Speed_sensorless_direct_torque_control_of_IMs_with_rotor_resistance_estimation
基于有效磁链观测器的内置式永磁同步电机的无差拍直接转矩控制

基于有效磁链观测器的内置式永磁同步电机的无差拍直接转矩控制文婷;张兴华【摘要】To improve the performance of permanent magnet synchronous motor drive system,a speed-sensorless deadbeat direct torque control (DB-DTC) of interior permanent magnet synchronous motor (IPMSM) was presented.Based on the discrete model of the motor,the deadbeat voltage control law of the torque and flux linkage was derived.By employing a graphical analysis method,the physical meanings of the voltage vector solution were explained clearly.The speed sensorless control of IPMSM was realized by combining the DB-DTC and the speed estimation method which based on the active flux observer.Simulation results verified the effectiveness of the proposed method.%为提高永磁同步电机驱动系统的性能,提出一种无速度传感器内置式永磁同步电机(IPMSM)无差拍直接转矩控制方法.在建立电机离散化模型的基础上,导出了转矩与磁链的无差拍电压控制律.采用图形化辅助解析的方法,直观地表达了无差拍直接转矩控制电压矢量解的物理含义.将无差拍直接转矩控制与基于有效磁链观测器的速度估算方法相结合,实现了IPMSM的无速度传感器控制.仿真结果验证了该方法的有效性.【期刊名称】《电机与控制应用》【年(卷),期】2017(044)005【总页数】5页(P27-31)【关键词】内置式永磁同步电机;无差拍直接转矩控制;空间矢量调制;有效磁链;无速度传感器【作者】文婷;张兴华【作者单位】南京工业大学电气工程与控制科学学院,江苏南京211816;南京工业大学电气工程与控制科学学院,江苏南京211816【正文语种】中文【中图分类】TM351永磁同步电机具有体积小、可控性好、调速范围广和功率因数高等一系列优点,在工业中获得了广泛应用。
ACS880 低压交流驱动器 crane 控制与安全说明书

—LOW VOLTAGE AC DRIVESCrane control and safety with ACS880 drives2LOW VO LTAG E AC D R I V E S B R O CH U R E—Safety. Performance. Efficiency. Speed. Everything countsOverhead cranes need to be carefully designed to operate efficiently and safely whether they are moving containers, buckets of liquid metal, rolls of paper, or waste. You know that every detail matters when selecting crane control for hoist, trolley and long travel movements. Our ACS880 industrial drives with built-in crane control software anda range of safety functions help you achieve excellent crane performance while minimizing your engineering time. Because everything counts.CR A N E CO NTR O L A N D S A FE T Y W ITH AC S880 D R I V E S34LOW VO LTAG E AC D R I V E S B R O CH U R E—ACS880 drives with built-in crane control software Minimizing your engineering timeCrane control highlightsSensorless anti-sway for indoor cranesDamps load sway in trolley and long travel directions at the same time.Mechanical brake controlIntegrated mechanical brake control with crane system check and torque memory.Hoist speed optimizationOptimizes hoist speed in the motor field weakening area.Master/followerDrive-to-drive link allows fast communication between drives in master/follower operation in speed-torque or speed-speed control modes.Synchro controlSynchronizes position of multiple hooks while moving.Direct torque control (DTC)ABB’s signature motor control technology providesprecise speed and torque control.Speed matching and overspeed protectionMakes sure that crane speed is always safe and within desired limits.Brake matchingDetects mechanical brake slips and holds the load electrically in case of brake failure.Smooth liftingDecreases mechanical stress on the bridge and ropes caused by starting to hoist withslack ropes.—The ACS880 product family is available with power range from 0.55 to 5,600 kW andvoltages of 230, 400, 500 and 690 V. Enclosure class options are IP20, IP21 and IP55.SpeedTorqueCR A N E CO NTR O L A N D S A FE T Y W ITH AC S 880 D R I V E S 5Extensive list of add-onsCrane control via I/O and fieldbus interfaces Wide range of interfaces for connecting cranecontrols like joysticks, radio control andpendant controllers.Speed and position feedbackI/O extension modules enable connectingspeed feedback interfaces, like incremental and absolute encoders.Removable memory unitStores the drive’s software and settingsfor fast and easy commissioningand maintenance.Flexible setup and monitoringStart up, configure and monitor your drive with a control panel, computer, or smartphone.ABB Ability™ Condition Monitoring for DrivesAccurate, real-time information about driveevents, and data-based analytics.Virtual realityVirtual commissioning and modellingof the crane behavior.Custom crane solutions with a PLCOur AC500 range of PLCs lets you develop custom crane solutions, even complex oneswith multiple inputs and outputs.Control interface optionsJoystick, pendant controller, wireless radio control, motor potentiometer, or fieldbus.Adaptive programmingFlexibility to add tailored functionality withlogical blocks.Braking optionsDynamic braking/resistors Regenerative braking6LOW VO LTAG E AC D R I V E S B R O CH U R E—Sensorless anti-sway for indoor cranesOperating mechanics of the anti-sway control programLoad sway can occur in trolley and long travelmovements. The ACS880 drive’s anti-sway control program automatically compensates for it when it happens. The control program creates a mathematical model of the crane’s pendulum.It estimates the pendulum’s time constant by continually measuring the hoist position andload properties, and then factors in the swing velocity and angle. When the operator changes the speed of the crane’s travel, the drive instantly recalculates the required speed reference to compensate for the crane’s speed change, preventing the load from swaying.Stationary Accelerating Constant speed Decelerating StationaryKey benefits of anti-sway control• Improves productivity by letting the crane operator fully focus on moving the goods rather than manually controlling the sway.• Lowers the risk of accidents and damage to the load caused by uncontrolled sway.• Built into the drive. Works without external anti-sway sensors and trolley/long travel motor encoders.• Works simultaneously with bridge and trolley movements in diagonal runs.—The drives communicate with each other via a D2D link. The hook position can also be transmitted with fieldbus or analog communication.CR A N E CO NTR O L A N D S A FE T Y W ITH AC S 880 D R I V E S 7ACS880 crane control software (+N5050)Application I/O board—Certified safety solutionsThe safe torque off (STO) safety function comes integrated into ACS880 drives. Optional safety functions modules (FSO-12 and -21) provide an easy way to extend safety functions. This plug-in module is installed and cabled inside the drive, enabling safety functions and diagnostics in one compact and reliable module.Both safety functions modules have SIL 3/PL e capability and conform to the European Union Machinery Directive 2006/42/EC. The safety functions modules are certified by TÜV Nord. You can enable PROFIsafe over PROFINET connectivity between your ACS880 drive and the safety PLC by adding a PROFIsafe fieldbus adapter module to your drive.Inside the FSO-12/FSO-21: • Safe stop 1 (SS1)• Safe stop emergency (SSE) • Safe brake control (SBC) • Safely limited speed (SLS) • Safe maximum speed (SMS)• Prevention of unexpected startup (POUS)Additional safety functions inside the FSO-21:• Safe direction (SDI), requires a safety pulse encoder interface module FSE-31• Safe speed monitor (SSM)When even more is neededThe AC500-S safety PLC offers a flexible platform for extending crane safety even further. In crane systems with several ABB drives, the AC500-S safety PLC can control the overall crane safety system, activating the drive-based safetyfunctions over PROFINET/PROFIsafe.How it’s all connected—01 Safety functionsmodules FSO-12, FSO-21 and safety pulse encoder module FSE-31—02 AC500-S Safety PLC—01—02Certified safety optionsDrive composer prosoftware toolCrane control configurationSafetyconfiguration3A U A 0000157591 R E V C E N 04.04.2018© Copyright 2018 ABB. All rights reserved.Specifications subject to change without notice.—For more information, please contact your local ABB representative or visit /drives/cranes /drivespartners。
基于静态补偿电压模型的改进转子磁链观测器

基于静态补偿电压模型的改进转子磁链观测器宋文祥;阮智勇;尹赟【摘要】为解决纯电压模型磁链观测器存在的积分漂移和饱和问题,常采用低通滤波器代替纯积分器.针对传统低通滤波器磁链观测方案的不足,本文提出一种改进的转子磁链观测方案,采用串联低通滤波器提取直流偏置得到理想的转子反电势,然后用可编程低通滤波器代替纯积分器,并在反电势低通滤波前补偿磁链误差.所提出的观测器可以有效消除直流偏置的影响,提高磁链观测的动态精度并改善系统的动态性能.在一台2.2kW感应电机无速度传感器矢量控制系统上对本文提出的改进转子磁链观测器方案进行了仿真和实验研究,结果验证了其正确性和有效性.%In the pure voltage model based flux observer, a LPF is normally used to replace the pure integrator to a-void integration drift and saturation problems. In order to eliminate the DC offset efficiently and compensate the error brought about by LPF as well as improve the dynamic performance, a modified rotor flux observer is proposed in this paper. In the proposed scheme, series LPF is used to remove the DC drift firstly, then a programmable LPF is used instead of the pure integrator, and the amplitude and phase error is compensated before the back EMF filtered for the flux estimation. Simulation and experiment based on induction motor speed sensor-less vector control systems verified its correctness and effectiveness.【期刊名称】《电工电能新技术》【年(卷),期】2012(031)004【总页数】5页(P19-23)【关键词】磁链观测器;电压模型;低通滤波器;直流偏置;矢量控制【作者】宋文祥;阮智勇;尹赟【作者单位】上海大学机电工程与自动化学院,上海200072;上海大学机电工程与自动化学院,上海200072;上海大学机电工程与自动化学院,上海200072【正文语种】中文【中图分类】TM343感应电机矢量控制和直接转矩控制系统中,准确观测磁链是获得高性能控制的关键。
基于TMS320F2808直接转矩控制系统的硬件设计实现

PE 电力电子年第期66基于TMS320F2808直接转矩控制系统的硬件设计实现高万兵1任一峰1王忠庆1赵敏2(1.中北大学,太原030051;2.北京茨浮测控技术研究所,北京101101)摘要本文采用TMS320F2808芯片作为控制核心,完成了一个全数字化直接转矩控制硬件系统,克服了采用TMS320F2407A 和TMS320F2812DSP 作为直接转矩控制系统的处理器所存在的缺点,给出了电流、电压检测电路。
实验结果表明,该系统作为无速度传感器直接转矩控制策略的硬件平台,具有抗干扰能力强,电流电压保护措施良好,体积小,软件可移植性强等特点。
关键词:直接转矩控制;TMS320F2808;电流电压检测;无速度传感器Hardware Design Implementation of Direct TorqueControl System Based-on TMS320F2808Gao W anbing 1Ren Y ifeng 1W ang Zhongqing 1Zhao Min 2(1.North University of China,Taiyuan 030051;2.Academy of Beijing Servo Technology,Beijing 101101)Abstr act In this paper,TMS320F2808is used as a master chip.A fully digital direct torque control of hardware systems is finished.The existence of disadvantage is overcome about TMS320F2407A and TMS320F2812DSP which is used as direct torque control system processors.The current detection circuit and voltage detection circuit is presented.The experimental results show that the system as a speed sensorless direct torque control strategy of the hardware platform,has anti-interference ability,good current and voltage protection measures,small size,strong software portability and so on.Key words :direct torque control ;TMS320F2808;current and voltage detection ;sensorless drives1引言异步电动机直接转矩控制技术是继矢量变换控制技术之后,于20世纪80年代中发展起来的一种新型的高性能的控制技术。
TI TIDA-00916民用无人机电子速度控制(ESC)参考设计

TI公司的TIDA-00916是用于无人驾驶飞机电子速度控制(ESC)的无传感器高速磁场定向控制(FOC)参考设计,提供最好的FOC算法,以达到更长的飞行时间,更好的动态范围,更高的集成度,更小的板尺寸和更少的BOM元件.采用3颗LiPo电池速度高达12000RPM.主要用在无人驾驶飞机和UAV,高速马达和电池动力的电动工具.本文介绍了参考设计TIDA-00916主要特性,框图,无人驾驶飞机系统主要指标以及电路图和材料清单.ESC modules are important subsystems for non-military drones andusers demanding more efficient models that provide longer flight timesand higher dynamic behavior with smoother and more stable performance. This design implements an Electronic Speed Controller (ESC) commonlyused for unmanned aerial vehicles (UAV) or drones.The speed control is done sensorless, and the motor has been tested up to 1.2 kHz electrical frequency (12kRPM with a 6 pole pair motor), using FOC speed control. Our high-speed sensorless-FOC reference design for Drone ESCs provides best-in-class FOC algorithm implementation toachieve longer flight time, better dynamic performance and higherintegration, resulting smaller board size and fewer BOM components.Sensorless high speed FOC control using TI’s FAST™ software observerleveraging InstaSPIN-Motion™ C2000™ LaunchPad and DRV8305BoosterPack.图1:无人驾驭飞机示意图参考设计TIDA-00916主要特性:InstaSPIN-FOC™ sensorless FOC achieves highest dynamic performance. Tested up to 12,000 RPM with 3 LiPo cellsHigh dynamic performance: 1 kRPM to 10 kRPM (electrical frequency 100 Hz to 1 kHz) speed in <0.2 s to provide high performance yaw and pitch movementFast speed reversal capability for roll movementLonger flight time due to improved efficiency of FOC over blockcommutationHigher PWM switching frequency, tested up to 60 kHz to reducecurrent/torque ripple with low inductance / high-speed motors, and to avoid interference with ultrasonic sensorsTI TIDA-00916民用无人机电子速度控制(ESC)参考设计Fast time-to market due to InstaSPIN-FOC’s automatic motor parameter identification: auto-tuning sensorless FOC solutionMotor temperature estimation from winding resistance changes to protect motor from damage during temporary overload conditions参考设计TIDA-00916应用:Drones and UAVs High-Speed MotorsBattery-Operated Power Tools图2:参考设计TIDA-00916完整系统外形图(顶视图)图3:LaunchPad 板外形图(顶视图)图4:无人驾驶飞机电子速度控制(ESC)框图图5:无人驾驶飞机系统模块图无人驾驶飞机系统主要指标:图7:LAUNCHXL-F28069M电路图(2)图8:LAUNCHXL-F28069M电路图(3)图9:LAUNCHXL-F28069M电路图(4)图UNCHXL-F28069M电路图(5))图UNCHXL-F28069M电路图(6)图12:LAUNCHXL-F28069M电路图(7)图13:MDBU003A电路图。
Sensitron半导体组件说明书

Transient Voltage SuppressorsMotor ControllersHAUPPAUGE, NY DEER PARK, NYThree Phase Full Wave Bridge Rectifiers, SBR Series·High voltage: available up to 1400V·Current range from 45A to 250A·Designed for harsh environments and wide temperature range (-65o C to 150o C)· 1.5kV to 2.5kV AC isolation to baseplate·Low VF, low thermal impedance, direct mount to heatsink·Light weight, designed for commercial aircraft applications·Extreme temp cycling capabilityOptional fuse links and TVSHigh Power Prime Power Rectification YOUR POWER SOLUTIONS PROVIDER*******************+1 (631) 586-7600O FFERING:RIDGES1000V, 150A 600V, 200AFully Integrated Analog 3Ph BLDCMotor ControllersSMC6, SMCT6, SMCS6 Series·Designed for applications startingfrom 800W·Up to 1200V, 150A·Hermetic & non-hermetic available·Speed, sensorless & torquecontrollers3Ph Digital Motor Controllers, SMCV & SECV Series·20A to 100A, 100V to 1200V·Field oriented control for smoother torque at low speed, betterefficiency at high speed·Near sinusoidal phase current for lower noise, smoother torque·Program for speed, torque or sensorless control·Top speed over 70,000 RPM (4 pole)·Easy to use GUI Configuration Utility·Interface by RS-232 or CAN·Reconfigurable firmware·Re-configurable firmware. Isolated interface provides feedbackEvaluation Boards for Motor Controllers·Provides the controller module witheasy connections, input caps & more·Options for resolver, brake switch·Connections for hall sensor inputs·Allows customer to evaluatecontrollers easily, or to support rapidprototype/system developmenttesting ahead of productionLow Cost, High Power Density ControllerOpen Frame Configuration·Low cost, open module construction·High power density, ~2KW per oz.·Available in 600V/20A, 100V/80A·Full load efficiency above 95%·Single supply·Lightweight. easy connections·Package size: 2.5” x 2.1” x 0.65”, 1oztotal weightFully Integrated BLDC Motor ControllersIntelligent DriveBridge & Drivers•Complete FET or IGBT3ph power stage•Drivers•Fault, sense, report ckts•Isolated interfacePower Bridge3ph and H-Bridge Modules•MOSFET•IGBTs w/Diodes•SiC FETs, Diodes•Brake switches•Temp senseControllerComplete Controller•Speed, Torque,Sensorless Control•Drivers•Complete FET or IGBT3ph power stage•Isolated interface &fault, sense, reports•Enclosure optionsIntegratedAssemblyComplete LRU•Input & EMI filters•Controller•Drivers•3ph power stage•Isolated interface &fault, sense, reports•Enclosure options•Interface options YOUR POWER SOLUTIONS PROVIDERThree Phase IGBT Bridge with Brake IGBT, 3Ph Half Controlled Bridge with Inrush SCR, SCM1001 · 1,200V, 150A, three-phase IGBT bridge · 1,200V, 57A SCR Half-Controlled Bridge with 63A diodes · Upper and lower regenerative brake IGBT switch · Next generation IGBT and diodes to minimize total losses· AlSiC base plate for high temperature cycling capability· Low profile, light weight package, near-hermetic constructionHigh Power Half-Bridge IGBT Module, SCP-5115i· 600V, 1200A· IGBTs and diodes · Creepage & clearance for altitude · Minimized & matched stray inductances · -55o C to 150o C · Package size: 4.5” x 3.6”Motor Controllers, Modules & AssembliesIntelligent Power Modules SPM6 Series · MOSFETs: 100V to 600V, Up to 150A · IGBTs: 600V to 1200V, Up to 140A· Most have isolated signal I/O· Most report baseplate temp ¤t · Most have overtemp, overcurrent, and de-saturation protection· -40o C to 150o C operating3Ph BLDC Motor Controller in Open Frame Assembly Includes all features of the SMC or SMCV Series, plus: · Small p ackage: 3.84” x 4.19” max x 1.74” max · Light weight: 20 oz. · Overvoltage and under-voltage shutdown · EMI filter to DO-160 & aux power supply · Intended for UAV, aircraft and military applications· Rugged design intended to drive fans, pumps,compressors3-Ph IGBT Bridge w/ Gate DriverSBM Series · IGBTs: 600 to 1200V, Up to 250A ·Overtemperature, UVLO, and desaturation protection ·2500V isolation to baseplate· -40o C to 150oC operatingLightweight Three Phase (IGBT or MOSFET) Power Bridge Modules, SPx10xx Series · Lightweight, fully isolated package · Si or SiC · High voltage up to 1200V, 15A to 150A · Designed for harsh environments and wide temperature range (-65o C to 175o C) · Available with high performance baseless format, or with a choice of baseplate materialsSECV Motor Control Boxes/Enclosures · IP/NEMA enclosures or open frame available· Input and MIL-STD-461/DO-16 EMI filters· Digital controller provides:▪ FOC w/Space Vector PWM ▪ Reconfigurable firmware ▪ Sensor (hall or resolver), sensorless, or torque control ▪ Serial digital interface for control and monitoring · Contact factory for analog controller options YOUR POWER SOLUTIONS PROVIDERMulti-Channel SSPCDiamondback Series, 16 Ch · 16 programmable channels· Paralleling of like channel groups · 8x5A, 3x15A, 5x25A· Up to 210A of total current· CAN Interface (up to 1Mbaud) J1939 ·Measurements include: output currents, input & output voltages, board temperature Features/ Benefits✓ Save weight and size compared to electromechanical designs✓ Solid State Reliability✓ True I 2t and Instant Trip Protection✓ Software and hardware current rating programmability✓ Accurate Current, Temperature and Voltage Measurements✓ Isolated Discrete or serial interface controls and load monitoring✓ SSPC combine protection, remote control and health monitoring functionalitiesMulti-Channel SSPC Diamondback Series, 32 Ch · 32 programmable channels· Paralleling of like channel groups · 8x8A, 12x7A, 12x6A,32x10A · Up to ~300A of total current· CAN Interface (up to 1Mbaud) J1939 ·Measurements include: output currents, input & output voltages, board temperatureMulti-Channel SSPC Boa Series, 2 Ch, 4 Ch· Highest current smart power module in the industry·Two or Four Individual Channels Programmable to 100A, up to 200A with Channel Paralleling· Total Current up to 400 amps · 28VDC-derived auxiliary power ·J1939 CAN bus communicationsMilitary Ground Vehicles Unmanned Aerial Vehicles Marine VesselsTest & Industrial EquipmentCommunication & Command Centers Energy Exploration Equipment Off Highway and Heavy Duty Vehicles Medical Emergency VehiclesSolid State Power Management *******************+1 (631) 586-7600YOUR POWER SOLUTIONS PROVIDER170Vdc/ 115VAC Module: SPD8A115 · 115VAC, 8A· True I 2t instant trip protection· 2-pole operation with 500V isolation between poles · Small footprint epoxy shell construction · Cross-trip, overtemp, TVS protectionSingle Channel SSPCs· 5:1 programming range for 28V · True I 2T with thermal memory· No heat sinking or cooling required· SPDPXXD28 Series : Up to 50A, 28V ultra small size, occupying ~57% of industry standard PCB space. Low weight, 30 grams (~1.1 oz)· SPDPXXD270 & SPDPXXD375: Up to 50A, 270V & 375V high voltage modules. 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Proven solutions for tough environments– 100 % surge testing!Space Diode Arrays, SDA Series· Up to 400V, 1A space level diode array · Devices are serialized· Die manufactured on qualified JANS line· Quality Conformance Inspection (QCI) in accordance with MIL-PRF-38534 is performed on each lot · Add suffix “S” for screening per MIL -PRF-38534, Class H· Add suffix “SS” for Space Level Screening per MIL -PRF-38534, Class KSpace TVS Arrays, STB Series · L ow capacitance, 500W capability for 8/20 μs repetitive pulses, 100% tested for clamp performance · 8 channel hybrid in a hermetic package, saves board space · S older temperature, 10s @260o C · A dd suffix “SS” for Space Level Screening per MIL -PRF-38534, Class K Drop in replacements for industry standard product in any package · Available screened up to JANS equivalentApplications/Markets:∙ Navigation and Guidance Systems ∙ Electrical Power System ∙ Solar Arrays∙ Power Conditioning∙ Satellites Power Distribution ∙ Orbit ControlSDA1009SSSDA1001SS SDA1009SSSDA1002SS SDA1003SSSDA1004SSSDA1005SS SDA1006SS SDA1008SSSpace Level Solutions *******************+1 (631) 586-7600YOUR POWER SOLUTIONS PROVIDERThe Sensitron Advantage:✓ Sensitron has supplied Axial & MELF diodes to the space market for over 15 years.✓ Sensitron is among the largest suppliers of Space Level Diodes, and has among the largest portfolios of Space LevelRectifiers, Zener Diodes, Transient Voltage Suppressors, and Switching Diodes in the world, having shipped over 3 million JANS and JANS-equivalent diodes to space applications.✓ Qualified per JANTXV/JANS on twenty (20) MIL-PRF-19500 slash sheets, encompassing over 250 JANS partnumbers, with more coming every quarter!✓ Additional cost savings for our customer comes from our standard process flow:o All parts are Hot Solder Dipped, therefore there is no need to send Sensitron diodes to a third party plating house or to pay a manufacturer for “special plating services”o No tags are used to serialize our JANS components, eliminating the need for tag removal and cleaning o These savings typically translate into a $3 - $7.00 price savings per device!QPL Product: JANTXV/JANS, JANHC/JANKC *******************+1 (631) 586-7600YOUR POWER SOLUTIONS PROVIDERHigh Reliability Hermetic DiscretesPower Rectifiers• Miniature power surface mount package • Low thermal resistance • High current•MIL-PRF-19500 Screening and QCI available *******************+1 (631) 586-7600SiC Schottky Rectifers & MOSFETs• SiC Schottky Rectifiers: Up to 1200 V • SiC Schottky MOSFETs: Up to 2500 V• No recovery time or reverse recovery losses •Mil/Space level screening options available • Surface mount packages- diopak, LCC, etc • Thru hole in TO-25x packages1N5822DP Schottky Rectifier• Rugged package and connections• Copper termination’s abili ty to flex eliminates strain and thermal fatigue • MIL-PRF-19500 screening and QCI available • Fits on 1N5822US footprintPower Rectifier in a Dual Die Series Redundant Configuration• Dual die design for fault tolerance • Hermetic, non-cavity glass package • Category I Metallurgically bonded • Hot solder dipped finish•SJ/SX/SV/SS screening available per equivalent flow of JAN/JX/JXV/JANSSMD-0.2, 0.5 High Strength Package, Patented Design• Sensitron patented rugged package design• Enhanced temp/power cycling capability over standard SMD package • Package and PCB Temperature cycling verification complete •Lid to pad connection optionsYOUR POWER SOLUTIONS PROVIDERSchottky Rectifier Discretes• Available Voltages: 15 to 200V • Ultralow leakage current for 100 & 150V • 200°C process • Low forward voltage drop • Drop in replacements for industry standard product in any packageHigh Reliability Hermetic Discretes and Assemblies *******************+1 (631) 586-7600MOSFET S• MOSFET Modules • 3 phase bridges• Full and half bridges• N-Channel - 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长城汽车故障码大全

monitoring of neutral position (Unwanted gear actuator movement of fork 1/5) 1/5挡拨叉中位电流错误 monitoring of neutral position (Unwanted gear actuator movement of fork 3/7) 3/7挡拨叉中位电流错误 monitoring of neutral position (Unwanted gear actuator movement of fork 2/6) 2/6挡拨叉中位电流错误 monitoring of neutral position (Unwanted gear actuator movement of fork 4/R) 4/R挡拨叉中位电流错误 gear actuator movement from gear 1 towards N without triggering ACS valve 挡位非预期由1挡变为N挡 gear actuator movement from gear 2 towards N without triggering ACS valve 挡位非预期由2挡变为N挡 gear actuator movement from gear 3 towards N without triggering ACS valve 挡位非预期由3挡变为N挡 gear actuator movement from gear 4 towards N without triggering ACS valve 挡位非预期由4挡变为N挡 gear actuator movement from gear 5 towards N without triggering ACS valve 挡位非预期由5挡变为N挡 gear actuator movement from gear 6 towards N without triggering ACS valve 挡位非预期由6挡变为N挡 gear actuator movement from gear 7 towards N without triggering ACS valve 挡位非预期由7挡变为N挡 gear actuator movement from gear R towards N without triggering ACS valve 挡位非预期由倒挡变为N挡 no gear actuator movement towards gear1 1挡挂挡失败
基于Ansoft的永磁同步电动机启动过程仿真研究_万红波

less, 绕组为铜 , 定子槽采用梨形槽 , 永 磁体材料采 用 NdFe35.电动机
结构尺寸等基本参数见表 1。
表 1 PMSM主要结构参数 Tab.1 MajorStructuralParametersofPMSM
参 数
数 值 参 数
定子外径 /mm
120 永磁体切向厚度 /mm
定子内径 /mm
Ansoft公司推出的 Maxwell2D电磁场分析软件不仅具 有完善的 静态电磁场分析功能 , 对瞬变电磁场的分析同样卓越 , 具有 强大的后 处理功能 , 这就为开关 磁阻电 动机 参数 的计算 提供 了一 个方 便、快 捷 、准确的计算工具 。
Ansoft软件相对于其他软件有许多新的特点和优势 [ 5] :一是该软 件具有许多开发成熟的电机模 型, 多 数电机都可以 在库中找到 , 给使 用者带来极大的方便 ;二是该软件设 计的电机驱动 电路部分 , 与电机 模型连在一起进行仿真 , 提出了一个 整体分析的思 想;三 是模型建立 后 , 可以输入需要优化的参 数, 软 件可以灵活进 行优化设计 。 本文采 用 Ansoft公司的 Maxwell2D瞬态模块对永磁同步电动机进行建模 , 加 载三相交流电源, 就可以进行汽车永磁同步电机启动性能的仿真研究。
4.2 空载启动转速 、启动转矩和启动电流仿真结果 空载启动转速随时间的变化 曲线仿真 结果如图 7 所示 , 可 以看
· 65·
拖拉机与农用运输车 第 2期 2009年 4月
出 :电机大致 在 0.10 s左右达到 了同步速 , 显然在不同 的时刻必将 得到一族速度曲线图 , 而且启动到 0.012 s时的凸点与脉振转矩在牵 入同步速附近所发生的振荡有关 。
由于异步启动是启动永磁同步电动机的常用方法 , 但电机交 、直 轴磁路磁导不相等以及永磁体 的存在 , 给 启动过程 的计算分 析带来 了困难 。 若启动绕组设计不当 , 即使电机运行性能很好 , 也可能使电 机不能牵入同步运行 [ 4] 。
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Speed sensorless direct torque control of IMswith rotor resistance estimationMurat Barut a ,Seta Bogosyanb,*,Metin GokasanaaDepartment of Electrical and Electronic Engineering,Faculty of Engineering,Istanbul Technical University,Maslak,34390Istanbul,TurkeybDepartment of Electrical and Computer Engineering,University of Alaska,P.O.Box 750145,Fairbanks,AK 997750145,USAReceived 17January 2004;accepted 29April 2004Available online 2July 2004AbstractDirect torque control (DTC)of induction motors (IMs)requires an accurate knowledge on the ampli-tude and angular position of the controlled flux in addition to the information related to angular velocity for velocity control applications.However,unknown load torque and uncertainties related to stator/rotor resistances due to operating conditions constitute major challenges for the performance of such systems.The determination of stator resistance can be performed by measurements,but methods must be developed for estimation and identification of rotor resistance and load torque.In this study,an EKF based solution is sought for determination of the rotor resistance and load torque as well as the above mentioned states required for DTC.The EKF algorithm used in conjunction with the speed sensorless DTC is tested under eleven scenarios comprised of various changes made in the velocity reference beside the load torque and rotor resistance values assigned in the model.With no a priori information in the estimated states and parameters,it has been demonstrated that the EKF estimation and sensorless DTC perform quite well in spite of the uncertainties and variations imposed on the system.Ó2004Elsevier Ltd.All rights reserved.Keywords:Induction motor;Extended Kalman filter;Sensorless direct torque control;Load torque and rotor resistanceestimationEnergy Conversion and Management 46(2005)335–349/locate/enconman*Corresponding author.Tel.:+1-907-475-2755;fax:+1-907-475-5135.E-mail address:s.bogosyan@ (S.Bogosyan).0196-8904/$-see front matter Ó2004Elsevier Ltd.All rights reserved.doi:10.1016/j.enconman.2004.04.002336M.Barut et al./Energy Conversion and Management46(2005)335–3491.IntroductionHigh efficiency control and estimation techniques related to induction motors(IMs)have been finding more and more application with Blaschke’s well-knownfield oriented control(FOC) method,established in1971.There has been an extensive amount of work to improve the dynamic response and reduce the complexity of FOC methods.One such technique is the direct torque control(DTC)method developed by Takahashi in1984[1],which has been getting increased attention due to the improved dynamic performance and simplified control strategy that it offers with respect to the FOC methods.The DTC method involves the direct choice of the appropriate/optimum switching modes,in order to keep theflux and torque errors within a predetermined band limit(in a hysteresis band) [2].The errors are defined as the difference between the reference and the measured/estimated values offlux and torque.Unlike FOC methods,DTC techniques require utilization of hysteresis band comparators instead offlux and torque controllers.To replace the coordinate transfor-mations and pulse width modulation(PWM)signal generators of FOC,DTC uses look-up tables to select the switching procedure based on the inverter states.However,both methods require accurate knowledge of the amplitude and angular position of the controlledflux(with respect to the stationary stator axis)in addition to the angular velocity for velocity control applications. As is well known,speed sensors like tachometers or incremental encoders increase the size and cost of systems unnecessarily.Similar problems arise with the addition of search coils or Hall effect sensors to the motor for measurement of theflux,hindering functionality in terms of implementation.Thus,to improve overall system performance,state estimators or observers are usually more preferable than physical measurements.However,thefifth order and nonlinear structure of the IM model[3],in addition to the sensitivity of the system parameters to tem-perature[4]and frequency[5],makes the design of observers for IMs a challenge.In this regard, for high performance sensorless vector control of IMs,it is essential to know the temperature and frequency dependent variation of the stator and rotor resistances in addition to the load torque.In a study addressing this issue[6],it has been stated that simultaneous estimation of the stator and rotor resistances gives rise to instability.Moreover,while the value of the stator resistance could be obtained by measuring the stator temperature,there are physical difficulties in determining the rotor resistance in a squirrel cage IM.Thus,estimating the rotor resistance and the load torque appears to be a reasonable approach.In DTC,theflux is conventionally obtained from the stator voltage model,using the measured stator voltages and currents.This method,utilizing open loop pure integration suffers from the well known problems of integration effects in digital systems,especially in the low speed operation range[7],even with the correct knowledge of the stator resistance.Moreover,it will require the rotor angular velocity for velocity control applications.Among the recent studies conducting simultaneousflux and velocity estimation for DTC,Ref.[8]studied the sensitivity to parameter variations with an artificial neural network approach,and a robust performance to50%variations in the stator resistance has been obtained in Ref.[9]with a sliding mode approach,while the adaptiveflux observer in Ref.[10],the extended Luenberger observer in Ref.[11]and the non-linear observer in Ref.[12]demonstrate robustness to step shaped load torque variations.Among studies using model reference adaptive laws,in Ref.[13],theflux and speed have been estimated, but the system response to load torque variations was not tested.In Ref.[14],the rotor velocity,x m,stator resistance,R s and rotor resistance R0r are individually estimated,and good results areobtained.However,in one of the trials where x m together with R0r and in another where x m,R0rand R s are estimated together,it has been stated that the resistances converge to inaccurate values. Moreover,no tests have been performed to test the effects of the load torque variations. Finally,in Ref.[6],the angular velocity and slip frequency,x r(reflecting the effect of the load torque)in addition to the rotor resistance have been taken into account starting with the initialvalue of R0r ð0Þ¼0:85R0r n.There are also extended Kalmanfilter(EKF)applications in the literature,taking a stochastic approach to solution of the problem.Unlike the other methods,the model uncertainties and nonlinearities inherent in IMs are well suited to the stochastic nature of EKFs[15].With this method,it is possible to make an online estimation of states while simultaneously performing identification of parameters in a relatively short time interval[16–18],also while taking system/ process and measurement noises directly into account.This is the reason why the EKF has found wide application in sensorless control of IM’s,in spite of its computational complexity.In the EKF based previous DTC studies,Ref.[19]estimates the statorflux components and velocity under the assumption of a known load,while in Ref.[20],the velocity is estimated as a constant parameter,avoiding the use of the equation of motion.In spite of an improved performance in the steady state,this approach has given rise to a significant observer error in the velocity during the transient state.The major contribution of this study is the development of an EKF based speed sensorless DTC system that achieves robustness to variations in rotor resistance and load torque,the uncertainties that are known to deteriorate system performance.It is thefirst known study to perform the estimation of load torque and rotor resistance simultaneously while also estimating the statorflux components,angular velocity and stator current components,also measured as output.The performance of the estimation and control schemes is tested with challenging vari-ations of the load torque,rotor resistance and velocity reference.The consideration of the load torque as a constant term in the estimation algorithm aims to capture other uncertainties besides the load torque that have a very slow or almost constant variation with time,i.e.viscous and Coulomb friction(in steady state).The results obtained through simulations under various challenging tests demonstrate the good performance of the estimation scheme requiring no a priori information on the states with their initial values taken as zero.2.Extended mathematical model of the IMThe sensorless DTC scheme developed for an IM requires estimation of the statorflux com-ponents,ws a ,ws b,angular velocity,x m and stator current components i s a and i s b,which are alsomeasured as output.In this study,due to the degrading effect of their unknown variations oncontrol performance,the load torque,t L and the rotor resistance,R0r (as referred to the stator side)are also included in the extended state vector as constant states based on their slow variation in time.Thus,the so-called extended model can be obtained(as referred to the stator stationary frame)in the following form:_x e ðtÞ¼feðx eðtÞ;u eðtÞÞþw1ðtÞ¼A eðx eðtÞÞx eðtÞþB e u eðtÞþw1ðtÞð1ÞM.Barut et al./Energy Conversion and Management46(2005)335–349337Here,the extended state vector x e ,representing the estimated states and parameters,consists of i s a ,i s b ,w s a ,w s b ,x m ,t L and R 0r ;f e is a nonlinear function of the states and inputs;A e is the system matrix;u e is the control input vector;B e is the input matrix;and w 1is process noise.The constant state representing the load torque is also designed to capture system uncertainties of constant nature once steady state is attained.In this study,those uncertainties are limited to viscous friction,as this was the only uncertainty included in the model simulating the system.With the above consideration,the extended model of an IM can be given as_i s a _i s b _w s a _w s b _x m _t L _R 0r 2666666666437777777775|fflfflffl{zfflfflffl}_xe ¼ÀR s r þR 0r L s 0r r Àp p x m R 0r0r r p p x m r 000p p x m ÀR s L r þR 0r L s L 0r L r Àp p x m L r R 0r L 0r L r 000ÀR s 0000000ÀR s 00000À3p p L w s b 3p p L w s a 000À1L 000000000000000266666666664377777777775|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}A ei s a i s b w s a w s b x m t L R 0r 26666666643777777775|fflfflffl{zfflfflffl}x e þ1r 001r 100100000026666666643777777775|fflfflfflfflffl{zfflfflfflfflffl}Bev s a v s b |fflffl{zfflffl}u e þw 1ðt Þð2ÞZ ðt Þ¼h e ðx e ðt ÞÞþw 2ðt Þðmeasurement equation Þ¼H e x e ðt Þþw 2ðt Þ¼10000000100000 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}H ei s a i s b w s a w s b x m t L R 0r26666666643777777775þw 2ðt Þð3Þwhere h e is a function of the outputs;H e is the measurement matrix;w 2is measurement noise;p p is the number of pole pairs;L r ¼r L s is the stator transient inductance;r is leakage or coupling factor;L s and R s are the stator inductance and resistance,respectively;L 0r and R 0r are the rotor inductance and resistance,referred to the stator side,respectively;v s a and v s b are the stator sta-tionary axis components of the stator voltages;w s a and w s b are the stator stationary axis com-ponents of stator flux;and x m is the angular velocity.3.Development of the EKF algorithmAn EKF algorithm is developed for estimation of the states in the extended IM model given in Eqs.(2)and (3)to be used in the sensorless direct torque control of the IM.The Kalman filter (KF)is a well known recursive algorithm that takes the stochastic state space model of the system into account,together with measured outputs,to achieve the optimal estimation of states [21]in multi-input,multi-output systems.The system and measurement noises are considered to be in the338M.Barut et al./Energy Conversion and Management 46(2005)335–349form of white noise.Optimality of the state estimation is achieved with minimization of the covariance of the estimation error.For nonlinear problems,the KF is not strictly applicable since linearity plays an important role in its derivation and performance as an optimalfilter.The EKF attempts to overcome this difficulty by using a linearized approximation where the linearization is performed about the current state estimate[22].This process requires the discretization of Eqs.(2) and(3)x e ðkþ1Þ¼feðx eðkÞ;u eðkÞÞþw1ðkÞð4ÞZðkÞ¼He xeðkÞþw2ðkÞð5ÞAs mentioned before,the EKF involves the linearized approximation of the nonlinear model(Eqs.4and5)and uses the current estimation of states^xe ðkÞand inputs^u eðkÞin the linearizationby usingF e ðkÞ¼o feðx eðkÞ;u eðkÞÞo x eðkÞ^xeðkÞ;^ueðkÞð6ÞF u ðkÞ¼o feðx eðkÞ;u eðkÞÞo u eðkÞ^xeðkÞ;^ueðkÞð7ÞThus,the EKF algorithm can be given in the following recursive relations:NðkÞ¼FeðkÞPðkÞF eðkÞTþF uðkÞD u F uðkÞTþQð8aÞPðkþ1Þ¼NðkÞÀNðkÞH Te ðD nþH e NðkÞH TeÞÀ1H e NðkÞð8bÞ^x e ðkþ1Þ¼^feðx eðkÞ;^u eðkÞÞþPðkþ1ÞH TeDÀ1nðZðkÞÀH e^x eðkÞÞð8cÞHere,Q is the covariance matrix of the system noise,namely model error;D n is the covariance matrix of the output noise,namely measurement noise;D u is the covariance matrix of the control input noise(v s a and v s b),namely input noise;and P and N are the covariance matrices of state estimation error and extrapolation error,respectively.The algorithm involves two main stages:prediction andfiltering.In the prediction stage,thenext predicted states^fe ðÁÞand predicted state error covariance matrices,PðÁÞand NðÁÞ,are pro-cessed,while in thefiltering stage,the next estimated states,^xe ðkþ1Þ,obtained as the sum of thenext predicted states and the correction term(2nd)term in Eq.(8c))are calculated.The schematic representation of the algorithm is given in Fig.1.The algorithm utilizes the extended or augmented model in Eqs.(2)and(3)to generate all output states required by the sensorless direct torque control scheme,in addition to the rotor resistance and the load torque,using measured phase currents and voltages.M.Barut et al./Energy Conversion and Management46(2005)335–349339340M.Barut et al./Energy Conversion and Management46(2005)335–3494.Speed sensorless DTC systemFig.2demonstrates the speed sensorless DTC system.Here,^h rf stands for the sector position of theflux with reference to the stationary axis.The velocity controller given in the diagram is a conventional proportional integral derivative(PID)controller.The development of the sector selector and the switching table is based on Takahashi’s study presented in Ref.[1].5.Simulation results and observationsTo test the performance of the estimation method,simulations were performed on an IM with the rated parameters given in Table1.The values of the system parameters and covariance matrix elements are very affective on the performance of the EKF estimation.In this study,to avoid computational complexity,the covariance matrix of the system noise Q is chosen in diagonal form,also satisfying the condition of positive definiteness.According to the KF theory,Q,D n(measurement error covariance ma-trix)and D u(input error covariance matrix)have to be obtained by considering the stochastic properties of the corresponding noises[7].However,since these are usually not known,in most cases,the covariance matrix elements are used as weighting factors or tuning parameters.In this study,tuning the initial values of P and Q is done by trial and error to achieve a rapid initial convergence and the desired transient and steady state behaviors of the estimated states andparameters,while D n and D u are determined taking into account the measurement errors of the current and voltage sensors and the quantization errors of the ADCs,as given below:Q ¼diag f 10À6½A 2 10À6½A 2 10À6½Wb 2 10À6½Wb 2 10À4½ðrad =s Þ2 10À5½ðNm Þ2 10À7½X 2 g P ¼diag f 9½A 29½A 29½Wb 2 9½Wb 2 9½ðrad =s Þ29½ðNm Þ29½X 2 gD n ¼diag f 10À6½A 2 10À6½A 2 g D u ¼diag f 10À3½V 210À3½V 2 gand sampling time T ¼100l s :The bandwidth ðb w Þof the flux comparator is chosen as 0.02[Wb],while that of the torque comparator ðb t e Þis 0.01[Nm].Table 1The nominal values and parameters of the induction motor used in the tests P [KW]f [Hz]J L[kg m 2]B L [Nm/(rad/s)]p pV [V]I [A]R s [X ]R 0r [X ]L s [H]L r [H]L m [H]N m[rpm]T e[Nm]3500.0060.0012380 6.9 2.283 2.1330.23110.23110.22143020M.Barut et al./Energy Conversion and Management 46(2005)335–349341Eleven different scenarios are created to test the performance of the estimation and control algorithm in the time interval of06t613s.Thefirst10scenarios are developed with simultaneous changes of the velocity reference (Fig.3a)and the load torque value(Fig.3b)used in the extended model.The last scenario(scenario11)is created by giving R0r in the model a step change to twice itsoriginal value,R0r ¼2R0r n.The estimation of all the states and parameters is started with an initial value of zero.The resulting system performance for all scenarios is given with Fig.4a representing thevelocity estimate,^n m,Fig.4b depicting the velocity error,ðn refm À^n mÞ,and Fig.4c giving theestimation error,n mÀ^n m.The variations of the applied and estimated load torque are given in Fig.5a,with Fig.5b representing the estimation error,ðt LÀ^t LÞ,for this variable.The variationsrelated to the rotor resistance,R0r ,are given in Fig.6a and b,with the former plot representing theactual and estimated variation of R0r with the initial value of the estimate taken as zero,while thelatter plot represents the estimation error,R0r À^R0r.Finally,Fig.7a–c represent the estimatedfluxmagnitude,j^ws j,the error between the reference and actual(estimated)flux magnitude,j w s j refÀj^w s j,and theflux estimation error,ðj w s jÀj^w s jÞ,respectively.Fig.8shows the trajectoryof ws a and ws b.342M.Barut et al./Energy Conversion and Management46(2005)335–349M.Barut et al./Energy Conversion and Management46(2005)335–3493435.1.Observations5.1.1.Operation under constant t L and constant/linear velocity referencesIn intervals where the load in the model is given a constant value(20Nm),the esti-mation and control algorithms perform very well under both step type and linear variations of the velocity reference.With no a priori information on the load torque(and an initial value of0Nm),the EKF algorithm and the control achieve a low velocity error,ranging between0.011%and0.031%,ascan be seen in the time intervals 06t 61s,1s 6t 62s,2s 6t 63s,3s 6t 64s,4s 6t 65s,7s 6t 68s,8s 6t 69s,10s 6t 611s and so on.In the first,third and fourth of the above intervals,a velocity reference with a linear variation in time has been applied to the system,while in the rest of the intervals,a constant velocity reference has been used.However,independent of the velocity reference,a very good performance has been obtained,mainly due to the consistence between the applied and assumed load torque in the model.5.1.2.Operation under linear t L and constant/linear velocity referencesIn the time interval 5s 6t 7s,t L is given a variation ðt L ¼À20þ20ðt À5ÞÞ,while n ref m isvaried as n refm ¼À1500þ1520ðt À5Þbetween 5s 6t 66s,during which the velocity error,e nm ð%Þ¼1:412120Â100¼7:06%and estimation error ^e nm ð%Þ¼0:9620Â100¼4:8%.As noted before,the increased errors in the velocity output and estimate are due to the inconsistency between the t L in the EKF model (which is constant)and the imposed variation of t L (linear)in the model representing the plant for simulation purposes.5.1.3.Operation in the low velocity region,with no load referencesIn the interval 8s 6t 69s,both the velocity reference and t L are made zero,giving rise to avelocity error of e nm ¼0:0308rpm in steady state and an estimation error of ^e nm ¼À0:5618rpm,344M.Barut et al./Energy Conversion and Management 46(2005)335–349which are acceptable results considering the challenge posed by the velocity region and change in t L.5.1.4.Operation with linear velocity reference and linear t LIn the interval9s6t610s,the variations n refm ¼1500ðtÀ9Þand t L¼20ðtÀ9Þgive rise to avelocity error of e nmð%Þ¼1:71500Â100¼0:11%and an estimation error that varies between^e nmð%Þ¼0:56Â100¼0:037%and^e nmð%Þ¼16:06Â100¼1:07%.Once again,relatively higher but still acceptable errors are caused mainly by the linear variation of t L.5.1.5.Operation under reversal of velocity referenceIn the interval2s6t64s,the velocity reference is reversed from1500rpm to)1500rpm witha linear variation of n refm ¼1500ðtÀ2ÞÀ1500ðtÀ2Þ.During this interval,t L is also given a var-iation of t L¼20sgnðn mÞ.After a brief transient while the velocity and torque pass through zero,velocity errors of e nmð%Þ¼0:39231500Â100¼0:026%and e nmð%Þ¼1:38251500Â100¼0:0923%occur att¼2and4s,respectively.The velocity estimation errors for the same instants are^e nmð%Þ¼0:04041500Â100¼0:0027%and^e nmð%Þ¼0:12961500Â100¼0:0086%,respectively.Consideringthe error,it can be noted that the system has responded quite well to the simultaneous reversal ofn ref m and t L.M.Barut et al./Energy Conversion and Management46(2005)335–3493455.1.6.Operation under R0r ¼2R0r n(constant velocity reference/load torque)As mentioned before,another challenge for the control of an IM system is the uncertaintiesrelated to R0r .The robustness of the performance of the estimation algorithm to variations is testedby increasing the value of R0r to twice the value assigned in the model,in the interval11s6t612s.The response of the system is noted to be quite satisfactory with a velocity error ofe nmð%Þ¼1:44421500Â100¼0:096%and velocity estimation error of^e nmð%Þ¼0:01221500Â100¼0:0081%after a brief transient state.Once again,the largest estimation error in R0r takes place in the346M.Barut et al./Energy Conversion and Management46(2005)335–349interval5s6t67s where the load torque is given a linear variation,while in all other intervals, very small errors are obtained in the transient and steady-state.5.1.7.Uncertainties captured in constant t LAs mentioned in Sections1and2,the EKF scheme also facilitates the indirect evaluation of uncertainties that have the same variation as a state or parameter that is being estimated.Con-sidering this study,in which viscous frictionðF v¼b L x mÞis taken into account in the model representing the system but not in the extended model,the estimate of t L as a constant state also should include the viscous friction value once steady-state is reached.This fact can be demon-strated easily with the calculations below.In the intervals1s6t62s and10s6t613s,during which both the velocity reference andload torque are given positive constant values,the error in the torque estimation is e tL ¼À0:571,and in the interval4s6t65s,where both the velocity reference and torque are given negativevalues,the error is found to be e tL ¼0:571.The angular velocity in all these intervals ise nm¼1500Æ0:2rpm.Thus,for the value of the viscous friction coefficient b L¼0:001used in the modelx mð1Þ¼2pÂn m=60¼2pð1500:2½rpm þ7:4Â10À5½rpm Þ=60¼157:1006½rad=sF v¼B L x mð1ÞF v¼0:001Â157:1006¼0:1571006½Nmwhich is equal to e tL ,as expected.This fact should also be taken into consideration in evaluation of the load torque estimation. By inspecting the t L estimate,it can be observed that although with the linear variations and reversals of t L,some estimation error is caused in a relatively short transient duration,in the intervals with constant velocity reference and constant t L,this error is much lower,with the subtraction of the F v,from t L,yielding an error approximately equal to zero.The applied algorithm has also kept the variation offlux magnitude in all intervals within the admissible hysteresis band.Thus,with consideration of all the results,it can be observed that the expected performance is attained.6.ConclusionIn this study,an extended Kalmanfilter(EKF)algorithm is developed for the speed sensorless direct torque control(DTC)of induction motors.DTC requires accurate knowledge of the amplitude and angular position of the controlledflux(with respect to the stationary stator axis)in addition to the angular velocity for the purpose of velocity control.The major contribution of this study is the increased robustness towards uncertainties in the rotor resistance and load torque,the effects of which are known to give rise to performance deteriorations in such systems.This is achieved by an EKF algorithm that performs simulta-neous estimation of the rotor resistance and load torque as well as the statorflux components and the angular velocity.The performance of the algorithm is tested with11scenarios devel-oped by giving step type and linear variations to the load torque and angular velocity reference,while robustness to rotor resistance,R0r ,variation is tested with step type changes imposed onR0 r .The system performance is observed to be quite good under step type variations and reversals inthe load–torque and step/linear changes and reversals in the angular velocity.The system has alsodemonstrated the expected robustness to step type variations forced on the R0r ,and acceptableerrors are obtained even with the linear variations and reversals of the load torque.The estimation of the load torque estimate,t L,as a constant state in this algorithm also accounts for the viscous friction in this case,thereby improving the estimation performance.AcknowledgementsThis work was supported in part by the Istanbul Technical University Research Foundation.References[1]Takahashi I,Noguchi T.A mew quick-response and high-efficiency control strategy of an induction motor.IEEETrans Ind Appl1986;IA-22(5):820–7.[2]Casadei D,Profumo F,Tani A.FOC and DTC:two viable schemes for induction motors torque control.IEEETrans Power Electron2002;17(5):779–87.348M.Barut et al./Energy Conversion and Management46(2005)335–349。