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_Sqrt_FLT In the above, the operations to remove last exponent bit and add the bias (according to standard IEEE754) can be combined into a single operation. The formula can be rewritten into C language as: Equation GFLIB_Sqrt_Eq2 For error elimination are the two Babylonian steps added to give a quadratic improvement: Equation GFLIB_Sqrt_Eq3 Equation GFLIB_Sqrt_Eq4 Figure 4-39 depicts a floating point sqrt(x) function generated from Matlab and the calculated value of the sqrt function obtained from GFLIB_Sqrt_FLT, plus their difference. The course of calculation accuracy as a function of the input value can be observed from this figure. The computed value is equal to or is 1LSB less than the true square root value. In order to obtain a value with a 0.5LSB (16bit) accuracy, additional iterations are required. Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0 418 Freescale Semiconductor, Inc.
Figure 4-39. real sqrt(x) vs. GFLIB_Sqrt(fltIn) Note Input argument is a single precision floating point number limited to the range [0, 2 128 ), if not within this range the computed value is undefined. 4.84.5 Re-entrancy The function is re-entrant. 4.84.6 Code Example #include "gflib.h" tFloat fltIn; tFloat fltOut; void main(void) { // input value = 0.5 fltIn = 0.5; // output should be 0.70710678 fltOut = GFLIB_Sqrt_FLT (fltIn); // output should be 0.70710678 fltOut = GFLIB_Sqrt (fltIn,Define FLT); Chapter 4 API References // ############################################################## // Available only if single precision floating point // implementation selected as default // ############################################################## Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0 Freescale Semiconductor, Inc. 419
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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
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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
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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 4-19. Course of the function
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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
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[- 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
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4.62.4 Description The GFLIB_Limit
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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
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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
Page 367 and 368: Equation GFLIB_Lut1D_Eq4 where y, y
Page 369 and 370: 4.70.2 Arguments Table 4-89. GFLIB_
Page 371 and 372: Equation GFLIB_Lut2D_Eq4 Equation G
Page 373 and 374: Equation GFLIB_Lut2D_Eq16 It should
Page 375 and 376: } // output should be 0x7A03D70A ~
Page 377 and 378: The Table 4-92 contains 4 interpola
Page 379 and 380: Equation GFLIB_Lut2D_Eq13 5. Final
Page 381 and 382: FRAC16 (0.2), FRAC16 (0.21), FRAC16
Page 383 and 384: where: Equation GFLIB_Lut2D_Eq3 •
Page 385 and 386: Equation GFLIB_Lut2D_Eq10 6. The sa
Page 387 and 388: 0.88}; tFloat pfltTable2D[81] = {0.
Page 389 and 390: 4.73.5 Re-entrancy The function is
Page 391 and 392: Figure 4-32. GFLIB_Ramp functionali
Page 393 and 394: If the desired (input) value is gre
Page 395 and 396: 4.76.3 Return The function returns
Page 397 and 398: In mathematical terms, the function
Page 399 and 400: Note The input and the output are i
Page 401 and 402: The 9th order polynomial approximat
Page 403 and 404: Figure 4-34. sin(x) vs. GFLIB_Sin_F
Page 405 and 406: 4.80.2 Arguments Table 4-101. GFLIB
Page 407 and 408: Therefore, the resulting equation h
Page 409 and 410: 4.81 Function GFLIB_Sin_FLT This fu
Page 411 and 412: Figure 4-36 depicts a floating poin
Page 413 and 414: 4.82.1 Declaration tFrac32 GFLIB_Sq
Page 415 and 416: } // output should be 0x5A820000 ~
Page 417: } // output should be 0x5A82 ~ FRAC
Page 421 and 422: Equation GFLIB_Tan_Eq1 Because both
Page 423 and 424: Figure 4-41. tan(x) vs. GFLIB_Tan(f
Page 425 and 426: 4.86.1 Declaration tFrac16 GFLIB_Ta
Page 427 and 428: Equation GFLIB_Tan_Eq3 The division
Page 431 and 432: Figure 4-44. Course of the function
Page 433 and 434: Figure 4-45. tan(x) vs. GFLIB_Tan(f
Page 435 and 436: 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 447 and 448: • x in, y in and x out, y out are
Page 449 and 450: 4.94.2 Arguments Table 4-119. GMCLI
Page 457 and 458: 4.98.1 Declaration void GMCLIB_Clar
Page 459 and 460: 4.99.1 Declaration void GMCLIB_Clar
Page 461 and 462: 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
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Equation GMCLIB_DecouplingPMSM_Eq4
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Scaling of both equations into the
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4.102.4 Description The quadrature
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available DC bus voltage. Therefore
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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
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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
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4.109 Function GMCLIB_ParkInv_F32 T
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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
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Figure 4-50. Basic space vectors Th
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Figure 4-51. Projection of referenc
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Equation GMCLIB_SvmStd_Eq7 Equation
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Equation GMCLIB_SvmStd_Eq11 and equ
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For the determination of auxiliary
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Equation GMCLIB_SvmStd_Eq25 Equatio
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} // output pwm dutycycles stored i
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Top and bottom switches work in a c
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For the determination of auxiliary
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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
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Table 4-150. Determination of t_1 a
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It should be pointed out that, in t
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calculation precision in boundary i
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Note Due to effectivity reason this
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4.116.3 Return Absolute value of in
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} // output should be FRAC16(0.25)
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tFrac32 f32Out; void main(void) { /
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4.120 Function MLIB_Add_F32 This fu
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4.121.6 Code Example #include "mlib
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4.122.4 Description This inline fun
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4.123 Function MLIB_AddSat_F32 This
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4.125.3 Return Converted input valu
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and converted to the output format.
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Equation MLIB_Convert_Eq1 Note Due
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4.132 Function MLIB_ConvertPU_F32FL
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4.133.3 Return Converted input valu
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4.136 Function MLIB_ConvertPU_FLTF3
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denominator, the output value is un
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Equation MLIB_Div_Eq1 Note Due to e
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} // output should be FRAC16(0.5) =
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} // 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
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} // ##############################
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4.147 Function MLIB_MacSat_F32F16F1
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4.148.2 Arguments Table 4-185. MLIB
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Table 4-186. MLIB_Mul_F32 arguments
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void main(void) { // first input =
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} // output should be 0x10000000 =
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4.152.4 Description Single precisio
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4.153 Function MLIB_MulSat_F32 This
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Equation MLIB_MulSat_Eq1 Note Overf
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Note Overflow is detected. The func
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4.155.3 Return Fractional multiplic
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} f16In2 = FRAC16 (0.75); // output
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4.157.1 Declaration tFrac16 MLIB_Ne
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4.162.1 Declaration tU16 MLIB_Norm_
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4.163.4 Description This function r
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} // output should be 0x10000000 ~
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4.168.4 Description Based on sign o
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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
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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 // ################
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} // input4 value = 0.45 fltIn4 = 0
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Chapter 5 5.1 Typedefs Index Table
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Chapter 6 Compound Data Types Table
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Table 6-1. Compound data types over
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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 #
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6.21 GDFLIB_FILTERFIR_STATE_T_FLT #
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6.25.1 Description Array of approxi
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6.29.2 Compound Type Members Table
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6.41 GFLIB_CONTROLLER_PI_P_T_F32 #i
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6.44 GFLIB_CONTROLLER_PI_R_T_F32 #i
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Table 6-47. GFLIB_CONTROLLER_PIAW_P
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6.49.1 Description Structure contai
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Table 6-52. GFLIB_CONTROLLER_PIAW_R
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6.59 GFLIB_INTEGRATOR_TR_T_F32 #inc
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6.63 GFLIB_LIMIT_T_FLT #include 6.
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6.71 GFLIB_LUT2D_T_F32 #include 6.
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Chapter 7 7.1 Macro Definitions 7.1
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#define GDFLIB_FILTERFIR_PARAM_T #d
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#define GFLIB_ASIN_T #define GFLIB_
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#define GFLIB_CONTROLLER_PI_R_T #de
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#define GFLIB_LUT1D_DEFAULT #define
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#define GFLIB_Tan #define GFLIB_UPP
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#define INT32TOINT64 #define INT32_
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Chapter 8 Macro References This sec
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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
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Definition of GDFLIB_FILTER_IIR1_DE
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8.21.2 Description This function im
Page 775 and 776:
8.25.2 Description Definition of GD
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Page 781 and 782:
Definition of GDFLIB_FILTER_MA_DEFA
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8.42.1 Macro Definition #define GFL
Page 785 and 786:
8.46.2 Description Definition of GF
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8.51 Define GFLIB_ACOS_DEFAULT_FLT
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8.59.2 Description Default approxim
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8.73.2 Description This function ca
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8.77 Define GFLIB_ControllerPIp #in
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Definition of GFLIB_CONTROLLER_PI_P
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8.84 Define GFLIB_CONTROLLER_PI_P_D
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Definition of GFLIB_CONTROLLER_PIAW
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8.92 Define GFLIB_CONTROLLER_PIAW_P
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8.96 Define GFLIB_CONTROLLER_PIAW_P
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8.100 Define GFLIB_CONTROLLER_PI_R_
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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:
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8.120 Define GFLIB_COS_T #include
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8.124 Define GFLIB_COS_DEFAULT_F32
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8.129 Define GFLIB_HYST_T #include
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8.133 Define GFLIB_HYST_DEFAULT #in
Page 829 and 830:
8.138 Define GFLIB_INTEGRATOR_TR_T
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Page 833 and 834:
Page 835 and 836:
8.150 Define GFLIB_LIMIT_T #include
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8.154 Define GFLIB_LIMIT_DEFAULT_F3
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8.159 Define GFLIB_LOWERLIMIT_T #in
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Definition of GFLIB_LOWERLIMIT_DEFA
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Page 847 and 848:
8.176 Define GFLIB_LUT1D_DEFAULT_FL
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8.184.2 Description Default value f
Page 853 and 854:
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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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8.225 Define GFLIB_UPPERLIMIT_DEFAU
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8.229 Define GFLIB_UPPERLIMIT_DEFAU
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Page 875 and 876:
8.237 Define GFLIB_VECTORLIMIT_DEFA
Page 877 and 878:
8.242.1 Macro Definition #define GM
Page 879 and 880:
8.246 Define GMCLIB_DECOUPLINGPMSM_
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8.249.2 Description Default value f
Page 883 and 884:
Page 885 and 886:
Definition of GMCLIB_ELIMDCBUSRIP_D
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8.267.2 Description This function r
Page 891 and 892:
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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