15 no.3
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    • pp.753-762
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    • 2015
  • This paper presents a nonlinear sliding mode control (SMC) scheme with a variable damping ratio for interior permanent magnet synchronous motors (IPMSMs). First, a nonlinear sliding surface whose parameters change continuously with time is designed. Actually, the proposed SMC has the ability to reduce the settling time without an overshoot by giving a low damping ratio at the initial time and a high damping ratio as the output reaches the desired setpoint. At the same time, it enables a fast convergence in finite time and eliminates the singularity problem with the upper bound of an uncertain term, which cannot be measured in practice, by using a simple adaptation law. To improve the efficiency of a system in the constant torque region, the control system incorporates the maximum torque per ampere (MTPA) algorithm. The stability of the nonlinear sliding surface is guaranteed by Lyapunov stability theory. Moreover, a simple sliding mode observer is used to estimate the load torque and system uncertainties. The effectiveness of the proposed nonlinear SMC scheme is verified using comparative experimental results of the linear SMC scheme when the speed reference and load torque change under system uncertainties. From these experimental results, the proposed nonlinear SMC method reveals a faster transient response, smaller steady-state speed error, and less sensitivity to system uncertainties than the linear SMC method.

Controlling robot by image-based visual servoing with stereo cameras

  • Fan, Jun-Min;Won, Sang-Chul
    • Proceedings of the Korea Society of Information Technology Applications Conference
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    • 2005.11a
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    • pp.229-232
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    • 2005
  • In this paper, an image-based "approach-align -grasp" visual servo control design is proposed for the problem of object grasping, which is based on the binocular stand-alone system. The basic idea consists of considering a vision system as a specific sensor dedicated a task and included in a control servo loop, and we perform automatic grasping follows the classical approach of splitting the task into preparation and execution stages. During the execution stage, once the image-based control modeling is established, the control task can be performed automatically. The proposed visual servoing control scheme ensures the convergence of the image-features to desired trajectories by using the Jacobian matrix, which is proved by the Lyapunov stability theory. And we also stress the importance of projective invariant object/gripper alignment. The alignment between two solids in 3-D projective space can be represented with view-invariant, more precisely; it can be easily mapped into an image set-point without any knowledge about the camera parameters. The main feature of this method is that the accuracy associated with the task to be performed is not affected by discrepancies between the Euclidean setups at preparation and at task execution stages. Then according to the projective alignment, the set point can be computed. The robot gripper will move to the desired position with the image-based control law. In this paper we adopt a constant Jacobian online. Such method describe herein integrate vision system, robotics and automatic control to achieve its goal, it overcomes disadvantages of discrepancies between the different Euclidean setups and proposes control law in binocular-stand vision case. The experimental simulation shows that such image-based approach is effective in performing the precise alignment between the robot end-effector and the object.

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Adaptive Feedback Linearization Control Based on Airgap Flux Model for Induction Motors

  • Jeon Seok-Ho;Baang Dane;Choi Jin-Young
    • International Journal of Control, Automation, and Systems
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    • v.4 no.4
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    • pp.414-427
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    • 2006
  • This paper presents an adaptive feedback linearization control scheme for induction motors with simultaneous variation of rotor and stator resistances. Two typical modeling techniques, rotor flux model and stator flux model, have been developed and successfully applied to the controller design and adaptive observer design, respectively. By using stator fluxes as states, over-parametrization in adaptive control can be prevented and control strategy can be developed without the need of nonlinear transformation. It also decrease the relative degree for the flux modulus by one, thereby, yielding, a simple control algorithm. However, when this method is used for flux observer, it cannot guarantee the convergence of flux. Similarly, the rotor flux model may be appropriate for observers, but it is not so for adaptive controllers. In addition, if these two existing methods are merged into overall adaptive control system, it brings about structural complexies. In this paper, we did not use these two modeling methods, and opted for the airgap flux model which takes on only the positive aspects of the existing rotor flux model and stator flux model and prevents structural complexity from occuring. Through theoretical analysis by using Lyapunov's direct method, simulations, and actual experiments, it is shown that stator and rotor resistances converge to their actual values, flux is well estimated, and torque and flux are controlled independently with the measurements of rotor speed, stator currents, and stator voltages. These results were achieved under the persistent excitation condition, which is shown to hold in the simulation.

Design of Robust Fuzzy Controllers via Inverse Optimal Approach (역최적화 방법을 이용한 강인한 퍼지 제어기의 설계)

  • 곽기호;임재환;박주영
    • Journal of the Korean Institute of Intelligent Systems
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    • v.11 no.6
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    • pp.477-486
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    • 2001
  • In this paper , we study the problem of designing TS(Takagi-Sugeno) fuzzy controllers for the systems that can be approximated or represented by the TS fuzzy model. The main strategy used in this paper is the inverse optimal approach, in which the cost function is determined later than the Lyapunov function and its corresponding control input satisfying the design requirements such as stability, decay rate, and robustness against uncertainty. This approach is useful because it yields controllers satisfying the inherent robustness of optimal controllers as well as the considered design goals. The design procedures established in this paper are all in the from of solving LMIs(Iinear matrix inequalities). Since the LMIs arising in the design procedures can be solved within a given tolerance by the interior point methods. the design method of the paper are efficient in practice. The applicability of the proposed design procedures is demonstrated by design examples.

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Fuzzy Disturbance Observer based Multiple Sliding Surface Control of Nonlinear Systems with Mismatched Disturbance (부정합조건 외란을 갖는 비선형 시스템의 퍼지 외란 관측기 기반 다중 슬라이딩 평면 제어)

  • Lee, Sang-Yun;Seo, Hyungkeun;Hyun, Chang-Ho;Park, Mignon
    • Journal of the Korean Institute of Intelligent Systems
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    • v.24 no.4
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    • pp.385-391
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    • 2014
  • This paper proposes fuzzy disturbance observer based multiple sliding surface control scheme for nonlinear systems with mismatched disturbance. In order to stabilize nonlinear systems with mismatched disturbance, a controller based on multiple sliding surface control scheme is designed. In addition, a fuzzy disturbance observer is used to estimate the disturbance. Using the fuzzy disturbance observer, "explosion of terms" problem and chattering problem were solved. The stability of the proposed control scheme is analyzed by Lyapunov stability theory. For the verification, we apply the proposed method to numerical examples and compare its result with that of the applied nonlinear disturbance observer based sliding mode control.

Fuzzy Modeling and Stability Analysis of Wind Power System with Doubly-fed Induction Generator (이중여자 유도발전기 기반 풍력발전 시스템의 퍼지 모델링 및 안정도 해석)

  • Kim, Jin-Kyu;Joo, Young-Hoon
    • Journal of the Korean Institute of Intelligent Systems
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    • v.22 no.1
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    • pp.56-61
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    • 2012
  • This paper propose the robust stability algorithm for controlling a variable speed wind power system which based on doubly-fed induction generator (DFIG). The control object in the wind power system enables the rotor to rotate without any physical contact by using magnetic force. Generally, the system dynamics of the wind power system has severe nonlinearity and uncertainty so that it is not easy to obtain the control objective. For solving these problems, we propose the fuzzy modelling and robust control algorithm for wind power system. The sufficient conditions for robust controller are obtained in terms of solutions to linear matrix inequalities (LMIs). Simulation results for wind power system based on DFIG are demonstrated to visualize the feasibility of the proposed method.

Sliding-Mode Control of Container Cranes (컨테이너크레인 시스템의 슬라이딩모드제어)

  • Lee Suk-Jae;Park Hahn;Hong Keum-Shik
    • Journal of Navigation and Port Research
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    • v.29 no.8 s.104
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    • pp.747-753
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    • 2005
  • In this paper, as an anti-sway control strategy of container cranes, we investigate a variable structure control in which the moving load follows a given trajectory, whereas both the trolley and hoist controllers achieve their positioning problems. It is crucial, in an automated container terminal, that collisions should be avoided during the transference of containers from one place to another. It is also necessary, in the case of a quay crane, to select suitable loading and unloading trajectories of containers, so that possible collisions with surrounding obstacles are avoided. After a brief introduction of the mathematical model, a robust control scheme (i.e., a second-order sliding mode control that guarantees a fast and precise transference and a suppression of the resulted swing) is presented. Despite model uncertainties and unmodeled actuators dynamics, the swing suppression from the given trajectory is obtained by constraining the system motion on suitable sliding surfaces, which include both the desired path and the swing angle. The proposed controller has been tested with a laboratory-size pilot crane. Experimental results are provided.