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Fujitsu Semiconductor Design (Chengdu) Co., Ltd.
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
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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
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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
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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
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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
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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
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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
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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:
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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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