Embedded Software and Motor Control Libraries for PXR40xx

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$Set of General Math and Motor Control Functions for ARM Cortex ...$

Section number Title Page 8.322.2 Description.....................................................................................................................................................909 8.323 Define F32TOINT16....................................................................................................................................................909 8.323.1 Macro Definition............................................................................................................................................909 8.323.2 Description.....................................................................................................................................................909 8.324 Define F64TOINT16....................................................................................................................................................910 8.324.1 Macro Definition............................................................................................................................................910 8.324.2 Description.....................................................................................................................................................910 8.325 Define F16TOINT32....................................................................................................................................................910 8.325.1 Macro Definition............................................................................................................................................910 8.325.2 Description.....................................................................................................................................................910 8.326 Define F32TOINT32....................................................................................................................................................910 8.326.1 Macro Definition............................................................................................................................................910 8.326.2 Description.....................................................................................................................................................911 8.327 Define F64TOINT32....................................................................................................................................................911 8.327.1 Macro Definition............................................................................................................................................911 8.327.2 Description.....................................................................................................................................................911 8.328 Define F16TOINT64....................................................................................................................................................911 8.328.1 Macro Definition............................................................................................................................................911 8.328.2 Description.....................................................................................................................................................911 8.329 Define F32TOINT64....................................................................................................................................................911 8.329.1 Macro Definition............................................................................................................................................912 8.329.2 Description.....................................................................................................................................................912 8.330 Define F64TOINT64....................................................................................................................................................912 8.330.1 Macro Definition............................................................................................................................................912 8.330.2 Description.....................................................................................................................................................912 8.331 Define INT16TOF16....................................................................................................................................................912 8.331.1 Macro Definition............................................................................................................................................912 8.331.2 Description.....................................................................................................................................................912 Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0 96 Freescale Semiconductor, Inc.
Section number Title Page 8.332 Define INT16TOF32....................................................................................................................................................913 8.332.1 Macro Definition............................................................................................................................................913 8.332.2 Description.....................................................................................................................................................913 8.333 Define INT32TOF16....................................................................................................................................................913 8.333.1 Macro Definition............................................................................................................................................913 8.333.2 Description.....................................................................................................................................................913 8.334 Define INT32TOF32....................................................................................................................................................913 8.334.1 Macro Definition............................................................................................................................................913 8.334.2 Description.....................................................................................................................................................914 8.335 Define INT64TOF16....................................................................................................................................................914 8.335.1 Macro Definition............................................................................................................................................914 8.335.2 Description.....................................................................................................................................................914 8.336 Define INT64TOF32....................................................................................................................................................914 8.336.1 Macro Definition............................................................................................................................................914 8.336.2 Description.....................................................................................................................................................914 8.337 Define F16_1_DIVBY_SQRT3....................................................................................................................................914 8.337.1 Macro Definition............................................................................................................................................915 8.337.2 Description.....................................................................................................................................................915 8.338 Define F32_1_DIVBY_SQRT3....................................................................................................................................915 8.338.1 Macro Definition............................................................................................................................................915 8.338.2 Description.....................................................................................................................................................915 8.339 Define F16_SQRT3_DIVBY_2....................................................................................................................................915 8.339.1 Macro Definition............................................................................................................................................915 8.339.2 Description.....................................................................................................................................................915 8.340 Define F32_SQRT3_DIVBY_2....................................................................................................................................916 8.340.1 Macro Definition............................................................................................................................................916 8.340.2 Description.....................................................................................................................................................916 8.341 Define F16_SQRT2_DIVBY_2....................................................................................................................................916 8.341.1 Macro Definition............................................................................................................................................916 Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0 Freescale Semiconductor, Inc. 97
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Embedded Software and Motor Control
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Contents Section number Title Page
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Section number Title Page 4.4.6 Cod
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Section number Title Page 4.13 Func
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Page 11 and 12:
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Section number Title Page 4.101 Fun
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Section number Title Page 4.109 Fun
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Section number Title Page 4.116.6 C
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Section number Title Page 4.123.5 R
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Section number Title Page 4.146.6 C
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Page 45 and 46: Section number Title Page 4.161.3 R
Page 53 and 54: Section number Title Page 6.17.2 Co
Page 63 and 64: Section number Title Page 8.9 Defin
Page 65 and 66: Section number Title Page 8.28 Defi
Page 73 and 74: Section number Title Page 8.104 Def
Page 95: Section number Title Page 8.313 Def
Page 101 and 102: Chapter 1 1.1 License Agreement IMP
Page 103 and 104: Agreement, and require that you sto
Page 105 and 106: Chapter 1 ENTIRE RISK ARISING OUT O
Page 107 and 108: confidential information. The Licen
Page 109 and 110: Chapter 2 Introduction The aim of t
Page 111 and 112: Chapter 2 Introduction 2.2 General
Page 113 and 114: For example if the MCLIB_DEFAULT_IM
Page 115 and 116: and gmclib.h. This was done to simp
Page 117 and 118: Chapter 2 Introduction Figure 2-4.
Page 119 and 120: In order to integrate the Embedded
Page 123 and 124: Figure 2-12. Opening the C editor f
Page 125 and 126: Figure 2-15. Selecting the include
Page 127 and 128: • Library binary files located in
Page 129 and 130: Chapter 2 Introduction In order to
Page 133 and 134: Figure 2-24. Principle of MCLib tes
Page 135 and 136: 2.13.2 MCLib target-in-loop Testing
Page 137 and 138: Chapter 3 3.1 Function Index Table
Page 139 and 140: Table 3-1. Quick function reference
Page 147 and 148:
Table 3-1. Quick function reference
Page 149 and 150:
Chapter 4 API References This secti
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F32); tFrac32 f32CoefBuf[FIR_NUMTAP
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Equation GDFLIB_FilterFIR_Eq1 where
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F32); } GDFLIB_FilterFIRInit (&Para
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F16); tFrac16 f16CoefBuf[FIR_NUMTAP
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F16); } GDFLIB_FilterFIRInit (&Para
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FLT); tFloat fltCoefBuf[FIR_NUMTAPS
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} } // ############################
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4.8.3 Return The function returns a
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macro during instance declaration o
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4.9.6 Code Example #include "gdflib
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signal entering the state delay-lin
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4.11.2 Arguments Table 4-11. GDFLIB
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A general form of the IIR filter ex
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} flttrMyIIR1.trFiltCoeff.fltB0 = (
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freq_bot = 400; freq_top = 625; T_s
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4.15.4 Description This function cl
Page 189 and 190:
In order to implement the second or
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} f16trMyIIR2.trFiltCoeff.f16B0 = F
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eplaced by output from the previous
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Note This function shall not be cal
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call. The number of the filtered po
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Figure 4-7. Course of the function
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Figure 4-8. acos(x) vs. GFLIB_Acos(
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4.26.2 Arguments Table 4-27. GFLIB_
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Table 4-28. Integer polynomial coef
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4.27 Function GFLIB_Acos_FLT This f
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The arccos(x) values are then calcu
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} // output should be 1.570796 fltA
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Equation GFLIB_Asin_Eq3 Equation GF
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4.28.5 Re-entrancy The function is
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where: Equation GFLIB_Asin_Eq1 •
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The computation algorithm for arcsi
Page 233 and 234:
Page 235 and 236:
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Figure 4-20 depicts a floating poin
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4.32.4 Description The GFLIB_Atan_F
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Figure 4-22. atan(x) vs. GFLIB_Atan
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Table 4-42. GFLIB_Atan_FLT argument
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Figure 4-24. atan(x) vs. GFLIB_Atan
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4.35.1 Declaration tFrac16 GFLIB_At
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4.36 Function GFLIB_AtanYX_FLT The
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4.37.1 Declaration tFrac32 GFLIB_At
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The algorithm can be easily justifi
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The function has been tested to be
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where: Equation GFLIB_AtanYXShifted
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The function initialization paramet
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} Param.f16Kx = FRAC16 (0.879052013
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where: Equation GFLIB_AtanYXShifted
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4.39.6 Code Example #include "gflib
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Equation GFLIB_ControllerPIp_Eq1 ca
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• f32PropGain - is the scaled val
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where Equation GFLIB_ControllerPIp_
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and where Equation GFLIB_Controller
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Proportional-Integral (PI) algorith
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} // output should be 1.5e-2 fltOut
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where T s [sec] is the sampling tim
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The bounds are described by a limit
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(GFLIB_CONTROLLER_PIAW_P_T_F16). If
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The sum of the scaled proportional
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as default // #####################
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where T s [sec] is the sampling tim
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where Equation GFLIB_ControllerPIr_
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} // output should be 0x00A3D70A f3
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Equation GFLIB_ControllerPIr_Eq5 Th
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GFLIB_CONTROLLER_PI_R_T_F16 trMyPI
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Note All controller parameters and
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Equation GFLIB_ControllerPIrAW_Eq2
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The introduced scaling shift u16NSh
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4.50 Function GFLIB_ControllerPIrAW
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Equation GFLIB_ControllerPIrAW_Eq5
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Note All controller parameters and
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Transforming equation GFLIB_Control
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4.52.1 Declaration tFrac32 GFLIB_Co
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where a 1...a 5 are coefficients of
Page 321 and 322:
Page 323 and 324:
[- π, π ), the input f16In must b
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Figure 4-26. cos(x) vs. GFLIB_Cos(f
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Table 4-71. Approximation polynomia
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4.55 Function GFLIB_Hyst_F32 This f
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tFrac32 f32In; tFrac32 f32Out; GFLI
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CAUTION For correct functionality,
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Equation GFLIB_Hyst_Eq1 A graphical
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4.58.4 Description The function GFL
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void main(void) { // Setting parame
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where E MAX is the input scale and
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4.60.4 Description The function GFL
Page 347 and 348:
Page 349 and 350:
4.62.4 Description The GFLIB_Limit
Page 351 and 352:
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} // output should be 0x60000000 ~
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4.66.1 Declaration tFloat GFLIB_Low
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4.67.4 Description where: Equation
Page 359 and 360:
It should be noted that the computa
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Table 4-86. GFLIB_Lut1D_F16 argumen
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Equation GFLIB_Lut1D_Eq4 where y, y
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4.69 Function GFLIB_Lut1D_FLT This
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Equation GFLIB_Lut1D_Eq4 where y, y
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Page 371 and 372:
Equation GFLIB_Lut2D_Eq4 Equation G
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Equation GFLIB_Lut2D_Eq16 It should
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} // output should be 0x7A03D70A ~
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The Table 4-92 contains 4 interpola
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Equation GFLIB_Lut2D_Eq13 5. Final
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FRAC16 (0.2), FRAC16 (0.21), FRAC16
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where: Equation GFLIB_Lut2D_Eq3 •
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Equation GFLIB_Lut2D_Eq10 6. The sa
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0.88}; tFloat pfltTable2D[81] = {0.
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Page 391 and 392:
Figure 4-32. GFLIB_Ramp functionali
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If the desired (input) value is gre
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4.76.3 Return The function returns
Page 397 and 398:
In mathematical terms, the function
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Note The input and the output are i
Page 401 and 402:
The 9th order polynomial approximat
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Figure 4-34. sin(x) vs. GFLIB_Sin_F
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4.80.2 Arguments Table 4-101. GFLIB
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Therefore, the resulting equation h
Page 409 and 410:
4.81 Function GFLIB_Sin_FLT This fu
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Figure 4-36 depicts a floating poin
Page 413 and 414:
4.82.1 Declaration tFrac32 GFLIB_Sq
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} // output should be 0x5A820000 ~
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} // output should be 0x5A82 ~ FRAC
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Figure 4-39. real sqrt(x) vs. GFLIB
Page 421 and 422:
Equation GFLIB_Tan_Eq1 Because both
Page 423 and 424:
Figure 4-41. tan(x) vs. GFLIB_Tan(f
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4.86.1 Declaration tFrac16 GFLIB_Ta
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Equation GFLIB_Tan_Eq3 The division
Page 429 and 430:
Page 431 and 432:
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Figure 4-45. tan(x) vs. GFLIB_Tan(f
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4.88.1 Declaration tFrac32 GFLIB_Up
Page 437 and 438:
4.89.4 Description The GFLIB_UpperL
Page 439 and 440:
void main(void) { // upper limit fl
Page 441 and 442:
Figure 4-46. Graphical interpretati
Page 443 and 444:
4.92.2 Arguments Table 4-117. GFLIB
Page 445 and 446:
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• x in, y in and x out, y out are
Page 449 and 450:
4.94.2 Arguments Table 4-119. GMCLI
Page 451 and 452:
Page 453 and 454:
Page 455 and 456:
Page 457 and 458:
4.98.1 Declaration void GMCLIB_Clar
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4.99.1 Declaration void GMCLIB_Clar
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4.100.1 Declaration void GMCLIB_Dec
Page 463 and 464:
The feed-forward voltages u_dq_comp
Page 465 and 466:
Equation GMCLIB_DecouplingPMSM_Eq10
Page 467 and 468:
4.101.2 Arguments Table 4-126. GMCL
Page 469 and 470:
Equation GMCLIB_DecouplingPMSM_Eq4
Page 471 and 472:
Scaling of both equations into the
Page 473 and 474:
4.102.4 Description The quadrature
Page 475 and 476:
Page 477 and 478:
available DC bus voltage. Therefore
Page 479 and 480:
SWLIBS_2Syst_F32 f32OutAB; GMCLIB_E
Page 481 and 482:
• maximal amplitude of the DC bus
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output beta component of the output
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• actual amplitude of the DC bus
Page 487 and 488:
4.106 Function GMCLIB_Park_F32 This
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4.107 Function GMCLIB_Park_F16 This
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4.108 Function GMCLIB_Park_FLT This
Page 493 and 494:
4.109 Function GMCLIB_ParkInv_F32 T
Page 495 and 496:
4.110 Function GMCLIB_ParkInv_F16 T
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4.111 Function GMCLIB_ParkInv_FLT T
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4.112 Function GMCLIB_SvmStd_F32 Th
Page 501 and 502:
Figure 4-50. Basic space vectors Th
Page 503 and 504:
Figure 4-51. Projection of referenc
Page 505 and 506:
Equation GMCLIB_SvmStd_Eq7 Equation
Page 507 and 508:
Equation GMCLIB_SvmStd_Eq11 and equ
Page 509 and 510:
For the determination of auxiliary
Page 511 and 512:
Equation GMCLIB_SvmStd_Eq25 Equatio
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} // output pwm dutycycles stored i
Page 515 and 516:
Top and bottom switches work in a c
Page 517 and 518:
Page 519 and 520:
Page 521 and 522:
Page 523 and 524:
For the determination of auxiliary
Page 525 and 526:
Equation GMCLIB_SvmStd_Eq25 Equatio
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} // output pwm dutycycles stored i
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such a vector allows a numerical de
Page 531 and 532:
Page 533 and 534:
Page 535 and 536:
Page 537 and 538:
Table 4-150. Determination of t_1 a
Page 539 and 540:
It should be pointed out that, in t
Page 541 and 542:
calculation precision in boundary i
Page 543 and 544:
Note Due to effectivity reason this
Page 545 and 546:
4.116.3 Return Absolute value of in
Page 547 and 548:
} // output should be FRAC16(0.25)
Page 549 and 550:
Page 551 and 552:
tFrac32 f32Out; void main(void) { /
Page 553 and 554:
4.120 Function MLIB_Add_F32 This fu
Page 555 and 556:
Page 557 and 558:
4.121.6 Code Example #include "mlib
Page 559 and 560:
4.122.4 Description This inline fun
Page 561 and 562:
4.123 Function MLIB_AddSat_F32 This
Page 563 and 564:
Page 565 and 566:
Page 567 and 568:
4.125.3 Return Converted input valu
Page 569 and 570:
Page 571 and 572:
and converted to the output format.
Page 573 and 574:
Equation MLIB_Convert_Eq1 Note Due
Page 575 and 576:
Page 577 and 578:
Page 579 and 580:
4.132 Function MLIB_ConvertPU_F32FL
Page 581 and 582:
4.133.3 Return Converted input valu
Page 583 and 584:
Page 585 and 586:
4.136 Function MLIB_ConvertPU_FLTF3
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Page 589 and 590:
denominator, the output value is un
Page 591 and 592:
Equation MLIB_Div_Eq1 Note Due to e
Page 593 and 594:
Page 595 and 596:
} // output should be FRAC16(0.5) =
Page 597 and 598:
} // output should be FRAC32(0.3025
Page 599 and 600:
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} f32Out = MLIB_Mac_F32F16F16(f32In
Page 603 and 604:
} // output should be FRAC16(0.3025
Page 605 and 606:
Page 607 and 608:
} // ##############################
Page 609 and 610:
4.147 Function MLIB_MacSat_F32F16F1
Page 611 and 612:
4.148.2 Arguments Table 4-185. MLIB
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Table 4-186. MLIB_Mul_F32 arguments
Page 615 and 616:
void main(void) { // first input =
Page 617 and 618:
} // output should be 0x10000000 =
Page 619 and 620:
Page 621 and 622:
4.152.4 Description Single precisio
Page 623 and 624:
4.153 Function MLIB_MulSat_F32 This
Page 625 and 626:
Equation MLIB_MulSat_Eq1 Note Overf
Page 627 and 628:
Note Overflow is detected. The func
Page 629 and 630:
4.155.3 Return Fractional multiplic
Page 631 and 632:
} f16In2 = FRAC16 (0.75); // output
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4.157.1 Declaration tFrac16 MLIB_Ne
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Page 637 and 638:
Page 639 and 640:
Page 641 and 642:
4.162.1 Declaration tU16 MLIB_Norm_
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4.163.4 Description This function r
Page 645 and 646:
Page 647 and 648:
} // output should be 0x10000000 ~
Page 649 and 650:
Page 651 and 652:
4.168.4 Description Based on sign o
Page 653 and 654:
Page 655 and 656:
} // output should be 0x4000 ~ FRAC
Page 657 and 658:
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Note The shift amount cannot exceed
Page 661 and 662:
} u16In2 = 1; // output should be 0
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} // ##############################
Page 665 and 666:
Subtraction of two fractional 16-bi
Page 667 and 668:
Page 669 and 670:
Page 671 and 672:
} // output should be 0x20000000 f3
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} // as default // ################
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} f32In3 = FRAC32 (0.35); // input4
Page 677 and 678:
Page 679 and 680:
} // output should be FRAC32(0.195)
Page 681 and 682:
} // as default // ################
Page 683 and 684:
Page 685 and 686:
} // input4 value = 0.45 fltIn4 = 0
Page 687 and 688:
Chapter 5 5.1 Typedefs Index Table
Page 689 and 690:
Chapter 6 Compound Data Types Table
Page 691 and 692:
Table 6-1. Compound data types over
Page 693 and 694:
6.2 GDFLIB_FILTER_IIR1_COEFF_T_F32
Page 695 and 696:
6.6 GDFLIB_FILTER_IIR1_T_FLT #inclu
Page 697 and 698:
6.9.2 Compound Type Members Table 6
Page 699 and 700:
6.13 GDFLIB_FILTER_MA_T_F16 #includ
Page 701 and 702:
6.17 GDFLIB_FILTERFIR_PARAM_T_F32 #
Page 703 and 704:
6.21 GDFLIB_FILTERFIR_STATE_T_FLT #
Page 705 and 706:
6.25.1 Description Array of approxi
Page 707 and 708:
6.29.2 Compound Type Members Table
Page 709 and 710:
Page 711 and 712:
Page 713 and 714:
6.41 GFLIB_CONTROLLER_PI_P_T_F32 #i
Page 715 and 716:
6.44 GFLIB_CONTROLLER_PI_R_T_F32 #i
Page 717 and 718:
Table 6-47. GFLIB_CONTROLLER_PIAW_P
Page 719 and 720:
6.49.1 Description Structure contai
Page 721 and 722:
Table 6-52. GFLIB_CONTROLLER_PIAW_R
Page 723 and 724:
Page 725 and 726:
6.59 GFLIB_INTEGRATOR_TR_T_F32 #inc
Page 727 and 728:
6.63 GFLIB_LIMIT_T_FLT #include 6.
Page 729 and 730:
Page 731 and 732:
6.71 GFLIB_LUT2D_T_F32 #include 6.
Page 733 and 734:
Page 735 and 736:
Page 737 and 738:
Page 739 and 740:
Page 741 and 742:
Page 743 and 744:
Page 745 and 746:
Page 747 and 748:
Page 749 and 750:
Chapter 7 7.1 Macro Definitions 7.1
Page 751 and 752:
#define GDFLIB_FILTERFIR_PARAM_T #d
Page 753 and 754:
#define GFLIB_ASIN_T #define GFLIB_
Page 755 and 756:
#define GFLIB_CONTROLLER_PI_R_T #de
Page 757 and 758:
#define GFLIB_LUT1D_DEFAULT #define
Page 759 and 760:
#define GFLIB_Tan #define GFLIB_UPP
Page 761 and 762:
#define INT32TOINT64 #define INT32_
Page 763 and 764:
Chapter 8 Macro References This sec
Page 765 and 766:
Definition of alias for GDFLIB_FILT
Page 767 and 768:
Definition of alias for GDFLIB_FILT
Page 769 and 770:
8.13.1 Macro Definition #define GDF
Page 771 and 772:
Definition of GDFLIB_FILTER_IIR1_DE
Page 773 and 774:
8.21.2 Description This function im
Page 775 and 776:
8.25.2 Description Definition of GD
Page 777 and 778:
Page 779 and 780:
Page 781 and 782:
Definition of GDFLIB_FILTER_MA_DEFA
Page 783 and 784:
8.42.1 Macro Definition #define GFL
Page 785 and 786:
8.46.2 Description Definition of GF
Page 787 and 788:
8.51 Define GFLIB_ACOS_DEFAULT_FLT
Page 789 and 790:
Page 791 and 792:
8.59.2 Description Default approxim
Page 793 and 794:
Page 795 and 796:
Page 797 and 798:
8.73.2 Description This function ca
Page 799 and 800:
8.77 Define GFLIB_ControllerPIp #in
Page 801 and 802:
Definition of GFLIB_CONTROLLER_PI_P
Page 803 and 804:
8.84 Define GFLIB_CONTROLLER_PI_P_D
Page 805 and 806:
Definition of GFLIB_CONTROLLER_PIAW
Page 807 and 808:
8.92 Define GFLIB_CONTROLLER_PIAW_P
Page 809 and 810:
8.96 Define GFLIB_CONTROLLER_PIAW_P
Page 811 and 812:
8.100 Define GFLIB_CONTROLLER_PI_R_
Page 813 and 814:
8.103.2 Description Definition of G
Page 815 and 816:
8.108.1 Macro Definition #define GF
Page 817 and 818:
Page 819 and 820:
Page 821 and 822:
8.120 Define GFLIB_COS_T #include
Page 823 and 824:
8.124 Define GFLIB_COS_DEFAULT_F32
Page 825 and 826:
8.129 Define GFLIB_HYST_T #include
Page 827 and 828:
8.133 Define GFLIB_HYST_DEFAULT #in
Page 829 and 830:
8.138 Define GFLIB_INTEGRATOR_TR_T
Page 831 and 832:
Page 833 and 834:
Page 835 and 836:
8.150 Define GFLIB_LIMIT_T #include
Page 837 and 838:
8.154 Define GFLIB_LIMIT_DEFAULT_F3
Page 839 and 840:
8.159 Define GFLIB_LOWERLIMIT_T #in
Page 841 and 842:
Definition of GFLIB_LOWERLIMIT_DEFA
Page 843 and 844:
Page 845 and 846:
Page 847 and 848:
8.176 Define GFLIB_LUT1D_DEFAULT_FL
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8.184.2 Description Default value f
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8.198.2 Description This function i
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Definition of GFLIB_SIN_DEFAULT as
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Page 869 and 870:
8.225 Define GFLIB_UPPERLIMIT_DEFAU
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8.229 Define GFLIB_UPPERLIMIT_DEFAU
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8.237 Define GFLIB_VECTORLIMIT_DEFA
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8.242.1 Macro Definition #define GM
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8.246 Define GMCLIB_DECOUPLINGPMSM_
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8.249.2 Description Default value f
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Definition of GMCLIB_ELIMDCBUSRIP_D
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8.267.2 Description This function r
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8.273 Define MLIB_Mac #include 8.2
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8.278.1 Macro Definition #define ML
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8.283.2 Description This function s
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8.289 Define MCLIB_VERSION #include
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8.294.2 Description 8.295 Define MC
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8.300.1 Macro Definition #define MC
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8.305.2 Description Constant repres
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8.310.2 Description Value 0.25 in 3
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8.316 Define FLOAT_MIN #include 8.
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8.321.1 Macro Definition #define IN
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8.326.2 Description Type casting -
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8.332 Define INT16TOF32 #include 8
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8.337.1 Macro Definition #define F1
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8.342.1 Macro Definition #define F3
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8.347.1 Macro Definition #define FL
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8.352.2 Description Double to singl
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8.358 Define FLOAT_MINUS_1 #include
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8.363.2 Description Library identif
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Embedded Software and Motor Control Libraries for PXR40xx

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