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_Lut1D_F16 Table 4-87. GFLIB_Lut1D example table (continued) 0.5 N/A 2*(2 -1 ) The Table 4-87 contains 4 interpolating points (note four rows). The interpolating interval length in this example is equal to 2 -1 . The pf16Table parameter points to the second row, defining also the interpolating index 0. The x-coordinates of the interpolating points are calculated in the right column. It should be noted that the pf16Table pointer does not have to point to the start of the memory area of ordinate values. Therefore, the interpolating index can be positive or negative or, even, does not have to have zero in its range. A special algorithm is used to make the computation efficient, however, under some additional assumptions, as provided below: • the values of the interpolated function are 16 bits long • the length of each interpolating interval is equal to 2 -n , where n is an integer in the range of 1, 2, ... 13 • the provided abscissa for interpolation is 16 bits long The algorithm performs the following steps: 1. Compute the index representing the interval, in which the linear interpolation will be performed: Equation GFLIB_Lut1D_Eq2 where I is the interval index and the s Interval the shift amount provided in the parameters structure as the member s16ShamIntvl. The operator >> represents the binary arithmetic right shift. 2. Compute the abscissa offset within an interpolating interval: 3. Equation GFLIB_Lut1D_Eq3 where Δ{x} is the abscissa offset within an interval and the s Offset is the shift amount provided in the parameters structure. The operators
Equation GFLIB_Lut1D_Eq4 where y, y 1 and y 2 are, respectively, the interpolated value, the ordinate at the start of the interpolating interval, the ordinate at the end of the interpolating interval. The pTable is the address provided in the parameters structure pParam->f16Table. It should be noted that due to assumption of equidistant data points, division by the interval length is avoided. It should be noted that the computations are performed with a 16-bit accuracy. In particular, the 16 least significant bits are ignored in all multiplications. The shift amounts shall be provided in the parameters structure (pParam- >s16ShamOffset, pParam->s16ShamIntvl). The address of the table with the data, the pTable, shall be defined by the parameter structure member pParam->pf16Table. The shift amounts, the s Interval and s Offset, can be computed with the following formulas: Equation GFLIB_Lut1D_Eq5 Chapter 4 API References where n is the integer defining the length of the interpolating interval in the range of -1, -2, ... -15. The computation of the abscissa offset and the interval index can be viewed also in the following way. The input abscissa value can be divided into two parts. The first n most significant bits of the 16-bit halfword, after the sign bit, compose the interval index, in which interpolation is performed. The rest of the bits form the abscissa offset within the interpolating interval. This simple way to calculate the interpolating interval index and the abscissa offset is the consequence of assuming that all interpolating interval lengths equal 2 -n . It should be noted that the input abscissa value can be positive or negative. If it is, positive then the ordinate values are read as in the ordinary data array, that is, at or after the data pointer provided in the parameters structure (pParam->pf16Table). However, if it is negative, then the ordinate values are read from the memory, which is located behind the pParam->pf16Table pointer. Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0 Freescale Semiconductor, Inc. 363
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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 4-20 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
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 and 318: 4.52.1 Declaration tFrac32 GFLIB_Co
Page 319 and 320: where a 1...a 5 are coefficients of
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 327 and 328: 4.54.2 Arguments Table 4-70. GFLIB_
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 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: Table 4-86. GFLIB_Lut1D_F16 argumen
Page 365 and 366: 4.69 Function GFLIB_Lut1D_FLT This
Page 367 and 368: Equation GFLIB_Lut1D_Eq4 where y, y
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 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
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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
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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
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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
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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
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4.94.2 Arguments Table 4-119. GMCLI
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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
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The feed-forward voltages u_dq_comp
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Equation GMCLIB_DecouplingPMSM_Eq10
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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
Page 555 and 556:
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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_
Page 763 and 764:
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
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
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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
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Page 791 and 792:
8.59.2 Description Default approxim
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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
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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:
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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:
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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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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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