Embedded Software and Motor Control Libraries for PXR40xx

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

Table 6-1. Compound data types overview (continued) Name Description GFLIB_ASIN_TAYLOR_COEF_T_F32 Array of approximation coefficients for piece-wise polynomial. GFLIB_ATAN_T_F16 Structure containing eight sub-structures with polynomial coefficients to cover all sub-intervals. GFLIB_ATAN_T_F32 Structure containing eight sub-structures with polynomial coefficients to cover all sub-intervals. GFLIB_ATAN_T_FLT Structure containing the approximation coefficients. GFLIB_ATAN_TAYLOR_COEF_T_F16 Array of polynomial approximation coefficients for one sub-interval. GFLIB_ATAN_TAYLOR_COEF_T_F32 Array of minimax polynomial approximation coefficients for one sub-interval. GFLIB_ATANYXSHIFTED_T_F16 Structure containing the parameter for the AtanYXShifted function. GFLIB_ATANYXSHIFTED_T_F32 Structure containing the parameter for the AtanYXShifted function. GFLIB_ATANYXSHIFTED_T_FLT Structure containing the parameter for the AtanYXShifted function. GFLIB_CONTROLLER_PI_P_T_F16 Structure containing parameters and states of the parallel form PI controller. GFLIB_CONTROLLER_PI_P_T_F32 Structure containing parameters and states of the parallel form PI controller. GFLIB_CONTROLLER_PI_P_T_FLT Structure containing parameters and states of the parallel form PI controller. GFLIB_CONTROLLER_PI_R_T_F16 Structure containing parameters and states of the recurrent form PI controller. GFLIB_CONTROLLER_PI_R_T_F32 Structure containing parameters and states of the recurrent form PI controller. GFLIB_CONTROLLER_PI_R_T_FLT Structure containing parameters and states of the recurrent form PI controller. GFLIB_CONTROLLER_PIAW_P_T_F16 Structure containing parameters and states of the parallel form PI controller with anti-windup. GFLIB_CONTROLLER_PIAW_P_T_F32 Structure containing parameters and states of the parallel form PI controller with anti-windup. GFLIB_CONTROLLER_PIAW_P_T_FLT Structure containing parameters and states of the parallel form PI controller with anti-windup. GFLIB_CONTROLLER_PIAW_R_T_F16 Structure containing parameters and states of the recurrent form PI controller with anti-windup. GFLIB_CONTROLLER_PIAW_R_T_F32 Structure containing parameters and states of the recurrent form PI controller with anti-windup. GFLIB_CONTROLLER_PIAW_R_T_FLT Structure containing parameters and states of the recurrent form PI controller with anti-windup. GFLIB_COS_T_F16 Array of four 16-bit elements for storing coefficients of the Taylor polynomial. GFLIB_COS_T_F32 Array of five 32-bit elements for storing coefficients of the Taylor polynomial. GFLIB_COS_T_FLT Array of three single precision floating point elements for storing coefficients of the floating point optimized minimax approximation polynomial. GFLIB_HYST_T_F16 Structure containing parameters and states for the hysteresis function. GFLIB_HYST_T_F32 Structure containing parameters and states for the hysteresis function. GFLIB_HYST_T_FLT Structure containing parameters and states for the hysteresis function. GFLIB_INTEGRATOR_TR_T_F16 Structure containing integrator parameters and coefficients. GFLIB_INTEGRATOR_TR_T_F32 Structure containing integrator parameters and coefficients. GFLIB_INTEGRATOR_TR_T_FLT Structure containing integrator parameters and coefficients. Table continues on the next page... Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0 690 Freescale Semiconductor, Inc.
Table 6-1. Compound data types overview (continued) Name Description GFLIB_LIMIT_T_F16 Structure containing the limits. GFLIB_LIMIT_T_F32 Structure containing the limits. GFLIB_LIMIT_T_FLT Structure containing the limits. GFLIB_LOWERLIMIT_T_F16 Structure containing the lower limit. GFLIB_LOWERLIMIT_T_F32 Structure containing the lower limit. GFLIB_LOWERLIMIT_T_FLT Structure containing the lower limit. GFLIB_LUT1D_T_F16 Structure containing 1D look-up table parameters. GFLIB_LUT1D_T_F32 Structure containing 1D look-up table parameters. GFLIB_LUT1D_T_FLT Structure containing 1D look-up table parameters. GFLIB_LUT2D_T_F16 Structure containing 2D look-up table parameters. GFLIB_LUT2D_T_F32 Structure containing 2D look-up table parameters. GFLIB_LUT2D_T_FLT Structure containing 2D look-up table parameters. GFLIB_RAMP_T_F16 Structure containing increment/decrement coefficients and state value for the ramp function implemented in GFLIB_Ramp. GFLIB_RAMP_T_F32 Structure containing increment/decrement coefficients and state value for the ramp function implemented in GFLIB_Ramp. GFLIB_RAMP_T_FLT Structure containing increment/decrement coefficients and state value for the ramp function implemented in GFLIB_Ramp. GFLIB_SIN_T_F16 Array of four 16-bit elements for storing coefficients of the Taylor polynomial. GFLIB_SIN_T_F32 Array of five 32-bit elements for storing coefficients of the Taylor polynomial. GFLIB_SIN_T_FLT Array of three single precision floating point elements for storing coefficients of the floating point optimized minimax approximation polynomial. GFLIB_TAN_T_F16 Output of tan( $\Pi$ * f16In) for interval [0, $\Pi$/4) of the input angles is divided into eight sub-sectors. Polynomial approximation is done using a 4th order polynomial, for each sub-sector respectively. Eight arrays, each including four polynomial coefficients for each sub-interval, are stored in this (GFLIB_TAN_T_F16) structure. GFLIB_TAN_T_F32 Output of tan( $\Pi$ * f32In) for interval [0, $\Pi$/4) of the input angles is divided into eight sub-sectors. Polynomial approximation is done using a 4th order polynomial, for each sub-sector respectively. Eight arrays, each including four polynomial coefficients for each sub-interval, are stored in this (GFLIB_TAN_T_F32) structure. GFLIB_TAN_T_FLT Polynomial coefficient for fractional approximation in single precision floating point format. GFLIB_TAN_TAYLOR_COEF_T_F16 Structure containing four polynomial coefficients for one sub-interval. GFLIB_TAN_TAYLOR_COEF_T_F32 Structure containing four polynomial coefficients for one sub-interval. GFLIB_UPPERLIMIT_T_F16 Structure containing the upper limit. GFLIB_UPPERLIMIT_T_F32 Structure containing the upper limit. GFLIB_UPPERLIMIT_T_FLT Structure containing the upper limit. GFLIB_VECTORLIMIT_T_F16 Structure containing the limit. GFLIB_VECTORLIMIT_T_F32 Structure containing the limit. GFLIB_VECTORLIMIT_T_FLT Structure containing the limit. Table continues on the next page... Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0 Chapter 6 Compound Data Types Freescale Semiconductor, Inc. 691
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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
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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
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Equation GFLIB_Lut1D_Eq4 where y, y
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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
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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
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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
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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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Page 639 and 640: 4.160.6 Code Example #include "mlib
Page 641 and 642: 4.162.1 Declaration tU16 MLIB_Norm_
Page 643 and 644: 4.163.4 Description This function r
Page 647 and 648: } // output should be 0x10000000 ~
Page 649 and 650: 4.167.2 Arguments Table 4-204. MLIB
Page 651 and 652: 4.168.4 Description Based on sign o
Page 655 and 656: } // output should be 0x4000 ~ FRAC
Page 659 and 660: Note The shift amount cannot exceed
Page 661 and 662: } u16In2 = 1; // output should be 0
Page 663 and 664: } // ##############################
Page 665 and 666: Subtraction of two fractional 16-bi
Page 671 and 672: } // output should be 0x20000000 f3
Page 673 and 674: } // as default // ################
Page 675 and 676: } f32In3 = FRAC32 (0.35); // input4
Page 677 and 678: 4.181.4 Description This inline fun
Page 679 and 680: } // output should be FRAC32(0.195)
Page 681 and 682: } // as default // ################
Page 683 and 684: 4.183.4 Description This inline fun
Page 685 and 686: } // input4 value = 0.45 fltIn4 = 0
Page 687 and 688: Chapter 5 5.1 Typedefs Index Table
Page 689: Chapter 6 Compound Data Types Table
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 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 725 and 726: 6.59 GFLIB_INTEGRATOR_TR_T_F32 #inc
Page 727 and 728: 6.63 GFLIB_LIMIT_T_FLT #include 6.
Page 731 and 732: 6.71 GFLIB_LUT2D_T_F32 #include 6.
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6.90.2 Compound Type Members Table
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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
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Definition of alias for GDFLIB_FILT
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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
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8.25.2 Description Definition of GD
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Definition of GDFLIB_FILTER_MA_DEFA
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8.42.1 Macro Definition #define GFL
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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
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8.108.1 Macro Definition #define GF
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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
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8.138 Define GFLIB_INTEGRATOR_TR_T
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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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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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