ACLCM4UG, Advanced Control Library for Cortex-M4 Core
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1. axes are identical to each other Advanced Control Library Rev 2 Freescale Semiconductor 3 15 ACLIB_PMSMBemfObsrvDQ 1 sLp Rs Us Figure 3 2 Block diagram of proposed Luenberger type stator current observer acting as state filter for back EMF The position estimation can now be performed by extracting the 0 term from the model and adjusting the position of the estimated reference frame to achieve 3 0 Because the 0 term is only included in the saliency based EMF component of both u us axis voltage equations the Luenberger based disturbance observer is designed to observe these voltage components u us The position displacement information 0 is then obtained from estimated back EMFs as follows error error Oorror atan Eqn 3 2 The estimated position 6 can be obtained by driving the position of the estimated reference frame to achieve zero displacement 6 0 The phase locked loop mechanism can be adopted where the loop compensator ensures correct tracking of the actual rotor flux position by keeping the error signal 6 to be zeroed 0 0 error error A perfect match between the actual and estimated motor model parameters is assumed and the back EMF transfer function is simplified as follows Boe F s E a s E 8 Pacresrc ee FTE Eqn 3 3 Appropriate dynamic behavior of the back EMFobserver is achieved by placement of the poles of the stator curren2. Dependencies SWLIBS_Typedefs h Advanced Control Library Rev 2 3 14 Freescale Semiconductor ACLIB_PMSMBemfObsrvDQ e SWLIBS_Defines h e SWLIBS_Inlines h e intrinsic h e Cortex_M4_IAR a library e ACLIB_PMSMBemfObsrvDQ h e aclib h 3 2 6 Description The estimation method for the rotor position and angular speed is based on the motor mathematical model of interior PMSM motor with an extended electro motive force function This is realized in an estimated quasi synchronous reference frame y as depicted in Figure 3 1 Figure 3 1 Estimated y and real rotor dq synchronous reference frames The back EMF observer detects the generated motor voltages induced by the permanent magnets A tracking observer uses the back EMF signals to calculate the position and speed of the rotor The transformed model is then derived as follows u j si y _ Rs sLp Lo ly AL icta ia k sin 9 or Eqn 3 1 Us OL Rst slp lis cos 0 be e R stator resistance e Lp L D axis and Q axis inductance e k back EMF constant e angular electrical speed up Ug Stator voltages e ipio Stator currents e s operator of derivative e i first derivative of i current The block diagram of the observer in the estimated reference frame is shown in Figure 3 2 The observer compensator is substituted by a standard PI controller As noted in Figure 3 2 the observer model and the PI controller gains in both
3. N A Pointer to structure which contain input signal of d q voltage components f32Speed in out Frac32 N A Fraction value of electrical speed pudtCtrl in out ACLIB BEMF OBSRV DQ T N A Pointer to an observer structure which contains coefficients Advanced Control Library Rev 2 Freescale Semiconductor ACLIB_PMSMBemfObsrvDQ Table 3 3 User types Typedef Name Format ae Description udtEObsrv 32D Frac32 eee reais back EMF voltage in udtEObsrv 320 Frac32 eee ee back EMF voltage in udtlObsrv f32D Frac32 PENS Estimated current in d axis udtlObsrv f32Q Frac32 ee eee Estimated current in q axis wacnisan_s Free panutone S verbo in spe pt oe aCe eas SOON aoe RTE ate udtCtrl f16PropScaled Frac16 E Observer proportional gain ACLIB_BEMF_OBSRV_DQ_T udtCtrl i1 6PropShift Word16 eae Observer proportional gain shift udtCtrl f16lntegScaled Frac16 panes Observer integral gain udtCtrl i1 6IntegShift Word16 F F Observer integral gain shift ae sey Samos ee reference system 16IScaled Frac16 T ae coefficient for current f16UScaled Frac16 pects a coefficient for voltage H6WIScaled E Sealed aciniet tata 16EScaled Frac16 penn i coefficient for back emf 3 2 4 Availability This library module is available in the C callable interface This library module is targeted for Cortex M4 platforms 3 2 5 List of all dependent files
4. 1 API functions summary Name Arguments Output Description This function calculates the tracking observer for void determination angular speed and position of input error functional signal Frac32 f32ThetaErr ACER TacnGhary ACLIB_ TRACK OBSRV_T const pudtCtrl MCLIB_2_COOR_SYST_D_Q_T pudtidq MCLIB_2_COOR_SYST_D_Q_T The function calculates the algorithm of back ACLIB_PMSMBemfObsrvDQ puatUdg Frac32 f32Speed void electromotive force observer ACLIB_BEMF_OBSRV_DQ_T const in rotating reference frame pudtCtrl Advanced Control Library for Cortex M4 Core Rev 1 1 3 12 Freescale Semiconductor 3 2 ACLIB_PMSMBemfObsrvDQ The function calculates the algorithm of back electro motive force observer in rotating reference frame ACLIB_PMSMBemfObsrvDQ 3 2 1 Synopsis include aclib h void ACLIB_PMSMBemfObsrvDQ MCLIB_2_COOR_SYST_D_Q_T pudtIDQ MCLIB_2_COOR_SYST_D_Q_T pudtUDQ Frac32 f 32Speed ACLIB_BEMF_OBSRV_DQ_T pudtCtrl 3 2 2 Prototype void ACLIB_PMSMBemfObsrvDQFC MCLIB_2_COOR_SYST_D_Q_T pudtIDQ MCLIB_2_COOR_SYST_D_Q_T pudtUDQ Frac32 f32Speed ACLIB_BEMF_OBSRV_DQ_T pudtCtrl 3 2 3 Arguments Table 3 2 Function arguments Name wy Format valid Description Out range pudtIDQ ii MCLIB 2 COOR SYST D QT NA Pointer to structure which contain input signal of d q current components pudtUDQ iA MCLIB 2 COOR SYST D QT
5. FRAC320 ee oe a a Advanced Conirol Library for Cortex M4 Core Rev 1 1 Freescale Semiconductor 2 9 Code size and execution time data Table 2 2 User Defined Typedefs in mclib_types h Name Structure members Description Frac32 f32A MCLIB_3 COOR_SYST_T Frac32 f32B three phase system Frac32 f32C Frac32 f32A MCLIB_2 COOR_SYST_T Frac32 32B two phase system Frac32 f32Alpha MCLIB_2_COOR_SYST_ALPHA_BETA_T Frac32 32Beta two phase system alpha beta Frac32 f32D MCLIB_2 COOR_SYST_D QT Frac32 f32Q two phase system generic DQ Frac32 f32Sin two phase system sine and MELIB ANGLET Frac32 f32Cos cosine components Code size and execution time data This document provides for each function the size of the compiled binary code and the execution time of the algorithms for each compiler The following table summarizes the settings of each supported compiler Table 2 3 Compilers settings Copolymer Optimization options IAR Embedded Workbench No size constraints checked Optimization level High Optimize for Speed All transformations enabled CodeWarrior for MCU Optimize most O3 Keil uVision Optimize for Time checked Optimization Level 3 O3 Advanced Conirol Library for Cortex M4 Core Rev 1 1 Freescale Semiconductor 2 11 API Summary Chapter 3 FUNCTION API 3 1 API Summary Table 3
6. Software is not fault tolerant and is not designed manufactured or intended by Freescale for Advanced Conirol Library for Cortex M4 Core Rev 1 1 Freescale Semiconductor incorporation into products intended for use or resale in on line control equipment in hazardous dangerous to life or potentially life threatening environments requiring fail safe performance such as in the operation of nuclear facilities aircraft navigation or communication systems air traffic control direct life support machines or weapons systems in which the failure of products could lead directly to death personal injury or severe physical or environmental damage High Risk Activities You specifically represent and warrant that you will not use the Software or any derivative work of the Software for High Risk Activities CHOICE OF LAW VENUE LIMITATIONS You agree that the statutes and laws of the United States and the State of Texas USA without regard to conflicts of laws principles will apply to all matters relating to this Agreement or the Software and you agree that any litigation will be subject to the exclusive jurisdiction of the state or federal courts in Texas USA You agree that regardless of any statute or law to the contrary any claim or cause of action arising out of or related to this Agreement or the Software must be filed within one 1 year after such claim or cause of action arose or be forever barred PRODUCT LABELING You are not
7. The unsigned integer numbers are positive only and they have nearly twice the magnitude of a signed number of the same size The unsigned integer numbers lie in the following range 0 lt UI lt 2I4 _ 1 Eqn 2 2 The binary word is interpreted as having a binary point immediately to the right of the integer s least significant bit This data format is available for bytes words and long words The most positive 16 bit unsigned integer is 65 535 FFFF and the most positive 32 bit unsigned integer is 4 294 967 295 FFFFFFFF The smallest unsigned integer number is zero 0000 regardless of size 2 7 3 Signed fractional SF In this format the N bit operand is represented using the 1 N 1 format one sign bit N 1 fractional bits The signed fractional numbers lie in the following range 1 0 lt SF lt 1 0 2 1 1 Eqn 2 3 This data format is available for words and long words For both word and long word signed fractions the most negative number that can be represented is 1 0 its internal representation is 8000 word or 80000000 long word The most positive word is 7FFF 1 0 2715 its most positive long word is 7FFFFFFF 1 0 27 2 7 4 Unsigned fractional UF The unsigned fractional numbers can only be positive and they have nearly twice the magnitude of a signed number with the same number of bits The unsigned fractional numbers lie in the following range 0 0 lt UF lt 2 0 2 14 1 E
8. declaration is not included in your program only the header file s should be included Prototype This subsection shows the original function prototype declaration with all its arguments Arguments This optional subsection describes input arguments to a function or macro Description This subsection is a description of the function or macro It explains algorithms being used by functions or macros Return This optional subsection describes the return value if any of the function or macro Range issues This optional subsection specifies the ranges of input variables Special issues This optional subsection specifies special assumptions that are mandatory for correct function calculation for example saturation rounding and so on Implementation This optional subsection specifies whether a call of the function generates a library function call or a macro expansion Advanced Control Library for Cortex M4 Core Rev 1 1 Freescale Semiconductor 2 7 Data types This subsection also consists of one or more examples of the use of the function The examples are often fragments of code not completed programs for illustration purposes See also This optional subsection provides a list of related functions or macros Performance This section specifies the actual requirements of the function or macro in terms of required code memory data memory and number of clock cycles to execute 2 7 Datatypes The 32 bit Co
9. part of the 13211 mout Fraca 0x7FFFFFFF observer integral part at step k 1 8000 f16PropScale in Frac16 7FFF Obsrever proportional gain i16PropShift in Word16 F F Obsrever proportional gain shift ACLIB TRACK OBST f16lntegScale in Frac16 8000 Obsrever integral gain 7FFF i16IntegShift in Word16 F F Obsrever integral gain shift 8000 Scaling coefficient for output feThScaled z ae 7FFF integrator of position 46THShift in Word16 FLF Scaling coefficient shift for output integrator of position 3 3 4 Availability This library module is available in the C callable interface This library module is targeted for Cortex M4 platforms 3 3 5 Dependencies List of all dependent files e SWLIBS_Typedefs h e SWLIBS_Defines h e SWLIBS_Inlines h e Cortex_M4_IAR a library e ACLIB_TrackObsrv h e aclib h 3 3 6 Description This function calculates the tracking observer algorithm where the phase locked loop mechanism is adopted It is recommended to call this function at every sampling period It requires a single input argument as phase error Such phase Advanced Control Library Rev 2 3 22 Freescale Semiconductor ACLIB_TrackObsrv tracking observer with standard PI controller used as the loop compensator is depicted in Figure 3 3 Oerror W 1 0 Figure 3 3 Block diagram of proposed PLL scheme for position estimation Depicted tracking observer structure has the transfer function as 0 s _ 5K Ki E
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11. 0 acBemfObsrv udtlObsrv f 32Q FRAC32 0 0 acBemfObsrv udtEObsrv f32D FRAC32 0 0 acBemfObsrv udtEObsrv f 32Q FRAC32 0 0 acBemfObsrv udtCtrl f32ID_1 FRAC32 0 0 acBemfObsrv udtCtrl f32IQ_1 FRAC32 0 0 acBemfObsrv udtCtrl f16PropScaled BEMFOBSRV_DQ_ PROP_GAIN_SCALED acBemfObsrv udtCtrl il6PropShift BEMFOBSRV_DQ_PROP_GAIN_SHIFT acBemfObsrv udtCtrl f16IntegScaled BEMFOBSRV_DQ_INTEG_GAIN_SCALED acBemfObsrv udtCtrl il6IntegShift BEMFOBSRV_DQ_INTEG_GAIN_SHIFT acBemfObsrv f16IScaled BEMFOBSRV_DQ_I_SCALED acBemfObsrv f16UScaled BEMFOBSRV_DQ_U_SCALED acBemfObsrv f16EScaled BEMFOBSRV_DQ_E_SCALED Advanced Control Library Rev 2 3 18 Freescale Semiconductor ACLIB_PMSMBemfObsrvDQ acBemfObsrv f1l6WIScaled BEMFOBSRV_DQ_WI_SCALED Periodical function or interrupt void ISR void ACLIB_PMSMBemfObsrvDQ amp mcIdq amp mcUdg f 32Speed amp acBemfObsrv 3 2 11 Performance Table 3 4 Performance of ACLIB_PMSMBemfObsrvD Q function Code size words IAR 584 196 GFLIB_AtanYX 220 GFLIB_ATAN cw 648 364 GFLIB_AtanYX 220 GFLIB_ATAN Keil 574 264 GFLIB_AtanYX 78 GFLIB_ATAN Data size words 0 Execution clock cycles Min 172 209 188 IAR CW Keil Max 290 501 298 The algorithm test was performed on the MK40X265VMD100 device The code ran from flash memory with the CPU speed set to 100 MHz Advanced Control Library Rev 2
12. 3 7 Returns The function returns an estimation of the actual rotor angle as 32 bit fractional value 3 3 8 Range issues The function works with the 32 bit signed fractional values in the range lt 1 1 3 3 9 Special issues N A 3 3 10 Implementation Example 3 2 Implementation Code include aclib h ACLIB_TRACK_OBSRV_T acTo Frac32 32ThetaError Frac32 32PositionEstim void main void acTo f32Theta FRAC32 0 0 acTo f32Speed FRAC32 0 0 acTo f321I_1 FRAC32 0 0 acTo f16PropScale TRACKOBSRV_PROP_GAIN_SCALED acTo il 6PropShift TRACKOBSRV_PROP_GAIN_SHIFT acTo fl6 IntegScale TRACKOBSRV_INTEG_GAIN_SCALED acTo il IntegShift TRACKOBSRV_INTEG_GAIN_SHIFT acTo f16ThScaled TRACKOBSRV_TH_SCALED acTo il6ThShift TRACKOBSRV_TH_SHIFT Periodical function or interrupt void ISR void 32PositionEstim ACLIB_ TrackObsrv f32ThetaError amp acTo Advanced Control Library Rev 2 3 24 Freescale Semiconductor ACLIB_TrackObsrv 3 3 11 Performance Table 3 7 Performance of ACLIB_TrackObsrv function Code size bytes AR CW Keil 194 228 184 Data size bytes 0 Execution clock cycles Min 49 57 52 IAR CW Keil Max 49 57 52 The algorithm test was performed on the MK40X265VMD100 device The code ran from flash memory with the CPU speed set to 100 MHz Advanced Control Lib
13. 4 based Kinetis family of microcontrollers This library contains optimized functions for the Kinetis family of microcontrollers The library is supplied in a binary form which is unique for its ease of integration with user applications The Set of General Math and Motor Control Functions for Cortex M4 Core must be included in the application project for correct functionality of the Advanced Motor Control Library References 1 MCLIBCORETXM4UG Set of General Math and Motor Control Functions for Cortex M4 Core User Reference Manual Freescale Semiconductor 2012 Supported compilers Advanced Control Library for Cortex M4 Core ACLIB is written in C language using some of the compiller s intrinsics functions in order to directly utilize specific core instructions The library was built and tested using following compilers 1 IAR Embedded Workbench for ARM v 4 40 2 2 CodeWarrior for MCU version 10 3 GCC build tools 3 Keil pVision V4 60 0 0 The library is delivered in the library module Cortex_M4_XX a together with Set of General Math and Motor Control Functions for Cortex M4 Core The XX denotes the particular compiller CW IAR KEIL The interfaces to the algorithms included in this library have been combined into a single public interface include file aclib h This was done to simplify the number of files required for inclusion by application programs Refer to the specific algorithm sections of this document for details
14. Advanced Control Library for Cortex M4 Core User Reference Manual ACLCM4UG Rev 1 1 3 2013 P freescale com 2 freescale The following revision history table summarizes changes contained in this document Table 0 1 Revision History Date Revision Description Label p 0 Initial release 03 2013 1 1 Support of additional compilers added Advanced Conirol Library for Cortex M4 Core Rev 1 1 2 Freescale Semiconductor Chapter 1 License Agreement FREESCALE SEMICONDUCTOR SOFTWARE LICENSE AGREEMENT This is a legal agreement between you either as an individual or as an authorized representative of your employer and Freescale Semiconductor Inc Freescale It concerns your rights to use this file and any accompanying written materials the Software In consideration for Freescale allowing you to access the Software you are agreeing to be bound by the terms of this Agreement If you do not agree to all of the terms of this Agreement do not download the Software If you change your mind later stop using the Software and delete all copies of the Software in your possession or control Any copies of the Software that you have already distributed where permitted and do not destroy will continue to be governed by this Agreement Your prior use will also continue to be governed by this Agreement OBJECT PROVIDED OBJECT REDISTRIBUTION LICENSE GRANT Freescale grants to you free of charge
15. Freescale Semiconductor 3 19 Pe a a A ACLIB_PMSMBemfObsrvDQ Advanced Control Library Rev 2 3 20 Freescale Semiconductor 3 3 ACLIB_ TrackObsrv The function calculates tracking observer for determination angular speed and ACLIB_TrackObsrv position of input error functional signal 3 3 1 Synopsis include aclib h Frac32 ACLIB_ TrackObsrv Frac32 f32Error ACLIB_TRACK_OBSRV_T pudtCtrl 3 3 2 Prototype Frac32 ACLIB_TrackObsrvFC Frac32 32Error ACLIB_TRACK_OBSRV_T pudtCtrl 3 3 3 Arguments Table 3 5 Function arguments In 7 eee Name Out Format Valid range Description 0x80000000 input signal representing phase error of f32Error in Frac32 ox7FFFFFFF Pur Signa repre gP system to be estimated pointer to a tracking observer structure pudtCtrl in out ACLIB_TRACK_OBSRV_T N A ACLIB_TRACK_OBSRV_T which contains algorithm coefficients Advanced Control Library Rev 2 Freescale Semiconductor 3 21 ACLIB_TrackObsrv Table 3 6 User type definitions Typedef In Name Out Format Valid range Description 0x80000000 Estimated position as output of the ACLIB_TRACK_OBSRV_T 82Theta mout i Eracas 0x7FFFFFFF second numerical integrator 0x80000000 Estimated speed as output of the 32Speed in out Frac32 0x7FFFFFFF first numerical integrator 0x80000000 State variable in controller
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20. on the software application programming interface API definitions and functionality provided for the individual algorithms Installation The ACLIB is delivered as a single executable file with Set of General Math and Motor Control Functions for Cortex M4 Core To install the ACLIB on a user computer run the installation file CORTEX_M4_FSLESL exe and follow Advanced Control Library for Cortex M4 Core Rev 1 1 Freescale Semiconductor 2 6 Library integration into the software project the steps that are listed in the user s manual dedicated to Set of General Math and Motor Control Functions for Cortex M4 Core 1 2 5 Library integration into the software project The procedure to include the library in the software project is described separately for each supported compiler in the user s manual dedicated to Set of General Math and Motor Control Functions for Cortex M4 Core 1 Special attention needs to be paid when this library is included in the CodeWarrior 10 3 project with ARM GCC build tools used 2 6 API definition The description of each function described in this Advanced Control Library for Cortex M4 Core user reference manual consists of a number of subsections Synopsis This subsection gives the header files that should be included within a source file that references the function or macro It also shows an appropriate declaration for the function or for a function that can be substituted by a macro This
21. qn 2 4 The binary word is interpreted as having a binary point after the MSB This data format is available for words and longs The most positive 16 bit unsigned number is FFFF or 1 0 1 0 2N 1 99997 The smallest unsigned fractional number is zero 0000 Advanced Conirol Library for Cortex M4 Core Rev 1 1 Freescale Semiconductor 2 9 User common types 2 8 User common types Table 2 1 User defined typedefs in MCF51_types h Mnemonics Size bits Description Word8 8 To represent 8 bit signed variable value UWord8 8 To represent 8 bit unsigned variable value Word16 16 To represent 16 bit signed variable value UWord16 16 To represent 16 bit unsigned variable value Word32 32 To represent 32 bit signed variable value UWord32 32 To represent 32 bit unsigned variable value Int8 8 To represent 8 bit signed variable value Ulnt8 8 To represent 8 bit unsigned variable value Int16 16 To represent 16 bit signed variable value Ulnt16 16 To represent 16 bit unsigned variable value Int32 32 To represent 32 bit signed variable value Ulnt32 32 To represent 32 bit unsigned variable value Fraci6 16 To represent 16 bit signed variable value Frac32 32 To represent 32 bit signed variable value NULL constant Represents NULL pointer bool 16 Boolean variable false constant Represents false value true constant Represents true value FRACIB eS es
22. qn 3 11 s s sK K where the controller gains K and K are calculated by comparing the characteristic polynomial of the resulting transfer function to a standard second order system polynomial The essential equations for implementation of the tracking observer according to block scheme in Figure 3 3 are as follows a k K e k ATs K e k 1 k 1 Eqn 3 12 I k ATs K e k k 1 O k O k 1 AT w K Eqn 3 13 In equations Equation 3 12 and Equation 3 13 there are coefficients and quantities that might be greater than one for example the actual rotor speed k or that are too small to be precisely represented within 16 bit fractional value Due to this fact a special transformation has to be carried out in order to be successfully implemented using fractional arithmetic K Kprrac 35 Eqn 3 14 MAX K Kirrac ATs Onan Eqn 3 15 T AT Max Eqn 3 16 hFRAC 7 S Omax qn 3 where the variables of the angle tracking observer are e e k is observer error in step k e AT is the sampling period s e k is the actual rotor speed rad s in step k e k is the actual rotor angle rad in step k Advanced Control Library Rev 2 Freescale Semiconductor 3 23 ACLIB_TrackObsrv The scaled coefficients which are suitable for implementation on the DSP core are as follows f16KPScaled K pgac 2 0 Eqn 3 17 f16KIScaled Kjrpac 2 Eqn 3 18 16ThScaled Tyrpac 2 E Eqn 3 19 3
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24. rtex M4 core supports two types of two s complement data formats e Signed integer e Unsigned integer The signed and unsigned integer data types are useful for general purpose computation they are familiar to the microprocessor and microcontroller programmers The calculations performed in the library functions utilize fractional data types e Signed fractional e Unsigned fractional Fractional data types allow powerful numeric and digital signal processing algorithms to be implemented Even though calulations in these fractional data types are not directly supported by Cortex M4 core architecture it is not difficult to emulate the calculations by software and therefore benefit from using the fractional arithmetic 2 7 1 Signed integer Sl This format is used for processing data as integers In this format the N bit operand is represented using the N O format N integer bits The signed integer numbers lie in the following range 2 N 1 lt s7 lt 2IN 11 1 Eqn 2 1 This data format is available for bytes words and longs The most negative signed word that can be represented is 32 768 8000 and the most negative signed long word is 2 147 483 648 80000000 The most positive signed word is 32 767 7FFF and the most positive signed long word is 2 147 483 647 S7FFFFFFF Advanced Conirol Library for Cortex M4 Core Rev 1 1 2 8 Freescale Semiconductor Data types 2 7 2 Unsigned integer Ul
25. rver is properly designed in the stationary reference frame the back EMF can be estimated as a disturbance produced by the observer controller This is only valid however if the back EMF term is not included in the observer model The observer is actually a closed loop current observer so it acts as a state filter for the back EMF term The estimate of extended EMF term can be derived from Equation 3 3 as follows Ep SKpt Ky Eqn 3 9 Els s L sRy sKp K Advanced Control Library Rev 2 Freescale Semiconductor 3 17 ACLIB_PMSMBemfObsrvDQ The observer controller can be designed by comparing the closed loop characteristic polynomial with that of a standard second order system as Kpt R K Se ee eg rion Eqn 3 10 Lp Lp where e is the natural frequency of the closed loop system loop bandwith e amp is the loop attenuation 3 2 7 Returns The function returns a phase error between the real rotating reference frame and the estimated one 3 2 8 Range issues The function works with the 32 bit signed fractional values in the range lt 1 1 3 2 9 Special issues N A 3 2 10 Implementation Example 3 1 Implementation Code include gflib h include mclib h include aclib h MCLIB_2_ COOR_SYST_D_Q T mcIdq mcUdq ACLIB_ BEMF_OBSRV_DQ_T acBemfObsrv Frac32 32Speed void main void acBemfObsrv udtlIObsrv f32D FRAC32 0
26. t observer characteristic polynomial This general method is based on matching the coefficients of the characteristic polynomial with the coefficients of the general second order system The back EMFobserver is a Luenberger type observer with motor model which is realized in fixed point arithmetic and transformed using backward Euler transformation Advanced Control Library Rev 2 3 16 Freescale Semiconductor ACLIB_PMSMBemfObsrvDQ ipgraclk Uprac Urractk Errac rraclk WlIrrac erpaclk t rraclk I prac trracl k 1 Eqn 3 4 where e irrractk i is is fractional representation of stator current vector Urrack u us is fractional representation of stator voltage vector errac k e es is fractional representation of stator back emf voltage vector e iprractk is i is fractional representation of complementary stator current vector rrrac k is fractional representation of angular speed Scaling coefficients relating to maximal values are expressed as ATs Umax 2 SO Eqn 3 5 Urrac Lijt AT Ry Imax q AT Emax E Eqn 3 6 PRAC Dat AT Re Iyuy q Wlrrac os MAX Eqn 3 7 byt AT Rs L a Eqn 3 8 I FRAC Ly PAT Re where e AT sampling time in sec e Iyax Maximal peak current in A Eyay Maximal peak back emf voltage in V e Uyax Maximal peak stator voltage in V Quay Maximal angular speed in rad sec If a Luenberger type stator current obse
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