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A Comprehensive Review of Torque and Speed Control Strategies for Switched Reluctance Motor Drives 被引量:1
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作者 Sreeram K Preetha P K +1 位作者 Javier Rodríguez-García Carlosálvarez-Bel 《CES Transactions on Electrical Machines and Systems》 2025年第1期46-75,共30页
Switched Reluctance Motors(SRMs),outfitted with rugged construction,good speed range,high torque density,and rare earth-free nature that outweigh induction motors(IM)and permanent magnet synchronous motor(PMSM),afford... Switched Reluctance Motors(SRMs),outfitted with rugged construction,good speed range,high torque density,and rare earth-free nature that outweigh induction motors(IM)and permanent magnet synchronous motor(PMSM),afford a broad range of applications in the domain of electric vehicles(EVs).Standard copper magnetic wire and low-carbon steel laminations are used to construct SRMs,which give them high efficiency in the range of 85-95%.Despite SRM's desirable features over traditional motor-speed drives,high torque ripples and radial distortions constrain their deployment in EVs.Precise rotor position is imperative for effective management of the speed and torque of SRMs.This paper provides an illustrative compendium on review of the torque-speed control and ripple mitigation techniques using design enhancements and control methods for SRM drives for EV applications.The various schemes were evaluated on their performance metricsoperational speed range,control complexity,practical realization,need for pre-stored parameters(look-up tables of current,inductance and torque profiles)and motor controller memory requirements.The findings provide valuable insights into balancing the gains and trade-offs associated with EV applications.Furthermore,they pinpoint opportunities for enhancement by analyzing the cost and technical aspects of different SRM controllers. 展开更多
关键词 Electric vehicles Switched reluctance motor speed control Torque control Traction motor Torque ripple
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Idle speed control of proton exchange membrane fuel cell system via extended Kalman filter observer
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作者 ZHAO Hong-hui DING Tian-wei +4 位作者 WANG Yi-lin HUANG Xing DU Jing HAO Zhi-qiang MIN Hai-tao 《控制理论与应用》 北大核心 2025年第8期1615-1624,共10页
When the proton exchange membrane fuel cell(PEMFC)system is running,there will be a condition that does not require power output for a short time.In order to achieve zero power output under low power consumption,it is... When the proton exchange membrane fuel cell(PEMFC)system is running,there will be a condition that does not require power output for a short time.In order to achieve zero power output under low power consumption,it is necessary to consider the diversity of control targets and the complexity of dynamic models,which brings the challenge of high-precision tracking control of the stack output power and cathode intake flow.For system idle speed control,a modelbased nonlinear control framework is constructed in this paper.Firstly,the nonlinear dynamic model of output power and cathode intake flow is derived.Secondly,a control scheme combining nonlinear extended Kalman filter observer and state feedback controller is designed.Finally,the control scheme is verified on the PEMFC experimental platform and compared with the proportion-integration-differentiation(PID)controller.The experimental results show that the control strategy proposed in this paper can realize the idle speed control of the fuel cell system and achieve the purpose of zero power output.Compared with PID controller,it has faster response speed and better system dynamics. 展开更多
关键词 proton exchange membrane fuel cell idle speed control zero power output output power nonlinear model extended Kalman filter observer
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Aerodynamic/control coupling optimization of reentry vehicle under wide speed range
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作者 Lulu Jiang Chao Dong +1 位作者 Xin Pan Gang Chen 《Acta Mechanica Sinica》 2025年第5期65-78,共14页
The high-speed reentry vehicle operates across a broad range of speeds and spatial domains,where optimal aerodynamic shapes for different speeds are contradictory.This makes it challenging for a single-Mach optimizati... The high-speed reentry vehicle operates across a broad range of speeds and spatial domains,where optimal aerodynamic shapes for different speeds are contradictory.This makes it challenging for a single-Mach optimization design to meet aerodynamic performance requirements throughout the vehicle’s flight envelope.Additionally,the strong coupling between aerodynamics and control adds complexity,as fluctuations in aerodynamic parameters due to speed variations complicate control system design.To address these challenges,this study proposes an aerodynamic/control coupling optimization design approach.This method,based on aerodynamic optimization principles,incorporates active control technology,treating aerodynamic layout and control system design as primary components during the conceptual design phase.By integrating the design and evaluation of aerodynamics and control,the approach aims to reduce design iterations and enhance overall flight performance.The comprehensive design of the rotary reentry vehicle,using this optimization strategy,effectively balances performance at supersonic and hypersonic speeds.The results show that the integrated design model meets aerodynamic and control performance requirements over a broader range of Mach numbers,preventing performance degradation due to deviations from the design Mach number,and providing a practical solution for high-speed reentry vehicle design. 展开更多
关键词 Aerodynamic/control coupling Surrogate-based optimization High-speed vehicle Wide speed range HYPERSONIC
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Challenges and suggestions for high-speed boundary layer transition control using surface microstructure
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作者 Jisen YUAN Shenghao YU Zhansen QIAN 《Chinese Journal of Aeronautics》 2025年第4期7-9,共3页
Due to the coexistence of compressibility,viscosity,and threedimensional effects,laminar flow is difficult to maintain for high-speed boundary layer on complex geometries.The unstable disturbance waves in the boundary... Due to the coexistence of compressibility,viscosity,and threedimensional effects,laminar flow is difficult to maintain for high-speed boundary layer on complex geometries.The unstable disturbance waves in the boundary layer are excited and rapidly increase during the receptivity process,so sufficiently large Reynolds stress causes the basic flow velocity profile to change,and the formation of turbulence is inevitable. 展开更多
关键词 high speed boundary layer large reynolds stress transition control surface microstructure unstable disturbance waves CHALLENGES suggestions boundary layer
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LOW COST IMPLEMENTATION OF SPEED SENSORLESS INDUCTION MOTOR CONTROL USING STATOR FLUX ORIENTATION 被引量:2
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作者 李勇 黄文新 胡育文 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2006年第1期34-40,共7页
The control platform of the induction motor (IM) with low costs is developed by using DSP MC56F8013 with a good performance/price rtaio. The control algorithm for the speed sensorless IM is studied based on the stat... The control platform of the induction motor (IM) with low costs is developed by using DSP MC56F8013 with a good performance/price rtaio. The control algorithm for the speed sensorless IM is studied based on the stator flux orientation (SFO). The algorithm structure is simple to be implemented and cannot be influenced by motor parameters, The improved stator flux estimation is used to compensate errors caused by the low pass filter (LPF). A new speed regulator is designed to ensure the system working with the maximal torque in the transient state. The system simulation and the prototype experiment are made. Results show that the con- trol system has good dynamic and static performance. 展开更多
关键词 induction motor stator flux orientation speed sensorless control algorithm
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INDUCTION MOTOR SPEED CONTROL SYSTEM BASED ON FUZZY NEURAL NETWORK 被引量:1
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作者 徐小增 李叶松 秦忆 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2004年第3期195-199,共5页
A fuzzy neural network controller with the teaching controller guidance and parameter regulations for vector-controlled induction motor is proposed. The design procedures of the fuzzy neural controller and the teachin... A fuzzy neural network controller with the teaching controller guidance and parameter regulations for vector-controlled induction motor is proposed. The design procedures of the fuzzy neural controller and the teaching controller are described. The parameters of the membership function are regulated by an on-line learning algorithm. The speed responses of the system under the condition, where the target functions are chosen as I qs and ω, are analyzed. The system responses with the variant of parameter moment of inertial J, viscous coefficients B and torque constant K tare also analyzed. Simulation results show that the control scheme and the controller have the advantages of rapid speed response and good robustness. 展开更多
关键词 induction motor fuzzy neural network vector control speed control system
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Speed Sensorless Vector Control of Induction Motor Based on Reduced Order Extended Kalman Filter 被引量:1
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作者 杨文强 贾正春 许强 《Journal of Southeast University(English Edition)》 EI CAS 2001年第1期41-45,共5页
A speed sensorless vector control system of induction motor with estimated rotor speed and rotor flux using a new reduced order extended Kalman filter is proposed. With this method, two rotor flux components are sele... A speed sensorless vector control system of induction motor with estimated rotor speed and rotor flux using a new reduced order extended Kalman filter is proposed. With this method, two rotor flux components are selected as the state variables, and the rotor speed as an estimated parameter is regarded as an augmented state variable. The algorithm with reduced order decreases the computational complexity and makes the proposed estimator feasible to be implemented in real time. The simulation results show high accuracy of the estimation algorithm and good performance of speed control, and verify the usefulness of the proposed algorithm. 展开更多
关键词 extended Kalman filter flux estimation speed estimation speed sensorless vector control induction motor
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Design of hydraulic motor speed control system based on co-simulation of AMESim and Matlab_Simulink 被引量:1
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作者 孟凡虎 赵素素 +2 位作者 雷晓顺 王娜 高峰 《Journal of Measurement Science and Instrumentation》 CAS CSCD 2016年第3期279-285,共7页
In order to design an effective hydraulic motor speed control system, Matlab_Simiulink and AMESim co-simulation technology is adopted to establish more accurate model and reflect the actual system. The neural... In order to design an effective hydraulic motor speed control system, Matlab_Simiulink and AMESim co-simulation technology is adopted to establish more accurate model and reflect the actual system. The neural network proportion-integration-differentiation (PID) control parameters on-line adjustment is utilized to improve system accuracy, celerity and stability. Simulation results indicate that with the control system proposed in this paper, the system deviation is reduced, therefore accuracy is improved; response speed for step signal and sinusoidal signal gets faster, thus acceleration is rapidly improved; and the system can be restored to the control value in case of interfering, so stability is improved. 展开更多
关键词 speed control system CO-SIMULATION neural network proportion-integration-differentiation (PID) control
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Speed Disturbance in the Diesel Engine Electronic Control System
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作者 刘兴华 张幽彤 《Journal of Beijing Institute of Technology》 EI CAS 2000年第4期387-390,共4页
In order to sample the speed signal of electronic diesel engine in real time and make the engine work reliable, the diesel engine control system's speed acquisition was studied and the problem of speed disturbance... In order to sample the speed signal of electronic diesel engine in real time and make the engine work reliable, the diesel engine control system's speed acquisition was studied and the problem of speed disturbance was solved. The control system was based on the 8?bit electronic control unit(ECU) system and the assembly language was used to design the software for controlling the engine fuel quantity and the turbocharger of the variable geometry turbine for the heavy duty diesel engine. By changing the timing method for speed acquisition, the problem of speed disturbance was solved and the reliability of the ECU was improved. 展开更多
关键词 diesel engine electronic control system speed disturbance
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Application of High-speed Solenoid Valve to the Semi-active Control of Landing Gear 被引量:7
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作者 刘晖 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2008年第3期232-240,共9页
To select or develop an appropriate actuator is one of the key and difficult issues in the study of semi-active controlled landing gear. Performance of the actuator may directly affect the effectiveness of semi-active... To select or develop an appropriate actuator is one of the key and difficult issues in the study of semi-active controlled landing gear. Performance of the actuator may directly affect the effectiveness of semi-active control. In this article, parallel high-speed solenoid valves are chosen to be the actuators for the semi-active controlled landing gear and being studied. A nonlinear high-speed solenoid valve model is developed with the consideration of magnetic saturation characteristics and verified by test. According to the design rule of keeping the peak load as small as possible while absorbing the specified shock energy, a fuzzy PD control rule is designed. By the rule controller parameters can be self-regulated. The simulation results indicate that the semi-active control based on high-speed solenoid valve can effectively improve the control performance and reduce impact load during landing. 展开更多
关键词 landing gear shock absorber semi-active control high-speed solenoid valve
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Intelligent control for large-scale variable speed variable pitch wind turbines 被引量:12
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作者 XinfangZHANG DapingXU YibingLIU 《控制理论与应用(英文版)》 EI 2004年第3期305-311,共7页
Large-scale wind turbine generator systems have strong nonlinear multivariable characteristics with many uncertain factors and disturbances. Automatic control is crucial for the efficiency and reliability of wind turb... Large-scale wind turbine generator systems have strong nonlinear multivariable characteristics with many uncertain factors and disturbances. Automatic control is crucial for the efficiency and reliability of wind turbines. On the basis of simplified and proper model of variable speed variable pitch wind turbines, the effective wind speed is estimated using extended Kaiman filter. Intelligent control schemes proposed in the paper include two loops which operate in synchronism with each other. At below-rated wind speed, the inner loop adopts adaptive fuzzy control based on variable universe for generator torque regulation to realize maximum wind energy capture. At above-rated wind speed, a controller based on least square support vector machine is proposed to adjust pitch angle and keep rated output power. The simulation shows the effectiveness of the intelligent control. 展开更多
关键词 Wind turbines Adaptive fuzzy control Least square support vector machine Variable speed Variable pitch
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PRINCIPLE TO CLOSED LOOP CONTROL DIFFERENTIAL CYLINDER WITH DOUBLE SPEED VARIABLE PUMPS AND SINGLE LOOP CONTROL SIGNAL 被引量:8
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作者 QuanLong NeubertT HelduserS 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2004年第1期85-88,共4页
To control the position of differential cylinder closed loop without usingany throttle elements, a flew idea that two speed variable pumps are used to compensate thenon-symmetric flow of differential cylinder is carri... To control the position of differential cylinder closed loop without usingany throttle elements, a flew idea that two speed variable pumps are used to compensate thenon-symmetric flow of differential cylinder is carried out. According to the leaking property of thesystem, a speed offset principle is also proposed to eliminate the cavitation and tension caused bythe leakage and condensation of oil, which makes the system be in the same state as a valvecontrolled circuit. This principle is explained theoretically and experimentally. Further therelationship that the pressures in cylinder chambers change with load and leakage, and therelationship between biasing speed and pre-load pressures in cylinder chambers are established. Theresearch has proved that the new system has similar technique features as those of controlled withservo valves, but due to the elimination of all the throttle lose the efficiency of system can beimproved greatly. 展开更多
关键词 Electro-hydraulic servo control speed variable pump Differential cylindersystem
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OPTIMAL CONTROL OF AN ACTIVE SUSPENSION SYSTEMEMPLOYING HIGH SPEED ON/OFF SOLENOID VALVE 被引量:4
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作者 Liu Shaojun Zhong Jue +1 位作者 Li Qingchun (College of Mechanical and Electrical Engineering,Central South University of Technology, Changsha 410083, China)HironaoYAMADA YoshikazuSUEMATSU(NAGOYAUniversity Japan) 《Journal of Central South University》 SCIE EI CAS 1997年第2期137-140,共4页
Previous studies have confirmed that an active suspension system with high speed ON/OFF solenoid valves could provide the same vibration isolation efficiency as that of system with pressure proportional valve. In this... Previous studies have confirmed that an active suspension system with high speed ON/OFF solenoid valves could provide the same vibration isolation efficiency as that of system with pressure proportional valve. In this study, by using Linear-quadratic optimization technique and Kalman filter method, an optimal regulator controller with a state observer was designed for the proposed system. Simulation and experimental research was conducted on a quarter car model. The simulation analysis of the system frequency characteristic suggested that the peak value of magnitude response curve in the case of system with an optimal controller would be lowered significantly, and the experiment results also showed that an improvement in the vibration isolation effect was obtained in using the designed optimal controller over the sky hook damper controller. 展开更多
关键词 active SUSPENSION high speed ON/OFF SOLENOID VALVE optimal control
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High Speed On/Off Valve Control Hydraulic Propeller 被引量:13
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作者 ZHU Kangwu GU Linyi +1 位作者 CHEN Yuanjie LI Wei 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2012年第3期463-473,共11页
The work-class remotely-operated-underwater-vehicles(ROVs) are mainly driven by hydraulic propulsion system,and the effeciency of hydraulic propulsion system is an important performance index of ROVs.However,the eff... The work-class remotely-operated-underwater-vehicles(ROVs) are mainly driven by hydraulic propulsion system,and the effeciency of hydraulic propulsion system is an important performance index of ROVs.However,the efficiency of traditional hydraulic propulsion system controlled by throttle valves is too low.Therefore,in this paper,for small and medium ROVs,a novel propulsion system with higher efficiency based on high speed on/off valve control hydraulic propeller is proposed.To solve the conflict between large flow rate and high frequency response performance,a two-stage high speed on/off valve-motor unit with large flow rate and high response speed simultaneously is developed.Through theoretical analysis,an effective fluctuation control method and a novel pulse-width-pulse-frequency-modulation(PWPFM) are introduced to solve the conflict among inherently fluctuation,valve dynamic performance and system efficiency.A simulation model is established to evaluate the system performance.To prove the advantage of system in energy saving,and test the dynamic control performance of high speed on/off valve control propeller,a test setup is developed and a series of comparative experiments is completed.The smimulation and experiment results show that the two-stage high speed on/off valve has an excellent dynamic response performance,and can be used to realize high accuracy speed control.The experiment results prove that the new propulsion system has much more advantages than the traditional throttle speed regulation system in energy saving.The lowest efficiency is more than 40%.The application results on a ROV indicate that the high speed on/off valve control propeller system has good dynamic and steady-state control performances.Its transient time is only about 1 s-1.5 s,and steady-state error is less than 5%.Meanwhile,the speed fluctuation is small,and the smooth propeller speed control effect is obtained.On the premise of good propeller speed control performance,the proposed high speed on/off valve control propeller can improve the effeciency of ROV propulsion system significantly,and provides another attractive ROV propulsion system choice for engineers. 展开更多
关键词 high speed on/off valve fluctuation control pulse-width-pulse-frequency-modulation(PWPFM) hydraulic propulsion system remotely-operated-underwater-vehicle(ROV) energy saving system
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MPC-based path tracking with PID speed control for high-speed autonomous vehicles considering time-optimal travel 被引量:31
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作者 CHEN Shu-ping XIONG Guang-ming +1 位作者 CHEN Hui-yan NEGRUT Dan 《Journal of Central South University》 SCIE EI CAS CSCD 2020年第12期3702-3720,共19页
In order to track the desired path as fast as possible,a novel autonomous vehicle path tracking based on model predictive control(MPC)and PID speed control was proposed for high-speed automated vehicles considering th... In order to track the desired path as fast as possible,a novel autonomous vehicle path tracking based on model predictive control(MPC)and PID speed control was proposed for high-speed automated vehicles considering the constraints of vehicle physical limits,in which a forward-backward integration scheme was introduced to generate a time-optimal speed profile subject to the tire-road friction limit.Moreover,this scheme was further extended along one moving prediction window.In the MPC controller,the prediction model was an 8-degree-of-freedom(DOF)vehicle model,while the plant was a 14-DOF vehicle model.For lateral control,a sequence of optimal wheel steering angles was generated from the MPC controller;for longitudinal control,the total wheel torque was generated from the PID speed controller embedded in the MPC framework.The proposed controller was implemented in MATLAB considering arbitrary curves of continuously varying curvature as the reference trajectory.The simulation test results show that the tracking errors are small for vehicle lateral and longitudinal positions and the tracking performances for trajectory and speed are good using the proposed controller.Additionally,the case of extended implementation in one moving prediction window requires shorter travel time than the case implemented along the entire path. 展开更多
关键词 model predictive control path tracking minimum-time speed profile vehicle dynamics arbitrary path
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Backstepping Control of Speed Sensorless Permanent Magnet Synchronous Motor Based on Slide Model Observer 被引量:10
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作者 Cai-Xue Chen Yun-Xiang Xie Yong-Hong Lan 《International Journal of Automation and computing》 EI CSCD 2015年第2期149-155,共7页
This paper presents a backstepping control method for speed sensorless permanent magnet synchronous motor based on slide model observer. First, a comprehensive dynamical model of the permanent magnet synchronous motor... This paper presents a backstepping control method for speed sensorless permanent magnet synchronous motor based on slide model observer. First, a comprehensive dynamical model of the permanent magnet synchronous motor(PMSM) in d-q frame and its space-state equation are established. The slide model control method is used to estimate the electromotive force of PMSM under static frame, while the position of rotor and its actual speed are estimated by using phase loop lock(PLL) method. Next,using Lyapunov stability theorem, the asymptotical stability condition of the slide model observer is presented. Furthermore, based on the backstepping control theory, the PMSM rotor speed and current tracking backstepping controllers are designed, because such controllers display excellent speed tracking and anti-disturbance performance. Finally, Matlab simulation results show that the slide model observer can not only estimate the rotor position and speed of the PMSM accurately, but also ensure the asymptotical stability of the system and effective adjustment of rotor speed and current. 展开更多
关键词 Permanent magnet synchronous motor(PMSM) slide model observer backstepping control speed sensorless alternating current(AC).
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ADAPTIVE VARIABLE STRUCTURE CONTROLLERS AND APPLICATION TO ENGINE IDLE SPEED CONTROL SIMULATION 被引量:3
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作者 Hui Qing Quyang MinggaoState Key Laboratory of AutomotiveSafety and Energy,Tsinghua University,Beijing 100084, China 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2003年第2期171-174,共4页
A neural-network-based adaptive variable structure control methodology isproposed for the tracking problem of nonlinear discrete-time input-output systems. The unknowndynamics of the system are approximated via radial... A neural-network-based adaptive variable structure control methodology isproposed for the tracking problem of nonlinear discrete-time input-output systems. The unknowndynamics of the system are approximated via radial basis function neural networks. The control lawis based on sliding modes and simple to implement. The discrete-time adaptive law for tuning theweight of neural networks is presented using the adaptive filtering algorithm with residueupper-bound compensation. The application of the proposed controller to engine idle speed controldesign is discussed. The results indicate the validation and effectiveness of this approach. 展开更多
关键词 variable structure control adaptive control neural networks nonlineardiscrete-time systems idle speed control
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Calculation Method of Optimal Speed Profile for Hot Plate During Controlled Cooling Process 被引量:4
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作者 WANG Bing-xing CHEN Xiao-lin TIAN Yong WANG Zhao-dong WANG Jun ZHANG Dian-hua 《Journal of Iron and Steel Research International》 SCIE EI CAS CSCD 2011年第5期38-41,共4页
The healthy and rapid development of the controlled cooling technology was hampered by the uneven cooling phenomenon. During the process of hot plate production,the homogeneous cooling along the length direction of pl... The healthy and rapid development of the controlled cooling technology was hampered by the uneven cooling phenomenon. During the process of hot plate production,the homogeneous cooling along the length direction of plate was constrained by lots of factors. And because the speed was a flexible control parameter,the calculation method of optimal speed profile was developed based on the measured start cooling temperature and its matrix equation was solved by the Cholesky decomposition method. The optimal speed profile was used in online control system. As a result,the temperature distribution along the plate length direction was relatively uniform,and 95% of measured final cooling temperature difference from the target temperature 700 ℃ was controlled within ±20 ℃. 展开更多
关键词 PLATE controlled cooling homogeneous cooling speed profile Cholesky decomposition method
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Research on cubic polynomial acceleration and deceleration control model for high speed NC machining 被引量:11
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作者 Hong-bin LENG Yi-jie WU Xiao-hong PAN 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2008年第3期358-365,共8页
To satisfy the need of high speed NC (numerical control) machining, an acceleration and deceleration (acc/dec) control model is proposed, and the speed curve is also constructed by the cubic polynomial. The proposed c... To satisfy the need of high speed NC (numerical control) machining, an acceleration and deceleration (acc/dec) control model is proposed, and the speed curve is also constructed by the cubic polynomial. The proposed control model provides continuity of acceleration, which avoids the intense vibration in high speed NC machining. Based on the discrete characteristic of the data sampling interpolation, the acc/dec control discrete mathematical model is also set up and the discrete expression of the theoretical deceleration length is obtained furthermore. Aiming at the question of hardly predetermining the deceleration point in acc/dec control before interpolation, the adaptive acc/dec control algorithm is deduced from the expressions of the theoretical deceleration length. The experimental result proves that the acc/dec control model has the characteristic of easy implementation, stable movement and low impact. The model has been applied in multi-axes high speed micro fabrication machining successfully. 展开更多
关键词 High speed NC machining Acceleration and deceleration (acc/dec) control model Cubic speed curve Discrete mathematical model Adaptive acceleration and deceleration control algorithm
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Stability and Hopf Bifurcation of the Maglev System with Delayed Speed Feedback Control 被引量:12
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作者 WANG Hong-Po LI Jie 《自动化学报》 EI CSCD 北大核心 2007年第8期829-834,共6页
The problem of time delay speed feedback in the control loop is considered here.Its effects on the linear stability and dynamic behavior of the maglev system are investigated.It is found that a Hopf bifurcation can ta... The problem of time delay speed feedback in the control loop is considered here.Its effects on the linear stability and dynamic behavior of the maglev system are investigated.It is found that a Hopf bifurcation can take place when the time delay exceeds certain values.The stability condition of the maglev system with the time delay is acquired.The direction and stability of the Hopf bifurcation are determined by constructing a center manifold and by applying the normal form method.Finally,numerical simulations are performed to verify the analytical result. 展开更多
关键词 Maglev system delayed speed feedback control STABILITY Hopf bifurcation center manifold normal form
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