• Title/Summary/Keyword: Nonlinearity error

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The Design of Optimal Fuzzy-Neural networks Structure by Means of GA and an Aggregate Weighted Performance Index (유전자 알고리즘과 합성 성능지수에 의한 최적 퍼지-뉴럴 네트워크 구조의 설계)

  • Oh, Sung-Kwun;Yoon, Ki-Chan;Kim, Hyun-Ki
    • Journal of Institute of Control, Robotics and Systems
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    • v.6 no.3
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    • pp.273-283
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    • 2000
  • In this paper we suggest an optimal design method of Fuzzy-Neural Networks(FNN) model for complex and nonlinear systems. The FNNs use the simplified inference as fuzzy inference method and Error Back Propagation Algorithm as learning rule. And we use a HCM(Hard C-Means) Clustering Algorithm to find initial parameters of the membership function. The parameters such as parameters of membership functions learning rates and momentum weighted value is proposed to achieve a sound balance between approximation and generalization abilities of the model. According to selection and adjustment of a weighting factor of an aggregate objective function which depends on the number of data and a certain degree of nonlinearity (distribution of I/O data we show that it is available and effective to design and optimal FNN model structure with a mutual balance and dependency between approximation and generalization abilities. This methodology sheds light on the role and impact of different parameters of the model on its performance (especially the mapping and predicting capabilities of the rule based computing). To evaluate the performance of the proposed model we use the time series data for gas furnace the data of sewage treatment process and traffic route choice process.

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Using GA-FSMC for Precise Water Level Control of Double Tank (GA-FSMC를 이용한 이중탱크의 정밀한 수위 제어)

  • Park, Hyun-Chul;Park, Doo-Hwan;Song, Hong-Jun;Jo, Hyun-Woo;Lee, Joon-Tark
    • Proceedings of the KIEE Conference
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    • 2002.07d
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    • pp.2192-2195
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    • 2002
  • Even though, tanks are used at the many industry plants, it is very difficult to control the tank level without any overflow and shortage; moreover, cause of its complication of dynamics and nonlinearity, it's impossible to realize the accurate control using the mathematical model which can be applied to the various operation modes. However, the sliding mode controller(SMC) is known as having the robust variable structures for the nonlinear control systems with the parametric perturbations and with the sudden disturbances. It's difficult to find SMC's parameters, and SMC is bring chattering which injures actuator and increases error. In this paper, Genetic Aloglism based Fuzzy Sliding Mode Controller(GA-FSMC) for the precise control of the coupled tank level was proposed. Genetic Algolism and Fuzzy logic are adapted to find SMC's parameters and reduce the chattering. The simulation result is shown that the tank level could be satisfactorily controlled with less overshoot and steady-state error by the proposed GA-FSMC.

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Whole learning algorithm of the neural network for modeling nonlinear and dynamic behavior of RC members

  • Satoh, Kayo;Yoshikawa, Nobuhiro;Nakano, Yoshiaki;Yang, Won-Jik
    • Structural Engineering and Mechanics
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    • v.12 no.5
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    • pp.527-540
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    • 2001
  • A new sort of learning algorithm named whole learning algorithm is proposed to simulate the nonlinear and dynamic behavior of RC members for the estimation of structural integrity. A mathematical technique to solve the multi-objective optimization problem is applied for the learning of the feedforward neural network, which is formulated so as to minimize the Euclidean norm of the error vector defined as the difference between the outputs and the target values for all the learning data sets. The change of the outputs is approximated in the first-order with respect to the amount of weight modification of the network. The governing equation for weight modification to make the error vector null is constituted with the consideration of the approximated outputs for all the learning data sets. The solution is neatly determined by means of the Moore-Penrose generalized inverse after summarization of the governing equation into the linear simultaneous equations with a rectangular matrix of coefficients. The learning efficiency of the proposed algorithm from the viewpoint of computational cost is verified in three types of problems to learn the truth table for exclusive or, the stress-strain relationship described by the Ramberg-Osgood model and the nonlinear and dynamic behavior of RC members observed under an earthquake.

Linearity Analysis and Calibration of a Cable-Conduit Bend Sensor (케이블 컨듀잇 굽힘 센서의 선형 특성 분석 및 켈리브레이션)

  • Jeong, Useok;Cho, Kyu-Jin
    • The Journal of Korea Robotics Society
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    • v.12 no.1
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    • pp.26-32
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    • 2017
  • Previous shape sensors including bend sensors and optic fiber based sensors are widely used in various applications including goniometer and surgical robots. But theses sensors have large nonlinearity, limited in the range of sensing curvature, and sometimes are expensive. This study suggests a new concept of bend sensor using cable-conduit which consists of the outer sheath and the inner wire. The outer sheath is made of helical coil whose length of the central line changes as the sheath bends. This length change of the central line can be measured with the length change of the inner cable. The modeling and the experimental results show that the output signal of the proposed sensor is linearly related with the bend angle of the sheath with root mean square error of 5.3% of $450^{\circ}$ sensing range. Also the polynomial calibration of the sensor can decrease the root mean square error to 2.1% of the full sensing range.

Waypoint Tracking of Large Diameter Unmanned Underwater Vehicles with X-stern Configuration (X-stern 배열을 가진 대형급 무인잠수정의 경로점 추적)

  • Kim, Do Wan;Kim, Moon Hwan;Park, Ho-Gyu;Kim, Tae-Yeong
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.66 no.2
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    • pp.387-393
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    • 2017
  • This paper focuses on a horizontal waypoint tracking and a speed control of large diameter unmanned underwater vehicles (LDUUVs) with X-stern configuration plane. The concerned design problem is converted into an asymptotic stabilization of the error dynamics with respect to the desired yaw angle and surge speed. It is proved that the error dynamics under the proposed control scheme based on the linear control and the feedback linearization can be considered as a cascade system; the cascade system is asymptotically stable if its nominal systems are so. This stability connection enables to separately deal with the waypoint tracking problem and the speed control one. By using the sector nonlinearity, the nominal system with nonlinearities is modeled as a polytopic linear parameter varying (LPV) system with parametric uncertainties. Then, sufficient linear matrix inequality (LMI) conditions for its asymptotic stabilizability are derived in the sense of Lyapunov stability criterion. An example is given to show the validity of the proposed methodology.

The Design of Target Tracking System Using the Identification of TS Fuzzy Model (TS 퍼지 모델 동정을 이용한 표적 추적 시스템 설계)

  • Lee, Bum-Jik;Joo, Young-Hoon;Park, Jin-Bae
    • Proceedings of the KIEE Conference
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    • 2001.07d
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    • pp.1958-1960
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    • 2001
  • In this paper, we propose the design methodology of target tracking system using the identification of TS fuzzy model based on genetic algorithm(GA) and RLS algorithm. In general, the objective of target tracking is to estimate the future trajectory of the target based on the past position of the target obtained from the sensor. In the conventional and mathematical nonlinear filtering method such as extended Kalman filter(EKF), the performance of the system may be deteriorated in highly nonlinear situation. In this paper, to resolve these problems of nonlinear filtering technique, the error of EKF by nonlinearity is compensated by identifying TS fuzzy model. In the proposed method, after composing training datum from the parameters of EKF, by identifying the premise and consequent parameters and the rule numbers of TS fuzzy model using GA, and by tuning finely the consequent parameters of TS fuzzy model using recursive least square(RLS) algorithm, the error of EKF is compensated. Finally, the proposed method is applied to three dimensional tracking problem, and the simulation results shows that the tracking performance is improved by the proposed method.

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Adaptive Fuzzy Sliding Mode Control for Nonlinear Systems Using Estimation of Bounds for Approximation Errors (근사화 오차 유계 추정을 이용한 비선형 시스템의 적응 퍼지 슬라이딩 모드 제어)

  • Seo Sam-Jun
    • Journal of the Korean Institute of Intelligent Systems
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    • v.15 no.5
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    • pp.527-532
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    • 2005
  • In this paper, we proposed an adaptive fuzzy sliding control for unknown nonlinear systems using estimation of bounds for approximation errors. Unknown nonlinearity of a system is approximated by the fuzzy logic system with a set of IF-THEN rules whose consequence parameters are adjusted on-line according to adaptive algorithms for the purpose of controlling the output of the nonlinear system to track a desired output. Also, using assumption that the approximation errors satisfy certain bounding conditions, we proposed the estimation algorithms of approximation errors by Lyapunov synthesis methods. The overall control system guarantees that the tracking error asymptotically converges to zero and that all signals involved in controller are uniformly bounded. The good performance of the proposed adaptive fuzzy sliding mode controller is verified through computer simulations on an inverted pendulum system.

Fast Analysis of Film Thickness in Spectroscopic Reflectometry using Direct Phase Extraction

  • Kim, Kwangrak;Kwon, Soonyang;Pahk, Heui Jae
    • Current Optics and Photonics
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    • v.1 no.1
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    • pp.29-33
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    • 2017
  • A method for analysis of thin film thickness in spectroscopic reflectometry is proposed. In spectroscopic reflectometry, there has been a trade-off between accuracy and computation speed using the conventional analysis algorithms. The trade-off originated from the nonlinearity of spectral reflectance with respect to film thickness. In this paper, the spectral phase is extracted from spectral reflectance, and the thickness of the film can be calculated by linear equations. By using the proposed method, film thickness can be measured very fast with high accuracy. The simulation result shows that the film thickness can be acquired with high accuracy. In the simulation, analysis error is lower than 0.01% in the thickness range from 100 nm to 4 um. The experiments also show good accuracy. Maximum error is under $40{\AA}$ in the thickness range $3,000-20,000{\AA}$. The experiments present that the proposed method is very fast. It takes only 2.6 s for volumetric thickness analysis of 640*480 pixels. The study suggests that the method can be a useful tool for the volumetric thickness measurement in display and semiconductor industries.

GA-LADRC based control for course keeping applied to a mariner class vessel (GA-LADRC를 이용한 Mariner class vessel의 선수각 제어)

  • Jong-Kap AHN
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.59 no.2
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    • pp.145-154
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    • 2023
  • In this study, to control the heading angle of a ship, which is constantly subjected to various internal and external disturbances during the voyage, an LADRC (linear active disturbance rejection control) design that focuses more on improving the disturbance removal performance was proposed. The speed rate of change of the ship's heading angle due to the turn of the rudder angle was selected as a significant factor, and the nonlinear model of the ship's maneuvering equation, including the steering gear, was treated as a total disturbance. It is the similar process with an LADRC design for the first-order transfer function model. At this time, the gains of the controller included in LADRC and the gains of the extended state observer were tuned to RCGAs (real-coded genetic algorithms) to minimize the integral time-weighted absolute error as an evaluation function. The simulation was performed by applying the proposed GA-LADRC controller to the heading angle control of the Mariner class vessel. In particular, it was confirmed that the proposed controller satisfactorily maintains and follows the set course even when the disturbances such as nonlinearity, modelling error, uncertainty and noise of the measurement sensor are considered.

A FINITE ELEMENT SOLUTION FOR THE CONSERVATION FORM OF BBM-BURGERS' EQUATION

  • Ning, Yang;Sun, Mingzhe;Piao, Guangri
    • East Asian mathematical journal
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    • v.33 no.5
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    • pp.495-509
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    • 2017
  • With the accuracy of the nonlinearity guaranteed, plenty of time and large memory space are needed when we solve the finite element numerical solution of nonlinear partial differential equations. In this paper, we use the Group Element Method (GEM) to deal with the non-linearity of the BBM-Burgers Equation with Conservation form and perform a numerical analysis for two particular initial-boundary value (the Dirichlet boundary conditions and Neumann-Dirichlet boundary conditions) problems with the Finite Element Method (FEM). Some numerical experiments are performed to analyze the error between the exact solution and the FEM solution in MATLAB.