Embedded Software and Motor Control Libraries for PXR40xx

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

Function GFLIB_Cos_F32 Because the GFLIB_Cos_F32 function is implemented with consideration to fixed point fractional arithmetic, all variables are normalized to fit into the [-1, 1) range. Therefore, in order to cast the fractional value of the input angle f32In [-1, 1) into the correct range [- π, π), the input f32In must be multiplied by π. So, the fixed point fractional implementation of the GFLIB_Sin_F32 function, using 9th order Taylor approximation, is given as follows: Equation GFLIB_Cos_Eq3 The 9th order polynomial approximation of the sine function has a very good accuracy in the range [- π/2, π/2) of the argument, but in wider ranges the calculation error quickly increases. To minimize the error without having to use a higher order polynomial, the symmetry of the sine function sin(x) = sin( π - x) is utilized. Therefore, the input argument is transferred to be always in the range [- π/2, π/2) and the Taylor polynomial is calculated only in the range of the argument [- π/2, π/2). To make calculations more precise, the given argument value f32In (that is to be transferred into the range [-0.5, 0.5) due to the sine function symmetry) is shifted by 1 bit to the left (multiplied by 2). Then, the value of f32In 2 , used in the calculations, is in the range [-1, 1) instead of [-0.25, 0.25]. Shifting the input value by 1 bit to the left will increase the accuracy of the calculated sin( π * f32In) function. Implementing such a scale on the approximation function described by equation GFLIB_Cos_Eq2, results in the following: Equation GFLIB_Cos_Eq4 Equation GFLIB_Cos_Eq3 can be further rewritten into the following form: Equation GFLIB_Cos_Eq5 Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0 318 Freescale Semiconductor, Inc.
where a 1...a 5 are coefficients of the approximation polynomial, which are calculated as follows (represented as 32-bit signed fractional numbers): Equation GFLIB_Cos_Eq6 Therefore, the resulting equation has the following form: Equation GFLIB_Cos_Eq7 Chapter 4 API References Figure 4-25 depicts a floating point cosine function generated from Matlab and the approximated value of the cosine function obtained from GFLIB_Cos_F32, plus their difference. The course of calculation accuracy as a function of the input angle can be observed from this figure. Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0 Freescale Semiconductor, Inc. 319
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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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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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Section number Title Page 6.17.2 Co
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Section number Title Page 8.9 Defin
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Section number Title Page 8.28 Defi
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Section number Title Page 8.104 Def
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Chapter 1 1.1 License Agreement IMP
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Agreement, and require that you sto
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Chapter 1 ENTIRE RISK ARISING OUT O
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confidential information. The Licen
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Chapter 2 Introduction The aim of t
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Chapter 2 Introduction 2.2 General
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For example if the MCLIB_DEFAULT_IM
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and gmclib.h. This was done to simp
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Chapter 2 Introduction Figure 2-4.
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In order to integrate the Embedded
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Figure 2-12. Opening the C editor f
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Figure 2-15. Selecting the include
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• Library binary files located in
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Chapter 2 Introduction In order to
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Figure 2-24. Principle of MCLib tes
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2.13.2 MCLib target-in-loop Testing
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Chapter 3 3.1 Function Index Table
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Table 3-1. Quick function reference
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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
Page 179 and 180:
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
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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
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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
Page 267 and 268: 4.39.6 Code Example #include "gflib
Page 269 and 270: Equation GFLIB_ControllerPIp_Eq1 ca
Page 271 and 272: • f32PropGain - is the scaled val
Page 273 and 274: where Equation GFLIB_ControllerPIp_
Page 275 and 276: and where Equation GFLIB_Controller
Page 277 and 278: Proportional-Integral (PI) algorith
Page 279 and 280: } // output should be 1.5e-2 fltOut
Page 281 and 282: where T s [sec] is the sampling tim
Page 283 and 284: The bounds are described by a limit
Page 285 and 286: (GFLIB_CONTROLLER_PIAW_P_T_F16). If
Page 287 and 288: The sum of the scaled proportional
Page 289 and 290: as default // #####################
Page 291 and 292: where T s [sec] is the sampling tim
Page 293 and 294: 4.46.2 Arguments Table 4-56. GFLIB_
Page 295 and 296: where Equation GFLIB_ControllerPIr_
Page 297 and 298: } // output should be 0x00A3D70A f3
Page 299 and 300: Equation GFLIB_ControllerPIr_Eq5 Th
Page 301 and 302: GFLIB_CONTROLLER_PI_R_T_F16 trMyPI
Page 303 and 304: Note All controller parameters and
Page 305 and 306: Equation GFLIB_ControllerPIrAW_Eq2
Page 307 and 308: The introduced scaling shift u16NSh
Page 309 and 310: 4.50 Function GFLIB_ControllerPIrAW
Page 311 and 312: Equation GFLIB_ControllerPIrAW_Eq5
Page 313 and 314: Note All controller parameters and
Page 315 and 316: Transforming equation GFLIB_Control
Page 317: 4.52.1 Declaration tFrac32 GFLIB_Co
Page 321 and 322: 4.52.5 Re-entrancy The function is
Page 323 and 324: [- π, π ), the input f16In must b
Page 325 and 326: Figure 4-26. cos(x) vs. GFLIB_Cos(f
Page 329 and 330: Table 4-71. Approximation polynomia
Page 331 and 332: 4.55 Function GFLIB_Hyst_F32 This f
Page 333 and 334: tFrac32 f32In; tFrac32 f32Out; GFLI
Page 335 and 336: CAUTION For correct functionality,
Page 337 and 338: Equation GFLIB_Hyst_Eq1 A graphical
Page 339 and 340: 4.58.4 Description The function GFL
Page 341 and 342: void main(void) { // Setting parame
Page 343 and 344: where E MAX is the input scale and
Page 345 and 346: 4.60.4 Description The function GFL
Page 349 and 350: 4.62.4 Description The GFLIB_Limit
Page 351 and 352: 4.63.5 Re-entrancy The function is
Page 353 and 354: } // output should be 0x60000000 ~
Page 355 and 356: 4.66.1 Declaration tFloat GFLIB_Low
Page 357 and 358: 4.67.4 Description where: Equation
Page 359 and 360: It should be noted that the computa
Page 361 and 362: Table 4-86. GFLIB_Lut1D_F16 argumen
Page 363 and 364: Equation GFLIB_Lut1D_Eq4 where y, y
Page 365 and 366: 4.69 Function GFLIB_Lut1D_FLT This
Page 367 and 368: 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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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
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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
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4.81 Function GFLIB_Sin_FLT This fu
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Figure 4-36 depicts a floating poin
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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
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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
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4.89.4 Description The GFLIB_UpperL
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void main(void) { // upper limit fl
Page 441 and 442:
Figure 4-46. Graphical interpretati
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4.92.2 Arguments Table 4-117. GFLIB
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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:
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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
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4.101.2 Arguments Table 4-126. GMCL
Page 469 and 470:
Equation GMCLIB_DecouplingPMSM_Eq4
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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
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• 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
Page 489 and 490:
4.107 Function GMCLIB_Park_F16 This
Page 491 and 492:
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
Page 497 and 498:
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
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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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denominator, the output value is un
Page 591 and 592:
Equation MLIB_Div_Eq1 Note Due to e
Page 593 and 594:
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} // output should be FRAC16(0.5) =
Page 597 and 598:
} // output should be FRAC32(0.3025
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} f32Out = MLIB_Mac_F32F16F16(f32In
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} // output should be FRAC16(0.3025
Page 605 and 606:
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} // ##############################
Page 609 and 610:
4.147 Function MLIB_MacSat_F32F16F1
Page 611 and 612:
4.148.2 Arguments Table 4-185. MLIB
Page 613 and 614:
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
Page 633 and 634:
4.157.1 Declaration tFrac16 MLIB_Ne
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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:
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} // output should be 0x10000000 ~
Page 649 and 650:
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4.168.4 Description Based on sign o
Page 653 and 654:
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} // output should be 0x4000 ~ FRAC
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Note The shift amount cannot exceed
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} u16In2 = 1; // output should be 0
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} // ##############################
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Subtraction of two fractional 16-bi
Page 667 and 668:
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} // output should be 0x20000000 f3
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} // as default // ################
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} f32In3 = FRAC32 (0.35); // input4
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} // output should be FRAC32(0.195)
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} // as default // ################
Page 683 and 684:
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} // 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
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Table 6-1. Compound data types over
Page 693 and 694:
6.2 GDFLIB_FILTER_IIR1_COEFF_T_F32
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6.6 GDFLIB_FILTER_IIR1_T_FLT #inclu
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6.9.2 Compound Type Members Table 6
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6.13 GDFLIB_FILTER_MA_T_F16 #includ
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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
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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.
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Page 739 and 740:
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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
Page 849 and 850:
Page 851 and 852:
8.184.2 Description Default value f
Page 853 and 854:
Page 855 and 856:
Page 857 and 858:
8.198.2 Description This function i
Page 859 and 860:
Definition of GFLIB_SIN_DEFAULT as
Page 861 and 862:
Page 863 and 864:
Page 865 and 866:
Page 867 and 868:
Page 869 and 870:
8.225 Define GFLIB_UPPERLIMIT_DEFAU
Page 871 and 872:
8.229 Define GFLIB_UPPERLIMIT_DEFAU
Page 873 and 874:
Page 875 and 876:
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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