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Application Note MCU-AN-510108-E-11 32-BIT MICROCONTROLLER MB9A310SERIES TORQUE COMPENSATION APPLICATION IN PMSM DRIVE APPLICATION NOTE ARM and Cortex-M3 are the trademarks of ARM Limited in the EU and other countries. Torque Compensation V1.1.0 Revision History Revision History Version Date Updated by Approved by Modifications 1.0.0 2011-08-23 Arthur Zhong First Draft 1.1.0 2012-06-14 Mona Chen Modified the format This manual contains 17 pages. Specifications are subject to change without notice. For further information please contact each office. All Rights Reserved. The contents of this document are subject to change without notice. Customers are advised to consult with sales representatives before ordering. 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Any information in this document, including descriptions of function and schematic diagrams, shall not be construed as license of the use or exercise of any intellectual property right, such as patent right or copyright, or any other right of FUJITSU SEMICONDUCTOR or any third party or does FUJITSU SEMICONDUCTOR warrant non-infringement of any third-party's intellectual property right or other right by using such information. FUJITSU SEMICONDUCTOR assumes no liability for any infringement of the intellectual property rights or other rights of third parties which would result from the use of information contained herein. The products described in this document are designed, developed and manufactured as contemplated for general use, including without limitation, ordinary industrial use, general office use, personal use, and household use, but are not designed, developed and manufactured as contemplated (1) for use accompanying fatal risks or dangers that, unless extremely high safety is secured, could have a serious effect to the public, and could lead directly to death, personal injury, severe physical damage or other loss (i.e., nuclear reaction control in nuclear facility, aircraft flight control, air traffic control, mass transport control, medical life support system, missile launch control in weapon system), or (2) for use requiring extremely high reliability (i.e., submersible repeater and artificial satellite). Please note that FUJITSU SEMICONDUCTOR will not be liable against you and/or any third party for any claims or damages arising in connection with above-mentioned uses of the products. Any semiconductor devices have an inherent chance of failure. You must protect against injury, damage or loss from such failures by incorporating safety design measures into your facility and equipment such as redundancy, fire protection, and prevention of over-current levels and other abnormal operating conditions. Exportation/release of any products described in this document may require necessary procedures in accordance with the regulations of the Foreign Exchange and Foreign Trade Control Law of Japan and/or US export control laws. The company names and brand names herein are the trademarks or registered trademarks of their respective owners. Copyright © 2011Fujitsu Semiconductor Design (Chengdu) Co. Ltd. All rights reserved. MCU-AN-510108-E-11 – Page 2 Torque Compensation V1.1.0 Contents Contents REVISION HISTORY ............................................................................................................ 2 CONTENTS .......................................................................................................................... 3 1 INTRODUCTION .............................................................................................................. 4 1.1 Purpose ................................................................................................................... 4 1.2 Definitions, Acronyms and Abbreviations ................................................................ 4 1.3 Document Overview ................................................................................................ 4 2 PRINCIPLES OF TORQUE COMPENSATION ................................................................ 5 2.1 Torque Equation ...................................................................................................... 5 2.2 Vibration Reason ..................................................................................................... 7 2.3 Measurement .......................................................................................................... 9 2.3.1 VoltageCompensation ............................................................................... 9 2.3.2 Current Compensation ............................................................................. 11 3 THEIMPLEMENTATION OF TC..................................................................................... 13 3.1 Feature.................................................................................................................. 13 3.2 The flowchartof voltage compensation .................................................................. 14 3.3 Waveform of TC .................................................................................................... 15 4 APPENDIX ..................................................................................................................... 17 4.1 List of Figures and Tables ..................................................................................... 17 MCU-AN-510108-E-11 – Page 3 Torque Compensation V1.1.0 Chapter 1 Introduction 1 Introduction 1.1 Purpose This application note describes the background, principle, implementation and test result of torque compensation. As you know, in order to decrease the cost of air conditioner system, more and more producers use low cost motor, such as single rotor motor. The load torque of this type motor in one mechanical circle is out of balance, which result in the speed of motor is fluctuated. Then the air conditioner system will be violent vibration. This phenomenon is very obvious especially when the frequency of the motor is very low.If we ignore this phenomenon, it will result in two kinds of bad result. One is noise, once we use air conditioner, it will influence our life. The other is life of air conditioner system, maybe we use two or three years, the air conditioner system will break down. So, we must research a technology to eliminate this phenomenon, torque compensation is just the technology that we need. 1.2 TC Definitions, Acronyms and Abbreviations - PMSM - Torque Compensation Permanent Magnet Synchronous Motor - Load torque - Electrical torque - Rotor inertia - Rotor pole pairs - Amplitude of natural magnetic flux of permanent magnets - Mechanical speed - Electrical speed - Electrical angle - phase current in d axis - phase current in q axis BEMF - BACKelectromotive force FOC - Field orient control - Viscosity coefficient 1.3 Document Overview The rest of document is organized as the following: Chapter 2 explains the principles of torque compensation. Chapter 3 explains the implementation of torque compensation. MCU-AN-510108-E-11 – Page 4 Torque Compensation V1.1.0 Chapter 2 Principles of Torque compensation 2 Principles of Torque compensation 2.1 Torque Equation For PMSM, one phase electrical voltage equation could be written like this: V = z*i = Ri + = Ri + (1) Where the term this: corresponds to BEMF, it also could be written like = (2) Where corresponds to rotor electrical speed. It is supposed that the flux is sinusoidal,the BEMF has the following equation: ̅=[ ]=- [ ]= (3) In PMSM system, the torque is expressed like this: =p*[ ]* (4) Where p is the pole pairs of rotor It could be proven that the best solution to produce a constant torque is to drive sinusoidal motor by sinusoidal current: =p* *( ) (5) Knowing that: (6) We could obtain: =p* *( ( ) ( = )) (7) Because according to the theory of FOC, the d axis current is equal to 0, the q axis current is equal to , we could obtain: (8) MCU-AN-510108-E-11 – Page 5 Torque Compensation V1.1.0 Chapter 2 Principles of Torque compensation The electrical power delivered to the motor, a part is transformed in joule losses, another part is going to the energy storing in magnetic field and the last part is transformed in mechanical energy. The last part could be understood as torque production. The torque created by energy conversion process is then used to drive mechanical load. Below is the torque balance equation: + +J (9) MCU-AN-510108-E-11 – Page 6 Torque Compensation V1.1.0 Chapter 2 Principles of Torque compensation 2.2 Vibration Reason For single rotor motor, the load torque curve like this: Torque 𝑻𝒆 Area II Area I 𝑻𝑳 ѳ𝑚 One Mechanical Circle Figure 2-1: Torque Curve In the above illustration, (red line) is the load torque and (black line) is electrical torque. You could find that the load torque curve is variable in one mechanical circle, this phenomenon will become graver and graver in low frequency area, especially when the frequency is less than 30HZ. MCU-AN-510108-E-11 – Page 7 Torque Compensation V1.1.0 Chapter 2 Principles of Torque compensation In Area I, because is less than , the speed of rotor will increase. On the other hand, in area II, the speed of rotor will decrease, the speed curve like this: Torque 𝑻𝒆 Area II Area I 𝑻𝑳 ѳ𝑚 𝜔𝑚 Average Speed Real time Speed ѳ𝑚 Figure 2-2: Rotor Speed Curve Where the green line represents average speed of rotor and the blue line represents the real time speed of rotor. MCU-AN-510108-E-11 – Page 8 Torque Compensation V1.1.0 Chapter 2 Principles of Torque compensation 2.3 Measurement Now, we have known the actual reason of speed ripple, but how to eliminate this phenomenon? Usually, there are two methods: voltage compensation and current compensation. 2.3.1 Voltage Compensation 𝜔𝑚 Decrease voltage Increase voltage ѳ𝑚 Figure 2-3: Principle of Voltage Compensation Above illustration is to explain the principle of voltage compensation. When the speed is lower than average speed, it needs to increase output voltage so that the real time speed could increase; but when the speed is higher than average speed, it needs to decrease the output voltage so that the real time speed could decrease. After compensation, the ripple of speed curve decreases obviously (blue line is the speed curve before compensation, green line is the speed curve after compensation). Where the red line represents the average speed before voltage compensation, the blue line represents real time speed before voltage compensation; the green line represents real time speed after voltage compensation. MCU-AN-510108-E-11 – Page 9 Torque Compensation V1.1.0 Chapter 2 Principles of Torque compensation After add voltage compensation module, PMSM controlling system will be changed as below: Voltage Compensation ωre + f - PI Park-1 Vq Iqref + - Idref + d,q PI Vα SV PI Vd α,β Vβ 3-Phase Bridge PWM - A C Iq Id R α,β Park k θestim ωm Isα d,q Position and speed Estimator α,β Isβ Isβ Isα Vβ Vα a,b,c B Ib Ic Clark e M Software Figure 2-4: PMSM Control Block with Voltage compensation MCU-AN-510108-E-11 – Page 10 Hardware Torque Compensation V1.1.0 Chapter 2 Principles of Torque compensation 2.3.2 Current Compensation Torque 𝑻𝒆𝟏 𝑻𝒆𝟐 𝑻𝑳 ѳ𝑚 Figure 2-5: Principle of Current Compensation Above illustration is to explain the principle of current compensation. Core ideology of this method is to generate one electrical torque curve, whose shape is the same as load torque curve, but amplitude is bigger load torque curve. The amplitude difference between electrical torque curve and load torque curve is to keep the rotor running at a certain speed. Where the blue line represents load torque, red line represents electrical torque before current compensation; green line represents electrical torque after current compensation. MCU-AN-510108-E-11 – Page 11 Torque Compensation V1.1.0 Chapter 2 Principles of Torque compensation After add current compensation module, PMSM controlling system will be changed as below: Current Compensation Iqref ωre + f - PI + - Idref + Park-1 Vq d,q PI Vα SV Vd PI α,β Vβ 3-Phase Bridge PWM - A C Iq Id R α,β Park k θestim ωm Isα d,q Position and speed Estimator α,β Isβ Isβ Isα Vβ Vα a,b,c B Ib Ic Clark e M Software Figure 2-6: PMSM Control Block with Current Compensation MCU-AN-510108-E-11 – Page 12 Hardware Torque Compensation V1.1.0 Chapter 3 Implementation of TC 3 Implementation of TC Now, we will use voltage compensation as example to explain the implementation of torque compensation. 3.1 Feature Set up torque compensation frequency range automatically, 5HZ~37HZ is recommended frequency range. Modify the compensation amplitude according to amplitude of load automatically, so that it could get good performance regardless of heavy load or light load. Parameters correlative with torque compensation module are less, only need to change compensate angle and compensate voltage amplitude (different frequency has different compensate voltage amplitude). MCU-AN-510108-E-11 – Page 13 Torque Compensation V1.1.0 Chapter 3 Implementation of TC 3.2 Flowchart of Voltage Compensation Start Check actual speed N TC enable? Y Y Compress and release circle check complete? N Check compress and release circle Check load torque amplitude Calculate amplitude of compensate voltage Compensate q axis voltage End Figure 3-1: Flowchart of Voltage Compensation MCU-AN-510108-E-11 – Page 14 Torque Compensation V1.1.0 Chapter 3 Implementation of TC 3.3 Waveform of TC Figure 3-2: Current Waveform before Torque Compensation Compress circle Release circle Figure 3-3: Current Waveform after Torque Compensation MCU-AN-510108-E-11 – Page 15 Torque Compensation V1.1.0 Chapter 3 Implementation of TC The above two illustrations show the phase current waveform before and after torque compensation. After add torque compensation function, the current waveform has been changed obviously. In compress circle, because the load becomes bigger and bigger, the speed of rotor will decrease, the BEMF will decrease at the same time, according to voltage balance formula: V= Ri + L +E (10) The phase current will increase. The target of torque compensation is to increase the speed, so we must increase the output voltage, then phase current will become bigger. On the other hand, in release circle, because the load becomes smaller and smaller, the speed of rotor will increase, the BEMF will increase at the same time, according to voltage balance equation also, the phase current will decrease. The target of torque compensation is to decrease the speed, so it must decrease the output voltage, then phase current will become smaller. When you see the phase current is strange after add torque compensation function, don’t be nervous, because it is just what we want to get. MCU-AN-510108-E-11 – Page 16 Torque Compensation V1.1.0 Chapter 4 Appendix 4 Appendix 4.1 List of Figures and Tables Figure 2-1: Torque Curve ....................................................................................................... 7 Figure 2-2: Rotor Speed Curve .............................................................................................. 8 Figure 2-3: Principle of Voltage Compensation ...................................................................... 9 Figure 2-4: PMSM Control Block with Voltage compensation ............................................... 10 Figure 2-5: Principle of Current Compensation..................................................................... 11 Figure 2-6: PMSM Control Block with Current Compensation .............................................. 12 Figure 3-1: Flowchart of Voltage Compensation................................................................... 14 Figure 3-2: Current Waveform before Torque Compensation ............................................... 15 Figure 3-3: Current Waveform after Torque Compensation .................................................. 15 MCU-AN-510108-E-11 – Page 17