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Application Note MCU-AN-510111-E-11 32-BIT MICROCONTROLLER MB9BFXXXX/ MB9AFXXXX SERIES MTPA APPLICATION NOTE ARM and Cortex-M3 are the trademarks of ARM Limited in the EU and other countries. MTPA V0.0.0 Revision History All Rights Reserved. The contents of this document are subject to change without notice. Customers are advised to consult with FUJITSU sales representatives before ordering. The information, such as descriptions of function and application circuit examples, in this document are presented solely for the purpose of reference to show examples of operations and uses of Fujitsu semiconductor device; Fujitsu does not warrant proper operation of the device with respect to use based on such information. When you develop equipment incorporating the device based on such information, you must assume any responsibility arising out of such use of the information. Fujitsu assumes no liability for any damages whatsoever arising out of the use of the information. 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 or any third party or does Fujitsu warrant non-infringement of any third-party’s intellectual property right or other right by using such information. Fujitsu 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 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. If any products described in this document represent goods or technologies subject to certain restrictions on export under the Foreign Exchange and Foreign Trade Law of Japan, the prior authorization by Japanese government will be required for export of those products from Japan. The company names and brand names herein are the trademarks or registered trademarks of their respective owners. Copyright© 2011 FUJITSU SEMICONDUCTOR LIMITED all rights reserved MCU-AN-510111-E-11 – Page 2 MTPA V0.0.0 Revision History Revision History Rev Date Author Remark 0.0.0 Sept. 05, 2012 Devin Zhang First Edition This manual contains 31 pages. MCU-AN-510111-E-11 – Page 3 MTPA V0.0.0 Contents Contents REVISION HISTORY................................................................................................................ 3 CONTENTS ............................................................................................................................... 4 1 INTRODUCTION ................................................................................................................. 5 2 MTPA PRINCIPLE ............................................................................................................... 7 2.1 Motor control theory................................................................................................................ 7 2.2 Motor torque formulary ........................................................................................................... 9 2.3 2.4 2.2.1 SPM motor module .................................................................................................. 9 2.2.2 IPM motor module ................................................................................................. 10 IPM MTPA control theory .................................................................................................... 12 2.3.1 Discursion the torque theory .................................................................................. 12 2.3.2 Distribute the current realize the MTPA ................................................................ 13 Simulator the MTPA theory .................................................................................................. 14 3 MTPA IMPLEMENTATION .............................................................................................. 19 3.1 Obtain the current of Id ......................................................................................................... 19 3.1.1 3.2 Obtain the steady Iq current ................................................................................... 19 MTPA Software implementation........................................................................................... 20 3.2.1 Software Flowchart ................................................................................................ 20 3.2.2 Software code implement ....................................................................................... 20 4 MTPA FUNCTION PERFORMANCE ................................................................................ 28 4.1 Basic Verification .................................................................................................................. 28 4.1.1 Test waveform of run motor .................................................................................. 28 5 CONCLUSION .................................................................................................................... 30 6 APPENDIX .......................................................................................................................... 31 6.1 List of Figures and Tables ..................................................................................................... 31 MCU-AN-510111-E-11 – Page 4 MTPA V0.0.0 Chapter 1 Introduction 1 Introduction This application note describes the maximum torque per ampere (MTPA) implementation in- MB9Bxxxx/MB9Axxxx Series. Salient-pole synchronous motors are widely used in variable speed drive applications due to their high efficiency. It is important not only to accurately detect rotor positions but also to control current at optimum phases for high efficiency and wide range operations such as maximum torque control and flux weakening control. Although rotor positions can be detected precisely with position sensors, mechanical position sensors have several problems such as cost and low reliability. Therefore, many sensorless control methods have been proposed. This document have also proposed sensor less control techniques with observers based on PLL observe model. In position sensorless controls, it is known that position estimation errors are sensitive to q-axis inductance set in the observers. Such parameter errors affect both position estimation and current vector phase accuracy. Position estimation errors caused by inductance errors have been analyzed. One of the typical trajectories in a current phase control is the maximum torque per ampere (MTPA) control, which is also called maximum torque control. It is important for high efficiency drives, because the reluctance torque can be used effectively the most and the copper losses are minimized. The conventional methods are that d-axis current commands for the current control loop are set to negative values at maximum torque per ampere trajectory. It can be obtained by solving an extremal problem that the motor torque is maximized with respect to the current phase angle at constant current amplitude. By utilizing these relations, unified methods for position estimation and current phase control with inductance setting have been reported. The inductance setting which is set so as to associate the current vector with a quasi-optimal trajectory is presented in. For example, the trajectory is located between unity power factor trajectory and minimum copper loss trajectory. According to theory as our known, the maximum torque control is realized with inductance setting in a modified control model. The robustness against magnetic saturation has been experimentally pointed out. However, this approach is based on a particular observe model constructed on maximum torque control frame. Therefore considerable knowledge on observe model must be reconsidered. Based on these concepts, this paper presents maximum torque control with inductance setting of normal PLL observers. In case of normal PLL observer, the relations between position estimation errors and parameter errors have been derived MCU-AN-510111-E-11 – Page 5 MTPA V0.0.0 Chapter 1 Introduction analytically in steady state. In addition, a phase angle of the maximum torque control frame which is equal to a current phase angle under the maximum torque control has also been derived. In the proposed method, the inductance is set so as to make the estimated position error equal to the phase angle of the maximum torque control frame. Also the proposed method is simply constructed and robust against magnetic saturation. Based on this approach, the validity of the proposed method can be explained in the conventional frame work. Figure 1-1: Salient-pole synchronous motors of torque MCU-AN-510111-E-11 – Page 6 MTPA V0.0.0 Chapter 2 MTPA Principle 2 MTPA Principle 2.1 Motor control theory Motor control structure as below figure show: Figure 2-1: motor control structure The structure including the content: 1. Permanent Magnet Synchronous Motor. 2. 3-Phase Bridge – rectifier, inverter and acquisition and protection circuitry. 3. Clarke forward transform block. 4. Park forward and inverse transform block. 5. Angle and speed estimator block. 6. Proportional integral controller block. 7. MTPA and Field weakening block. 8. Space vector modulation block. In the structure of upper if Ld equal to Lq and no flied weakening that Idref is equal to zero, The particularity of the FOC in the case of PMSM is that the stator’s d-axis current reference Idref (corresponding to the armature reaction MCU-AN-510111-E-11 – Page 7 MTPA V0.0.0 Chapter 2 MTPA Principle flux on d-axis) is set to zero. The rotor’s magnets produce the rotor flux linkage, ΨPM, unlike ACIM, which needs a constant reference value Idref for the magnetizing current, thereby producing the rotor flux linkage. The air gap flux is equal to the sum of the rotor’s flux linkage, which is generated by the permanent magnets plus the armature reaction flux linkage generated by the stator current. For the constant torque mode in FOC, the d-axis air gap flux is solely equal to ΨPM, and the d-axis armature reaction flux is zero. On the contrary, in constant power operation, the flux generating component of the stator current, Id, is used for air gap field weakening to achieve higher speed. In sensorless control, where no position or speed sensors are needed, the challenge is to implement a robust speed estimator that is able to reject perturbations such as temperature, electromagnetic noise and so on. Sensorless control is usually required when applications are very cost sensitive, where moving parts are not allowed such as position sensors or when the motor is operated in an electrically hostile environment. However, requests for precision control, especially at low speeds, should not be considered a critical matter for the given application. The position and speed estimation is based on the mathematical model of the motor. Therefore, the closer the model is to the real hardware, the better the estimator will perform. The PMSM mathematical modeling depends on its topology, differentiating mainly two types: surface-mounted and interior permanent magnet. Each type has its own advantages and disadvantages with respect to the application needs. The proposed control scheme has been developed around an interior permanent magnet synchronous motor, because we need to realize the maximum torque per ampere function. Because the surface-mounted permanent magnet which has the advantage of low torque ripple and lower price in comparison with other types of PMSMs. The air gap flux for the motor type considered is smooth so that the stator’s inductance value, Ld equal to Lq and the Back Electromagnetic Force (BEMF) is sinusoidal. The fact that the air gap is large (it includes the surface mounted magnets, being placed between the stator teeth and the rotor core), implies a smaller inductance for this kind of PMSM with respect to the other types of motors with the same dimension and nominal power values. These motor characteristics enable some simplification of the mathematical model used in the speed and position estimator, while at the same time enabling the efficient use of FOC. The FOC maximum torque per ampere is obtained by uninterruptedly keeping the motor’s rotor flux linkage situated at 90 degrees behind the armature generated flux linkage. But the interior permanent magnet motor need to special function control of MTPA, because the maximum torque per ampere of the motor’s rotor flux linkage MCU-AN-510111-E-11 – Page 8 MTPA V0.0.0 Chapter 2 MTPA Principle situated don’t at 90 degrees position. So this document to explain how to realize this function and how to obtain the Idref negative value. 2.2 Motor torque formulary The motor torque formulary as equation as below: (1) Where, Pn is the number of poles Ψm is the permanent magnet linked flux Ld and Lq are the direct and quadrature axis inductances As this total torque Te includes tow part of torque: one is cylindrical torque (Ψm*Iq) and the other is the angle advance curve torque ((Ld-Lq)*Iq*Id). 2.2.1 SPM motor module The SPM synchronous motor parameters Ld equal to Lq, the angle advance curve torque is zero, there is zero saliency and Idref is set to zero for maximum efficiency at 90 degrees position. The IPM motor torque curve as bellow: MCU-AN-510111-E-11 – Page 9 MTPA V0.0.0 Chapter 2 MTPA Principle Figure 2-2: SPM motor torque structure From above figure, we can obtain the episteme that total torque as the same as the cylindrical torque. The reluctance torque is equal to zero. 2.2.2 IPM motor module The IPM synchronous motor parameters Ld not equal to Lq, the angle advance curve torque is nonzero value, there is saliency and Idref is set to nonzero value for maximum efficiency at maximum 90 degrees position The IPM motor torque curve as bellow: MCU-AN-510111-E-11 – Page 10 MTPA V0.0.0 Chapter 2 MTPA Principle Figure 2-3: IPM motor torque structure From above figure, we can obtain the episteme that total torque as the same as the cylindrical torque add to reluctance torque. The maximum torque position is maximum 90 degrees position. Figure 2-4: IPM motor torque theta The Idref value curve as below figure, they have different position at different current and different motor parameters. At below document we will to analyses the relator parameters and what it is influent this value. MCU-AN-510111-E-11 – Page 11 MTPA V0.0.0 Chapter 2 MTPA Principle Figure 2-5: IPM motor at different current Id reference 2.3 IPM MTPA control theory 2.3.1 Discursion the torque theory From above the explain and the follow torque formulary, (2) When driving a surface magnet motor, there is zero saliency (Ld=Lq) and Id is set to zero for maximum efficiency. In the case of IPM motor which has saliency (Ld< Lq) a negative Id will produce positive reluctance torque. The most efficient operating point is when the total torque is maximized for a given current magnitude. This is found by transforming Equation 1 into a form with current magnitude (Im) and phase advance (β) terms by substituting Id with Im.cos(β) and Iq with Im.sin(β). So the torque formulary will instead of bellow: (3) So we can using the sin function Equation to express the torque formulary. (4) From above equation we can realize the maximum torque when β and other parameters were confirmed. MCU-AN-510111-E-11 – Page 12 MTPA V0.0.0 Chapter 2 MTPA Principle 2.3.2 Distribute the current realize the MTPA If we can obtain the max value of Te the β degree, we can make sure the Id and Iq reference value from the total current Im. So now we consequence the equation for below: Differential the equation, (5) The equation change to, (6) When Te’ = 0, the Te has maximum value at [0,180] degree region. So above equation will change to, (7) Or, (8) Ψ Perform mathematical trigonometric function calculations, √ (9) using , (10) Obtain , MCU-AN-510111-E-11 – Page 13 MTPA V0.0.0 Chapter 2 MTPA Principle √ (11) Using Iq express Id, √ (12) Because Ψm、Ld、Lq is the motor parameters, Iq is the contorl signal so we can obtain the Id value from above equation. 2.4 Simulator the MTPA theory When IPM motor parameters: Ld = 10.4mh Lq = 18.6mh Ψm = 0.404Wb Iq = 8A The simulator figure as below， Figure 2-6: Salient-pole synchronous motors of torque MCU-AN-510111-E-11 – Page 14 MTPA V0.0.0 Chapter 2 MTPA Principle Figure 2-7: Salient-pole synchronous motors of Id reference Figure 2-8: Salient-pole synchronous motors of torque theta When other IPM motor parameters: Ld = 5.4mh Lq = 15.6mh Ψm = 0.204Wb Iq = 20A MCU-AN-510111-E-11 – Page 15 MTPA V0.0.0 Chapter 2 MTPA Principle The simulator figure as below， Figure 2-9: Salient-pole synchronous motors of torque Figure 2-10: Salient-pole synchronous motors of Id reference MCU-AN-510111-E-11 – Page 16 MTPA V0.0.0 Chapter 2 MTPA Principle Figure 2-11: Salient-pole synchronous motors of torque theta When other surface-mounted motor parameters: Ld = 8.4mh Lq = 8.4mh Ψm = 0.204Wb Iq = 20A The simulator figure as below， Figure 2-12 surface-mounted motor of torque MCU-AN-510111-E-11 – Page 17 MTPA V0.0.0 Chapter 2 MTPA Principle Figure 2-13: surface-mounted motor of Id reference Figure 2-14: surface-mounted motor of torque theta From above simulator figure, our theory of the maximum torque per ampere is impactful. MCU-AN-510111-E-11 – Page 18 MTPA V0.0.0 Chapter 3 MTPA Implementation 3 MTPA Implementation 3.1 Obtain the current of Id 3.1.1 Obtain the steady Iq current In AD and PI control system has some disturb, in order to obtain the data cleanly, we will add the low pass filter. The Iq input and Iqf will output. So the high frequency yawp will be filtered. And the flow chart as below: Iq Low pass filter Iqf Figure 3-1: Iq low pass filter Using the below equation to catch the Idref value. Idref value added the low pass filter if some system control need. The equation as below: √ (13) Figure 3-2: MTPA equation By the current Idref from the equation was calculated. We can add the daxis to control motor to realize the maximum torque per ampere function. MCU-AN-510111-E-11 – Page 19 MTPA V0.0.0 Chapter 3 MTPA Implementation 3.2 MTPA Software implementation 3.2.1 Software Flowchart By up explain to write the flow chart as below. Start Initialize the parameters and state of MTPA Filter the Iq signal obtain the Iqf By the MTPA equation to calculator the Idref Obtain the d-axis reference value Return to the step two Figure 3-3: Dead Time Compensation Software Flowchart Algorithm flow explanation: 1. Initialize the parameters and state of MTPA. 2. Filter the Iq signal to obtain Iqf. 3. Using filter signal obtain the d-axis current reference; 4. Return to the step two. 3.2.2 Software code implement /**************************************************** Function name: MTPA MCU-AN-510111-E-11 – Page 20 MTPA V0.0.0 Chapter 3 MTPA Implementation Description: realize the maximum torque per ampere Input: none Output: none ****************************************************/ void MTPA(void) { //to realize the MTPA function NAME MTPA #define SHT_PROGBITS 0x1 EXTERN Ld EXTERN Lq EXTERN PLL_LPF EXTERN __aeabi_d2uiz EXTERN __aeabi_f2uiz EXTERN __aeabi_fdiv EXTERN __aeabi_fmul EXTERN __aeabi_fsub EXTERN __aeabi_ui2d EXTERN isq_tempf EXTERN pmsm_isdref EXTERN sqrt PUBLIC MTPA_Function MCU-AN-510111-E-11 – Page 21 MTPA V0.0.0 Chapter 3 MTPA Implementation PUBLIC MTPA_initialize PUBLIC MTPA_isdref PUBLIC MTPA_isdreff PUBLIC MTPA_lpf PUBLIC Q0_Inv_DetaL PUBLIC Q12_Flux PUBLIC Q16_DetaL PUBLIC Q24_Square_DetaL PUBLIC Q24_Square_Flux PUBLIC motor_Flux SECTION `.data`:DATA:REORDER:NOROOT(2) MTPA_initialize: DATA DC8 0 DC8 0, 0, 0 motor_Flux: DC32 3EA6E979H Q16_DetaL: DC8 0, 0, 0, 0 Q24_Square_DetaL: DC8 0, 0, 0, 0 Q0_Inv_DetaL: DC8 0, 0, 0, 0 MCU-AN-510111-E-11 – Page 22 MTPA V0.0.0 Chapter 3 MTPA Implementation Q12_Flux: DC8 0, 0, 0, 0 Q24_Square_Flux: DC8 0, 0, 0, 0 MTPA_isdref: DC8 0, 0, 0, 0 MTPA_isdreff: DC8 0, 0, 0, 0 MTPA_lpf: DC16 50 SECTION `.text`:CODE:NOROOT(2) THUMB MTPA_Function: PUSH {R4-R6,LR} LDR.N R4,??MTPA_Function_0 LDRB R0,[R4, #+0] CBNZ.N R0,??MTPA_Function_1 MOVS STRB R0,#+1 R0,[R4, #+0] LDR.N R0,??MTPA_Function_0+0x4 LDR R0,[R0, #+0] LDR.N R1,??MTPA_Function_0+0x8 LDR BL R1,[R1, #+0] __aeabi_fsub MCU-AN-510111-E-11 – Page 23 MTPA V0.0.0 Chapter 3 MTPA Implementation MOV R5,R0 LDR.N R6,??MTPA_Function_0+0xC ;; 0x447a0000 MOV BL R1,R6 __aeabi_fdiv LDR.N R1,??MTPA_Function_0+0x10 ;; 0x477fff00 BL __aeabi_fmul BL __aeabi_f2uiz STR R0,[R4, #+8] LSRS R0,R0,#+4 MULS R0,R0,R0 STR R0,[R4, #+12] MOV R0,R6 MOV R1,R5 BL __aeabi_fdiv BL __aeabi_f2uiz STR R0,[R4, #+16] LDR R1,[R4, #+4] LDR.N R0,??MTPA_Function_0+0x14 ;; 0x457ff000 BL __aeabi_fmul BL __aeabi_f2uiz STR R0,[R4, #+20] MULS R0,R0,R0 STR R0,[R4, #+24] POP {R4-R6,PC} ??MTPA_Function_1: MCU-AN-510111-E-11 – Page 24 MTPA V0.0.0 Chapter 3 MTPA Implementation LDR.N R5,??MTPA_Function_0+0x18 LDR R0,[R4, #+8] CMP R0,#+0 BEQ.N ??MTPA_Function_2 LDR.N R0,??MTPA_Function_0+0x1C LDR R1,[R0, #+0] LDR R0,[R0, #+0] LDR R6,[R4, #+20] LDR R2,[R4, #+24] LDR R3,[R4, #+12] ASRS R1,R1,#+4 MULS R1,R1,R3 ASRS R0,R0,#+4 MULS R0,R0,R1 ADD R0,R2,R0, LSR #+6 BL __aeabi_ui2d BL sqrt BL __aeabi_d2uiz SUBS R0,R6,R0 LDR R1,[R4, #+16] MULS R0,R0,R1 ASRS R0,R0,#+5 STR R0,[R4, #+28] ADD R2,R4,#+36 ADD R1,R4,#+32 MCU-AN-510111-E-11 – Page 25 MTPA V0.0.0 Chapter 3 MTPA Implementation BL PLL_LPF LDR B.N R0,[R4, #+32] ??MTPA_Function_3 ??MTPA_Function_2: STR R0,[R4, #+28] ??MTPA_Function_3: STRH POP R0,[R5, #+0] {R4-R6,PC} ;; return Nop DATA ??MTPA_Function_0: DC32 MTPA_initialize DC32 Lq DC32 Ld DC32 0x447a0000 DC32 0x477fff00 DC32 0x457ff000 DC32 pmsm_isdref DC32 isq_tempf SECTION `.iar_vfe_header`:DATA:REORDER:NOALLOC:NOROOT(2) SECTION_TYPE SHT_PROGBITS, 0 DATA DC32 0 MCU-AN-510111-E-11 – Page 26 MTPA V0.0.0 Chapter 3 MTPA Implementation SECTION __DLIB_PERTHREAD:DATA:REORDER:NOROOT(0) SECTION_TYPE SHT_PROGBITS, 0 SECTION __DLIB_PERTHREAD_init:DATA:REORDER:NOROOT(0) SECTION_TYPE SHT_PROGBITS, 0 END } MCU-AN-510111-E-11 – Page 27 MTPA V0.0.0 Chapter 4 MTPA Function Performance 4 MTPA Function Performance 4.1 Basic Verification 4.1.1 Test waveform of run motor By the theory of the up expound, realize the algorithm and obtain the perfect performance, as show as below figure added MTPA function and no-added MTPA function waveform: Figure 4-1: added the MTPA function MCU-AN-510111-E-11 – Page 28 MTPA V0.0.0 Chapter 4 MTPA Function Performance Figure 4-2: no-added the MTPA function From above, maximum torque per ampere function performance is very well. From the test motors purpose, also decrease the power waste and pyrotoxin. So the MTPA theory can carry into execution. MCU-AN-510111-E-11 – Page 29 MTPA V0.0.0 Chapter 5 CONCLUSION 5 CONCLUSION This paper presented maximum torque control only with PLL observers and general current control systems. In the proposed method, the d-axis current in the PLL observer for the sensorless control are set to the different values from the motor one so as to make the estimated reference frame equal to maximum torque control frame. The proposed system give explicitly have maximum torque controller, and the calculation is not complicated. Moreover, the proposed control is easy applying other motor and control system. The effectiveness of the proposed method has been confirmed by experimental results. MCU-AN-510111-E-11 – Page 30 MTPA V0.0.0 Chapter 6 Appendix 6 Appendix 6.1 List of Figures and Tables Figure 1-1: Salient-pole synchronous motors of torque .......................................................................... 6 Figure 2-1: motor control structure ......................................................................................................... 7 Figure 2-2: SPM motor torque structure ............................................................................................... 10 Figure 2-3: IPM motor torque structure ................................................................................................ 11 Figure 2-4: IPM motor torque theta ...................................................................................................... 11 Figure 2-5: IPM motor at different current Id reference ....................................................................... 12 Figure 2-6: Salient-pole synchronous motors of torque ........................................................................ 14 Figure 2-7: Salient-pole synchronous motors of Id reference ............................................................... 15 Figure 2-8: Salient-pole synchronous motors of torque theta .............................................................. 15 Figure 2-9: Salient-pole synchronous motors of torque ........................................................................ 16 Figure 2-10: Salient-pole synchronous motors of Id reference ............................................................. 16 Figure 2-11: Salient-pole synchronous motors of torque theta ............................................................ 17 Figure 2-12 surface-mounted motor of torque ..................................................................................... 17 Figure 2-13: surface-mounted motor of Id reference ........................................................................... 18 Figure 2-14: surface-mounted motor of torque theta........................................................................... 18 Figure 3-1: Iq low pass filter ................................................................................................................... 19 Figure 3-2: MTPA equation .................................................................................................................... 19 Figure 3-3: Dead Time Compensation Software Flowchart ................................................................... 20 Figure 4-1: added the MTPA function .................................................................................................... 28 Figure 4-2: no-added the MTPA function .............................................................................................. 29 MCU-AN-510111-E-11 – Page 31

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