• 제목/요약/키워드: Lyapunov Function

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새로운 구조의 L-K함수를 이용한 시간 지연 선형시스템의 시간 종속 안정성 (Delay Dependent Stability of Time-delayed Linear Systems using New Structure of L-K Funciton)

  • 김진훈
    • 전기학회논문지
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    • 제62권2호
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    • pp.246-251
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    • 2013
  • In this paper, we consider the stability of linear systems without delay decomposition. A less conservative result obtained without delay decomposition is strongly required since it is a basis to get an improved result by applying simple delay decomposition. Unlike the most popular Lyapunov-Krasovski(L-K) function, we consider the cross terms between variables. Based on this new structure of L-K function, we derive a delay-dependent stability criterion in the form of linear matrix inequality(LMI). Finally, we show, by well-known two examples, that our result is less conservative than the recent results.

새로운 적응 슬라이딩 모드 관측기를 이용한 PMSM 센서리스 속도 응답특성 향상 (Enhancement of the Speed Response of PMSM Sensorless Control Using A New Adaptive Sliding Mode Observer)

  • 김홍열;손주범;이장명
    • 전기학회논문지
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    • 제59권1호
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    • pp.160-167
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    • 2010
  • This paper proposes an adaptive sliding mode observer (SMO), which adds the estimation function of the stator resistance to a new sliding mode observer for the robust sensorless control of permanent magnet synchronous motor (PMSM) with variable parameters. To reduce the chattering problem commonly found in the conventional sliding mode observer where the low-pass filter and additional position compensation of the rotor are used, the sigmoid function is used for the control of a switching function in this research. With the estimation of the stator resistance, the proposed observer can improve the control performance by reducing the estimation error of the motor's speed. Note that the stator resistance is varying with the ambient temperature and becomes an error source for the sensorless control of PMSM. The new sliding mode observer has better efficiency than the conventional adaptive sliding mode observer by reducing the time consuming integral calculations. The stability of the proposed adaptive sliding mode observer is verified by the Lyapunov function in determining the observer gains, and the effectiveness of the observer is demonstrated by simulations and experiments.

Nonlinear Backstepping Control of SynRM Drive Systems Using Reformed Recurrent Hermite Polynomial Neural Networks with Adaptive Law and Error Estimated Law

  • Ting, Jung-Chu;Chen, Der-Fa
    • Journal of Power Electronics
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    • 제18권5호
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    • pp.1380-1397
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    • 2018
  • The synchronous reluctance motor (SynRM) servo-drive system has highly nonlinear uncertainties owing to a convex construction effect. It is difficult for the linear control method to achieve good performance for the SynRM drive system. The nonlinear backstepping control system using upper bound with switching function is proposed to inhibit uncertainty action for controlling the SynRM drive system. However, this method uses a large upper bound with a switching function, which results in a large chattering. In order to reduce this chattering, a nonlinear backstepping control system using an adaptive law is proposed to estimate the lumped uncertainty. Since this method uses an adaptive law, it cannot achiever satisfactory performance. Therefore, a nonlinear backstepping control system using a reformed recurrent Hermite polynomial neural network with an adaptive law and an error estimated law is proposed to estimate the lumped uncertainty and to compensate the estimated error in order to enhance the robustness of the SynRM drive system. Further, the reformed recurrent Hermite polynomial neural network with two learning rates is derived according to an increment type Lyapunov function to speed-up the parameter convergence. Finally, some experimental results and a comparative analysis are presented to verify that the proposed control system has better control performance for controlling SynRM drive systems.

Designing an Emotional Intelligent Controller for IPFC to Improve the Transient Stability Based on Energy Function

  • Jafari, Ehsan;Marjanian, Ali;Solaymani, Soodabeh;Shahgholian, Ghazanfar
    • Journal of Electrical Engineering and Technology
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    • 제8권3호
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    • pp.478-489
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    • 2013
  • The controllability and stability of power systems can be increased by Flexible AC Transmission Devices (FACTs). One of the FACTs devices is Interline Power-Flow Controller (IPFC) by which the voltage stability, dynamic stability and transient stability of power systems can be improved. In the present paper, the convenient operation and control of IPFC for transient stability improvement are considered. Considering that the system's Lyapunov energy function is a relevant tool to study the stability affair. IPFC energy function optimization has been used in order to access the maximum of transient stability margin. In order to control IPFC, a Brain Emotional Learning Based Intelligent Controller (BELBIC) and PI controller have been used. The utilization of the new controller is based on the emotion-processing mechanism in the brain and is essentially an action selection, which is based on sensory inputs and emotional cues. This intelligent control is based on the limbic system of the mammalian brain. Simulation confirms the ability of BELBIC controller compared with conventional PI controller. The designing results have been studied by the simulation of a single-machine system with infinite bus (SMIB) and another standard 9-buses system (Anderson and Fouad, 1977).

On the Design of Simple-structured Adaptive Fuzzy Logic Controllers

  • Park, Byung-Jae;Kwak, Seong-Woo
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제3권1호
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    • pp.93-99
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    • 2003
  • One of the methods to simplify the design process for a fuzzy logic controller (FLC) is to reduce the number of variables representing the rule antecedent. This in turn decreases the number of control rules, membership functions, and scaling factors. For this purpose, we designed a single-input FLC that uses a sole fuzzy input variable. However, it is still deficient in the capability of adapting some varying operating conditions although it provides a simple method for the design of FLC's. We here design two simple-structured adaptive fuzzy logic controllers (SAFLC's) using the concept of the single-input FLC. Linguistic fuzzy control rules are directly incorporated into the controller by a fuzzy basis function. Thus some parameters of the membership functions characterizing the linguistic terms of the fuzzy control rules can be adjusted by an adaptive law. In our controllers, center values of fuzzy sets are directly adjusted by an adaptive law. Two SAFLC's are designed. One of them uses a Hurwitz error dynamics and the other a switching function of the sliding mode control (SMC). We also prove that 1) their closed-loop systems are globally stable in the sense that all signals involved are bounded and 2) their tracking errors converge to zero asymptotically. We perform computer simulations using a nonlinear plant.

PD-슬라이딩 모드 제어의 절환을 통한 강인한 SPMSM 속도 제어기 설계 (Design of SPMSM Robust Speed Servo Controller Switching PD and Sliding Mode Control Strategies)

  • 손주범;서영수;이장명
    • 제어로봇시스템학회논문지
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    • 제16권3호
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    • pp.249-255
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    • 2010
  • The paper proposes a new type of robust speed control strategy for permanent magnet synchronous motor by using PD-sliding mode hybrid control. The PD control has a good performance in the transient region while the sliding mode controller provides the robustness against system uncertainties. Taking advantages of the two control strategies, the proposed control method utilizes the PD control in the approaching region to the sliding surface and the sliding mode control near at the sliding surfaces. The chattering problem of the sliding mode controller is eliminated by applying the saturation function for the switching function of the sliding mode control. The stability of the sliding mode control is verified by using Lyapunov function with the proper selection of variable gains. It is shown that with this simple switching algorithm, stability of the overall hybrid control system is ensured. Through the simulations, the PD-sliding mode algorithm is shown to have a good performance in the transient response as well as being robust against disturbances. The robustness of the PD-sliding mode algorithm is further demonstrated against various external disturbances in the real experiments of SPMSM motor control.

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.

적응형 되먹임 기반 종방향 자율주행 구동기 고장 탐지 및 허용 제어 알고리즘 개발 (Development of an Adaptive Feedback based Actuator Fault Detection and Tolerant Control Algorithms for Longitudinal Autonomous Driving)

  • 오광석;이종민;송태준;오세찬;이경수
    • 자동차안전학회지
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    • 제12권4호
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    • pp.13-22
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    • 2020
  • This paper presents an adaptive feedback based actuator fault detection and tolerant control algorithms for longitudinal functional safety of autonomous driving. In order to ensure the functional safety of autonomous vehicles, fault detection and tolerant control algorithms are needed for sensors and actuators used for autonomous driving. In this study, adaptive feedback control algorithm to compute the longitudinal acceleration for autonomous driving has been developed based on relationship function using states. The relationship function has been designed using feedback gains and error states for adaptation rule design. The coefficients in the relationship function have been estimated using recursive least square with multiple forgetting factors. The MIT rule has been adopted to design the adaptation rule for feedback gains online. The stability analysis has been conducted based on Lyapunov direct method. The longitudinal acceleration computed by adaptive control algorithm has been compared to the actual acceleration for fault detection of actuators used for longitudinal autonomous driving.

Backstepping Sliding Mode-based Model-free Control of Electro-hydraulic Systems

  • Truong, Hoai-Vu-Anh;Trinh, Hoai-An;Ahn, Kyoung-Kwan
    • 드라이브 ㆍ 컨트롤
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    • 제19권1호
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    • pp.51-61
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    • 2022
  • This paper presents a model-free system based on a framework of a backstepping sliding mode control (BSMC) with a radial basis function neural network (RBFNN) and adaptive mechanism for electro-hydraulic systems (EHSs). First, an EHS mathematical model was dedicatedly derived to understand the system behavior. Based on the system structure, BSMC was employed to satisfy the output performance. Due to the highly nonlinear characteristics and the presence of parametric uncertainties, a model-free approximator based on an RBFNN was developed to compensate for the EHS dynamics, thus addressing the difficulty in the requirement of system information. Adaptive laws based on the actor-critic neural network (ACNN) were implemented to suppress the existing error in the approximation and satisfy system qualification. The stability of the closed-loop system was theoretically proven by the Lyapunov function. To evaluate the effectiveness of the proposed algorithm, proportional-integrated-derivative (PID) and improved PID with ACNN (ACPID), which are considered two complete model-free methods, and adaptive backstepping sliding mode control, considered an ideal model-based method with the same adaptive laws, were used as two benchmark control strategies in a comparative simulation. The simulated results validated the superiority of the proposed algorithm in achieving nearly the same performance as the ideal adaptive BSMC.

무인 컨테이너 운송 조향 제어의 적응 퍼지 제어와 응용 (Design of the Adaptive Fuzzy Control Scheme and its Application on the Steering Control of the UCT)

  • 이규준;이영진;윤영진;이원구;김종식;이만형
    • 한국항만학회지
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    • 제15권1호
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    • pp.37-46
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    • 2001
  • Fuzzy logic control(FLC) is composed of three parts : fuzzy rule-bases, membership functions, and scaling factors. Well-defined fuzzy rule-base should contain proper physical intuition on the plant, so are needed lots of experiences of the skillful expert. When membership functions are considered, some parameters on the memberships function such as function shape, support, allocation density should be selected well. The rule of scaling factors is 'scaling'(amplifying or reducing) for both input and output signals of the FLC to fit in the membership function support and to operate the plant intentionally. To get a better performance of the FLC, it is necessary to adjust the parameters of the FLC. In general, the adaptation of the scaling factors is the most effective adjustment scheme, compared with that of the fuzzy rule-base or membership function parameters. This study proposes the adaptation scheme of the scaling factors. When the adaptation is performed on-line, the stability of the adaptive FLC should be guaranteed. The stable FLC system can be designed with stability analysis in the sense of Lyapunov stability. To adapt the scaling factors for the error signals, the concept of the conventional MRAC would be introduced into slightly modified form. A tracking accuracy of the control system would be enhanced by the modified shape and support of the membership function. The simulation is achieved on the pilot plant with the hydraulic steering control of a UCT(Unmanned Container Transporter) of which modeling dynamics have lots of severe uncertainties and modeling errors.

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