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A Double-Interactively Recurrent Fuzzy Cerebellar Model Articulation Controller Model Combined with an Improved Particle Swarm Optimization Method for Fall Detection
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作者 Jyun-Guo Wang 《Computer Systems Science & Engineering》 2024年第5期1149-1170,共22页
In many Eastern and Western countries,falling birth rates have led to the gradual aging of society.Older adults are often left alone at home or live in a long-term care center,which results in them being susceptible t... In many Eastern and Western countries,falling birth rates have led to the gradual aging of society.Older adults are often left alone at home or live in a long-term care center,which results in them being susceptible to unsafe events(such as falls)that can have disastrous consequences.However,automatically detecting falls fromvideo data is challenging,and automatic fall detection methods usually require large volumes of training data,which can be difficult to acquire.To address this problem,video kinematic data can be used as training data,thereby avoiding the requirement of creating a large fall data set.This study integrated an improved particle swarm optimization method into a double interactively recurrent fuzzy cerebellar model articulation controller model to develop a costeffective and accurate fall detection system.First,it obtained an optical flow(OF)trajectory diagram from image sequences by using the OF method,and it solved problems related to focal length and object offset by employing the discrete Fourier transform(DFT)algorithm.Second,this study developed the D-IRFCMAC model,which combines spatial and temporal(recurrent)information.Third,it designed an IPSO(Improved Particle Swarm Optimization)algorithm that effectively strengthens the exploratory capabilities of the proposed D-IRFCMAC(Double-Interactively Recurrent Fuzzy Cerebellar Model Articulation Controller)model in the global search space.The proposed approach outperforms existing state-of-the-art methods in terms of action recognition accuracy on the UR-Fall,UP-Fall,and PRECIS HAR data sets.The UCF11 dataset had an average accuracy of 93.13%,whereas the UCF101 dataset had an average accuracy of 92.19%.The UR-Fall dataset had an accuracy of 100%,the UP-Fall dataset had an accuracy of 99.25%,and the PRECIS HAR dataset had an accuracy of 99.07%. 展开更多
关键词 Double interactively recurrent fuzzy cerebellar model articulation controller(D-IRFCMAC) improved particle swarm optimization(IPSO) fall detection
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Neural-networks-based Modelling and a Fuzzy Neural Networks Controller of MCFC
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作者 沈承 Cao +2 位作者 Guangyi Zhu Xinjian 《High Technology Letters》 EI CAS 2002年第2期76-82,共7页
Molten Carbonate Fuel Cells (MCFC) are produced with a highly efficient and clean power generation technology which will soon be widely utilized. The temperature characters of MCFC stack are briefly analyzed. A radial... Molten Carbonate Fuel Cells (MCFC) are produced with a highly efficient and clean power generation technology which will soon be widely utilized. The temperature characters of MCFC stack are briefly analyzed. A radial basis function (RBF) neural networks identification technology is applied to set up the temperature nonlinear model of MCFC stack, and the identification structure, algorithm and modeling training process are given in detail. A fuzzy controller of MCFC stack is designed. In order to improve its online control ability, a neural network trained by the I/O data of a fuzzy controller is designed. The neural networks can memorize and expand the inference rules of the fuzzy controller and substitute for the fuzzy controller to control MCFC stack online. A detailed design of the controller is given. The validity of MCFC stack modelling based on neural networks and the superior performance of the fuzzy neural networks controller are proved by Simulations. 展开更多
关键词 Molten Carbonate Fuel Cells (MCFC) Radial Basis Function (RBF) fuzzy neural networks control modelling
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SIMULATING RHYTHMIC MOVEMENT OF HUMAN ELBOW JOINT USING A NEURAL NETWORK PREDICTIVE MODEL
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作者 李醒飞 张国雄 肖少君 《Transactions of Tianjin University》 EI CAS 2001年第1期40-43,共4页
Human brain is hypothesized to store a geometry and dynamic model of the limb.A multilayer perceptron (or MLP) network is used to stand for the model.In this paper the human elbow joint rhythmic movement is simulated ... Human brain is hypothesized to store a geometry and dynamic model of the limb.A multilayer perceptron (or MLP) network is used to stand for the model.In this paper the human elbow joint rhythmic movement is simulated in three cases:1)Parameters of the MLP,the limb geometry and dynamic model match completely,2)Parameters mismatch between them,and 3)Disturbance exists.The results show that parameters mismatch is the main error source,which causes the elbow joint movement to be aberrant.From this we can infer that movement study is a process in which the internal model is updated continuously to match the geometry and dynamic model of limb. 展开更多
关键词 MPC neural network predictive model rhythmic movement control
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Nonlinear Decoupling PID Control Using Neural Networks and Multiple Models 被引量:8
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作者 Lianfei ZHAI Tianyou CHAI 《控制理论与应用(英文版)》 EI 2006年第1期62-69,共8页
For a class of complex industrial processes with strong nonlinearity, serious coupling and uncertainty, a nonlinear decoupling proportional-integral-differential (PID) controller is proposed, which consists of a tra... For a class of complex industrial processes with strong nonlinearity, serious coupling and uncertainty, a nonlinear decoupling proportional-integral-differential (PID) controller is proposed, which consists of a traditional PID controller, a decoupling compensator and a feedforward compensator for the unmodeled dynamics. The parameters of such controller is selected based on the generalized minimum variance control law. The unmodeled dynamics is estimated and compensated by neural networks, a switching mechanism is introduced to improve tracking performance, then a nonlinear decoupling PID control algorithm is proposed. All signals in such switching system are globally bounded and the tracking error is convergent. Simulations show effectiveness of the algorithm. 展开更多
关键词 NONLINEAR Decoupling control PID neural networks Multiple models Generalized minimum variance
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Dynamics Modeling and Robust Trajectory Tracking Control for a Class of Hybrid Humanoid Arm Based on Neural Network 被引量:4
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作者 WANG Yueling JIN Zhenlin 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2009年第3期355-363,共9页
In order to solve the problem of trajectory tracking for a class of novel serial-parallel hybrid humanoid arm(HHA), which has parameters uncertainty, frictions, disturbance, abrasion and pulse forces derived from mo... In order to solve the problem of trajectory tracking for a class of novel serial-parallel hybrid humanoid arm(HHA), which has parameters uncertainty, frictions, disturbance, abrasion and pulse forces derived from motors, a multistep dynamics modeling strategy is proposed and a robust controller based on neural network(NN)-adaptive algorithm is designed. At the first step of dynamics modeling, the dynamics model of the reduced HHA is established by Lagrange method. At the second step of dynamics modeling, the parameter uncertain part resulting mainly from the idealization of the HHA is learned by adaptive algorithm. In the trajectory tracking controller, the radial basis function(RBF) NN, whose optimal weights are learned online by adaptive algorithm, is used to learn the upper limit function of the total uncertainties including frictions, disturbances, abrasion and pulse forces. To a great extent, the conservatism of this robust trajectory tracking controller is reduced, and by this controller the HHA can impersonate mostly human actions. The proof and simulation results testify the validity of the adaptive strategy for parameter learning and the neural network-adaptive strategy for the trajectory tracking control. 展开更多
关键词 hybrid humanoid arm dynamic modeling neural network adaptive control trajectory tracking
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Hybrid Neural Network Model for RH Vacuum Refining Process Control 被引量:6
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作者 ZHANGChun-xia WANGBao-jun +4 位作者 ZHOUShi-guang LIULiu XUJing-bo LINLi-ping ZHANGCheng-fu 《Journal of Iron and Steel Research International》 SCIE EI CAS CSCD 2004年第1期12-16,共5页
A hybrid neural network model,in which RH process(theoretical)model is combined organically with neural network(NN)and case-base reasoning(CBR),was established.The CBR method was used to select the operation mode and ... A hybrid neural network model,in which RH process(theoretical)model is combined organically with neural network(NN)and case-base reasoning(CBR),was established.The CBR method was used to select the operation mode and the RH operational guide parameters for different steel grades according to the initial conditions of molten steel,and a three-layer BP neural network was adopted to deal with nonlinear factors for improving and compensating the limitations of technological model for RH process control and end-point prediction.It was verified that the hybrid neural network is effective for improving the precision and calculation efficiency of the model. 展开更多
关键词 RH vacuum refining process process control model hybrid neural network
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Neural-Network-Based Nonlinear Model Predictive Tracking Control of a Pneumatic Muscle Actuator-Driven Exoskeleton 被引量:8
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作者 Yu Cao Jian Huang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2020年第6期1478-1488,共11页
Pneumatic muscle actuators(PMAs)are compliant and suitable for robotic devices that have been shown to be effective in assisting patients with neurologic injuries,such as strokes,spinal cord injuries,etc.,to accomplis... Pneumatic muscle actuators(PMAs)are compliant and suitable for robotic devices that have been shown to be effective in assisting patients with neurologic injuries,such as strokes,spinal cord injuries,etc.,to accomplish rehabilitation tasks.However,because PMAs have nonlinearities,hysteresis,and uncertainties,etc.,complex mechanisms are rarely involved in the study of PMA-driven robotic systems.In this paper,we use nonlinear model predictive control(NMPC)and an extension of the echo state network called an echo state Gaussian process(ESGP)to design a tracking controller for a PMA-driven lower limb exoskeleton.The dynamics of the system include the PMA actuation and mechanism of the leg orthoses;thus,the system is represented by two nonlinear uncertain subsystems.To facilitate the design of the controller,joint angles of leg orthoses are forecasted based on the universal approximation ability of the ESGP.A gradient descent algorithm is employed to solve the optimization problem and generate the control signal.The stability of the closed-loop system is guaranteed when the ESGP is capable of approximating system dynamics.Simulations and experiments are conducted to verify the approximation ability of the ESGP and achieve gait pattern training with four healthy subjects. 展开更多
关键词 Echo state Gaussian process model predictive control neural network pneumatic muscle actuators-driven exoskeleton
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Model algorithm control using neural networks for input delayed nonlinear control system 被引量:2
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作者 Yuanliang Zhang Kil To Chong 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2015年第1期142-150,共9页
The performance of the model algorithm control method is partially based on the accuracy of the system's model. It is difficult to obtain a good model of a nonlinear system, especially when the nonlinearity is high. ... The performance of the model algorithm control method is partially based on the accuracy of the system's model. It is difficult to obtain a good model of a nonlinear system, especially when the nonlinearity is high. Neural networks have the ability to "learn"the characteristics of a system through nonlinear mapping to represent nonlinear functions as well as their inverse functions. This paper presents a model algorithm control method using neural networks for nonlinear time delay systems. Two neural networks are used in the control scheme. One neural network is trained as the model of the nonlinear time delay system, and the other one produces the control inputs. The neural networks are combined with the model algorithm control method to control the nonlinear time delay systems. Three examples are used to illustrate the proposed control method. The simulation results show that the proposed control method has a good control performance for nonlinear time delay systems. 展开更多
关键词 model algorithm control neural network nonlinear system time delay
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Batch Process Modelling and Optimal Control Based on Neural Network Model 被引量:6
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作者 JieZhang 《自动化学报》 EI CSCD 北大核心 2005年第1期19-31,共13页
This paper presents several neural network based modelling, reliable optimal control, and iterative learning control methods for batch processes. In order to overcome the lack of robustness of a single neural network,... This paper presents several neural network based modelling, reliable optimal control, and iterative learning control methods for batch processes. In order to overcome the lack of robustness of a single neural network, bootstrap aggregated neural networks are used to build reliable data based empirical models. Apart from improving the model generalisation capability, a bootstrap aggregated neural network can also provide model prediction confidence bounds. A reliable optimal control method by incorporating model prediction confidence bounds into the optimisation objective function is presented. A neural network based iterative learning control strategy is presented to overcome the problem due to unknown disturbances and model-plant mismatches. The proposed methods are demonstrated on a simulated batch polymerisation process. 展开更多
关键词 批量处理 神经网络模型 聚合 重复学习控制 最佳控制
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Hybrid Power Systems Energy Controller Based on Neural Network and Fuzzy Logic 被引量:2
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作者 Emad M. Natsheh Alhussein Albarbar 《Smart Grid and Renewable Energy》 2013年第2期187-197,共11页
This paper presents a novel adaptive scheme for energy management in stand-alone hybrid power systems. The proposed management system is designed to manage the power flow between the hybrid power system and energy sto... This paper presents a novel adaptive scheme for energy management in stand-alone hybrid power systems. The proposed management system is designed to manage the power flow between the hybrid power system and energy storage elements in order to satisfy the load requirements based on artificial neural network (ANN) and fuzzy logic controllers. The neural network controller is employed to achieve the maximum power point (MPP) for different types of photovoltaic (PV) panels. The advance fuzzy logic controller is developed to distribute the power among the hybrid system and to manage the charge and discharge current flow for performance optimization. The developed management system performance was assessed using a hybrid system comprised PV panels, wind turbine (WT), battery storage, and proton exchange membrane fuel cell (PEMFC). To improve the generating performance of the PEMFC and prolong its life, stack temperature is controlled by a fuzzy logic controller. The dynamic behavior of the proposed model is examined under different operating conditions. Real-time measured parameters are used as inputs for the developed system. The proposed model and its control strategy offer a proper tool for optimizing hybrid power system performance, such as that used in smart-house applications. 展开更多
关键词 Artificial neural network Energy Management Fuzzy Control Hybrid POWER Systems MAXIMUM POWER Point TRACKER modeling
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Multiple-model-and-neural-network-based nonlinear multivariable adaptive control
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作者 Yue FU Tianyou CHAI 《控制理论与应用(英文版)》 EI 2007年第2期121-126,共6页
A multivariable adaptive controller feasible for implementation on distributed computer systems (DCS) is presented for a class of uncertain nonlinear multivariable discrete time systems. The adaptive controller is c... A multivariable adaptive controller feasible for implementation on distributed computer systems (DCS) is presented for a class of uncertain nonlinear multivariable discrete time systems. The adaptive controller is composed of a linear adaptive controller, a neural network nonlinear adaptive controller and a switching mechanism. The linear controller can provide boundedness of the input and output signals, and the nonlinear controller can improve the performance of the system. The purpose of using the switching mechanism is to obtain the improved system performance and stability simultaneously. Theory analysis and simulation results are presented to show the effectiveness of the proposed method. 展开更多
关键词 Adaptive control neural network Multiple models SWITCHING Stability
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NONLINEAR MODELING AND CONTROLLING OF ARTIFICIAL MUSCLE SYSTEM USING NEURAL NETWORKS
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作者 Tian Sheping Ding Guoqing +1 位作者 Yan Detian Lin Liangming Department of Information Measurement and Instrumentation,Shanghai Jiaotong University,Shanghai 200030, China 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2004年第2期306-310,共5页
The pneumatic artificial muscles are widely used in the fields of medicalrobots, etc. Neural networks are applied to modeling and controlling of artificial muscle system. Asingle-joint artificial muscle test system is... The pneumatic artificial muscles are widely used in the fields of medicalrobots, etc. Neural networks are applied to modeling and controlling of artificial muscle system. Asingle-joint artificial muscle test system is designed. The recursive prediction error (RPE)algorithm which yields faster convergence than back propagation (BP) algorithm is applied to trainthe neural networks. The realization of RPE algorithm is given. The difference of modeling ofartificial muscles using neural networks with different input nodes and different hidden layer nodesis discussed. On this basis the nonlinear control scheme using neural networks for artificialmuscle system has been introduced. The experimental results show that the nonlinear control schemeyields faster response and higher control accuracy than the traditional linear control scheme. 展开更多
关键词 Artificial muscle neural networks Recursive prediction error algorithm Nonlinear modeling and controlling
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A new neural network model for the feedback stabilization of nonlinear systems
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作者 Mei-qin LIU Sen-lin ZHANG Gang-feng YAN 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2008年第8期1015-1023,共9页
A new neural network model termed ‘standard neural network model’ (SNNM) is presented, and a state-feedback control law is then designed for the SNNM to stabilize the closed-loop system. The control design constrain... A new neural network model termed ‘standard neural network model’ (SNNM) is presented, and a state-feedback control law is then designed for the SNNM to stabilize the closed-loop system. The control design constraints are shown to be a set of linear matrix inequalities (LMIs), which can be easily solved by the MATLAB LMI Control Toolbox to determine the control law. Most recurrent neural networks (including the chaotic neural network) and nonlinear systems modeled by neural networks or Takagi and Sugeno (T-S) fuzzy models can be transformed into the SNNMs to be stabilization controllers synthesized in the framework of a unified SNNM. Finally, three numerical examples are provided to illustrate the design developed in this paper. 展开更多
关键词 Standard neural network model (SNNM) Linear matrix inequality (LMI) Nonlinear control Asymptotic stability Chaotic cellular neural network Takagi and Sugeno (T-S) fuzzy model
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Synthetical Control of AGC/LPC System Based on Neural Networks Internal Model Control
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作者 Hu He, Xiaodong Luan, Yikang Sun Information Engineering School, University of Science and Technology Beijing, Beijing 100083, China 《Journal of University of Science and Technology Beijing》 CSCD 2001年第1期75-77,共3页
One synthetical control method of AGC/LPC system based on intelligence control theory-neural networks internal model control method is presented. Genetic algorithm (GA) is applied to optimize the parameters of the neu... One synthetical control method of AGC/LPC system based on intelligence control theory-neural networks internal model control method is presented. Genetic algorithm (GA) is applied to optimize the parameters of the neural networks. Simulation results prove that this method is effective. 展开更多
关键词 hot strip rolling AGC LOOPER neural networks internal model control GA
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Interval standard neural network models for nonlinear systems
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作者 LIU Mei-qin 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第4期530-538,共9页
A neural-network-based robust control design is suggested for control of a class of nonlinear systems. The design ap- proach employs a neural network, whose activation functions satisfy the sector conditions, to appro... A neural-network-based robust control design is suggested for control of a class of nonlinear systems. The design ap- proach employs a neural network, whose activation functions satisfy the sector conditions, to approximate the nonlinear system. To improve the approximation performance and to account for the parameter perturbations during operation, a novel neural network model termed standard neural network model (SNNM) is proposed. If the uncertainty is bounded, the SNNM is called an interval SNNM (ISNNM). A state-feedback control law is designed for the nonlinear system modelled by an ISNNM such that the closed-loop system is globally, robustly, and asymptotically stable. The control design equations are shown to be a set of linear matrix inequalities (LMIs) that can be easily solved by available convex optimization algorithms. An example is given to illustrate the control design procedure, and the performance of the proposed approach is compared with that of a related method reported in literature. 展开更多
关键词 Interval standard neural network model (ISNNM) Linear matrix inequality (LMI) Nonlinear system Asymptotic stability Robust control
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Nonlinear model predictive control based on hyper chaotic diagonal recurrent neural network
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作者 Samira Johari Mahdi Yaghoobi Hamid RKobravi 《Journal of Central South University》 SCIE EI CAS CSCD 2022年第1期197-208,共12页
Nonlinear model predictive controllers(NMPC)can predict the future behavior of the under-controlled system using a nonlinear predictive model.Here,an array of hyper chaotic diagonal recurrent neural network(HCDRNN)was... Nonlinear model predictive controllers(NMPC)can predict the future behavior of the under-controlled system using a nonlinear predictive model.Here,an array of hyper chaotic diagonal recurrent neural network(HCDRNN)was proposed for modeling and predicting the behavior of the under-controller nonlinear system in a moving forward window.In order to improve the convergence of the parameters of the HCDRNN to improve system’s modeling,the extent of chaos is adjusted using a logistic map in the hidden layer.A novel NMPC based on the HCDRNN array(HCDRNN-NMPC)was proposed that the control signal with the help of an improved gradient descent method was obtained.The controller was used to control a continuous stirred tank reactor(CSTR)with hard-nonlinearities and input constraints,in the presence of uncertainties including external disturbance.The results of the simulations show the superior performance of the proposed method in trajectory tracking and disturbance rejection.Parameter convergence and neglectable prediction error of the neural network(NN),guaranteed stability and high tracking performance are the most significant advantages of the proposed scheme. 展开更多
关键词 nonlinear model predictive control diagonal recurrent neural network chaos theory continuous stirred tank reactor
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Nonlinear model predictive control with guaranteed stability based on pseudolinear neural networks
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作者 WANGYongji WANGHong 《Journal of Chongqing University》 CAS 2004年第1期26-29,共4页
A nonlinear model predictive control problem based on pseudo-linear neural network (PNN) is discussed, in which the second order on-line optimization method is adopted. The recursive computation of Jacobian matrix is ... A nonlinear model predictive control problem based on pseudo-linear neural network (PNN) is discussed, in which the second order on-line optimization method is adopted. The recursive computation of Jacobian matrix is investigated. The stability of the closed loop model predictive control system is analyzed based on Lyapunov theory to obtain the sufficient condition for the asymptotical stability of the neural predictive control system. A simulation was carried out for an exothermic first-order reaction in a continuous stirred tank reactor.It is demonstrated that the proposed control strategy is applicable to some of nonlinear systems. 展开更多
关键词 pseudolinear neural networks (PNN) nonlinear model predictive control continuous stirred tank reactor (CSTR) asymptotic stability
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Adaptive Internal Model Control of a DC Motor Drive System Using Dynamic Neural Network
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作者 Farouk Zouari Kamel Ben Saad Mohamed Benrejeb 《Journal of Software Engineering and Applications》 2012年第3期168-189,共22页
This work concerns the study of problems relating to the adaptive internal model control of DC motor in both cases conventional and neural. The most important aspects of design building blocks of adaptive internal mod... This work concerns the study of problems relating to the adaptive internal model control of DC motor in both cases conventional and neural. The most important aspects of design building blocks of adaptive internal model control are the choice of architectures, learning algorithms, and examples of learning. The choice of parametric adaptation algorithm for updating elements of the conventional adaptive internal model control shows limitations. To overcome these limitations, we chose the architectures of neural networks deduced from the conventional models and the Levenberg-marquardt during the adjustment of system parameters of the adaptive neural internal model control. The results of this latest control showed compensation for disturbance, good trajectory tracking performance and system stability. 展开更多
关键词 Adaptive Internal model Control RECURRENT neural network DC MOTOR PARAMETRIC ADAPTATION Algorithm LEVENBERG-MARQUARDT
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Single Phase Induction Motor Drive with Restrained Speed and Torque Ripples Using Neural Network Predictive Controller
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作者 S. Saravanan K. Geetha 《Circuits and Systems》 2016年第11期3670-3684,共15页
In industrial drives, electric motors are extensively utilized to impart motion control and induction motors are the most familiar drive at present due to its extensive performance characteristic similar with that of ... In industrial drives, electric motors are extensively utilized to impart motion control and induction motors are the most familiar drive at present due to its extensive performance characteristic similar with that of DC drives. Precise control of drives is the main attribute in industries to optimize the performance and to increase its production rate. In motion control, the major considerations are the torque and speed ripples. Design of controllers has become increasingly complex to such systems for better management of energy and raw materials to attain optimal performance. Meager parameter appraisal results are unsuitable, leading to unstable operation. The rapid intensification of digital computer revolutionizes to practice precise control and allows implementation of advanced control strategy to extremely multifaceted systems. To solve complex control problems, model predictive control is an authoritative scheme, which exploits an explicit model of the process to be controlled. This paper presents a predictive control strategy by a neural network predictive controller based single phase induction motor drive to minimize the speed and torque ripples. The proposed method exhibits better performance than the conventional controller and validity of the proposed method is verified by the simulation results using MATLAB software. 展开更多
关键词 Dynamic model Low Torque Ripples neural model neural network Predictive controller Unstable Operation Single Phase Induction Motor Variable Speed Drives
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Application of an expert system using neural network to control the coagulant dosing in water treatment plant 被引量:3
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作者 HangZHANG 《控制理论与应用(英文版)》 EI 2004年第1期89-92,共4页
The coagulation process is one of the most important stages in water treatment plant, which involves many complex physical and chemical phenomena. Moreover, coagulant dosing rate is non-linearly correlated to raw wate... The coagulation process is one of the most important stages in water treatment plant, which involves many complex physical and chemical phenomena. Moreover, coagulant dosing rate is non-linearly correlated to raw water characteristics such as turbidity, conductivity, PH, temperature, etc. As such, coagulation reaction is hard or even impossible to control satisfactorily by conventional methods. Based on neural network and rule models, an expert system for determining the optimum chemical dosage rate is developed and used in a water treatment work, and the results of actual runs show that in the condition of satisfying the demand of drinking water quality, the usage of coagulant is lowered. 展开更多
关键词 Water treatment Process control Expert system neural network Rule models
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