Embedded Software and Motor Control Libraries for PXR40xx

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

Function GDFLIB_FilterIIR2_FLT In order to implement the second order IIR filter on a microcontroller, the discrete time domain representation of the filter, described by eq. GDFLIB_FilterIIR2_Eq2, must be transformed into a time difference equation as follows: Equation GDFLIB_FilterIIR2_Eq3 where: x[k] is the input signal, y[k] is the output signal, a i and b i are the filter coefficients. Equation GDFLIB_FilterIIR2_Eq3 represents a Direct Form I implementation of a second order IIR filter. It is well known that Direct Form I (DF-I) and Direct Form II (DF-II) implementations of an IIR filter are generally sensitive to parameter quantization if a finite precision arithmetic is considered. This, however, can be neglected when the filter transfer function is broken down into lower order sections, i.e. first or second order. The main difference between DF-I and DF-II implementations of an IIR filter is in the number of delay buffers and in the number of guard bits required to handle the potential overflow. The DF-II implementation requires less delay buffers than DF-I, hence less data memory is utilized. On the other hand, since the poles come first in the DF-II realization, the signal entering the state delay-line typically requires a larger dynamic range than the output signal y(k). Therefore, overflow can occur at the delay-line input of the DF-II implementation, unlike in the DF-I implementation. Figure 4-6. Direct Form 1 second order IIR filter The coefficients of the filter depicted in Figure 4-6 can be designed to meet the requirements for the second order Band Pass (BPF) or Band Stop (BSF) filters. Filter coefficients can be calculated using various tools, for example the Matlab butter function. Note To enumerate the computation error in one calculation cycle, the internal accumulator is not used for testing purposes and is Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0 194 Freescale Semiconductor, Inc.
eplaced by output from the previous calculation step of the Matlab precise reference model. CAUTION The filter delay line includes four delay buffers which should be reset after filter initialization. This can be done by assigning to the filter instance a GDFLIB_FILTER_IIR2_DEFAULT_FLT macro during instance declaration or by calling the GDFLIB_FilterIIR2Init_FLT function. 4.18.5 Re-entrancy The function is re-entrant. 4.18.6 Code Example #include "gdflib.h" tFloat fltIn; tFloat fltOut; GDFLIB_FILTER_IIR2_T_FLT flttrMyIIR2 = GDFLIB_FILTER_IIR2_DEFAULT_FLT; void main(void) { // input value = 0.25 fltIn = (tFloat)(0.25); } // filter coefficients (BPF 400-625Hz, Ts=100e-6) flttrMyIIR2.trFiltCoeff.fltB0 = (tFloat)(0.066122101544579); flttrMyIIR2.trFiltCoeff.fltB1 = (tFloat)(0.0); flttrMyIIR2.trFiltCoeff.fltB2 = (tFloat)(-0.066122101544579); flttrMyIIR2.trFiltCoeff.fltA1 = (tFloat)(-1.776189018043779); flttrMyIIR2.trFiltCoeff.fltA2 = (tFloat)(0.867755796910841); // output should be 0.01651 GDFLIB_FilterIIR2Init_FLT (&flttrMyIIR2); fltOut = GDFLIB_FilterIIR2_FLT (fltIn, &flttrMyIIR2); // output should be 0.01651 GDFLIB_FilterIIR2Init (&flttrMyIIR2, Define FLT); fltOut = GDFLIB_FilterIIR2 (fltIn, &flttrMyIIR2, Define FLT); // ############################################################## // Available only if single precision floating point // implementation selected as default // ############################################################## // output should be 0.01651 GDFLIB_FilterIIR2Init (&flttrMyIIR2); fltOut = GDFLIB_FilterIIR2 (fltIn, &flttrMyIIR2); Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0 Chapter 4 API References Freescale Semiconductor, Inc. 195
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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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Table 3-1. Quick function reference
Page 143 and 144: Table 3-1. Quick function reference
Page 149 and 150: Chapter 4 API References This secti
Page 151 and 152: F32); tFrac32 f32CoefBuf[FIR_NUMTAP
Page 153 and 154: Equation GDFLIB_FilterFIR_Eq1 where
Page 155 and 156: F32); } GDFLIB_FilterFIRInit (&Para
Page 157 and 158: F16); tFrac16 f16CoefBuf[FIR_NUMTAP
Page 161 and 162: F16); } GDFLIB_FilterFIRInit (&Para
Page 163 and 164: FLT); tFloat fltCoefBuf[FIR_NUMTAPS
Page 167 and 168: } } // ############################
Page 169 and 170: 4.8.3 Return The function returns a
Page 171 and 172: macro during instance declaration o
Page 173 and 174: 4.9.6 Code Example #include "gdflib
Page 175 and 176: signal entering the state delay-lin
Page 177 and 178: 4.11.2 Arguments Table 4-11. GDFLIB
Page 179 and 180: A general form of the IIR filter ex
Page 181 and 182: } flttrMyIIR1.trFiltCoeff.fltB0 = (
Page 183 and 184: 4.14.2 Arguments Table 4-14. GDFLIB
Page 185 and 186: freq_bot = 400; freq_top = 625; T_s
Page 187 and 188: 4.15.4 Description This function cl
Page 189 and 190: In order to implement the second or
Page 191 and 192: } f16trMyIIR2.trFiltCoeff.f16B0 = F
Page 193: 4.18.2 Arguments Table 4-18. GDFLIB
Page 197 and 198: Note This function shall not be cal
Page 199 and 200: call. The number of the filtered po
Page 209 and 210: Figure 4-7. Course of the function
Page 211 and 212: Figure 4-8. acos(x) vs. GFLIB_Acos(
Page 213 and 214: 4.26.2 Arguments Table 4-27. GFLIB_
Page 215 and 216: Table 4-28. Integer polynomial coef
Page 217 and 218: 4.27 Function GFLIB_Acos_FLT This f
Page 219 and 220: The arccos(x) values are then calcu
Page 221 and 222: } // output should be 1.570796 fltA
Page 223 and 224: Equation GFLIB_Asin_Eq3 Equation GF
Page 225 and 226: 4.28.5 Re-entrancy The function is
Page 227 and 228: where: Equation GFLIB_Asin_Eq1 •
Page 231 and 232: The computation algorithm for arcsi
Page 235 and 236: Figure 4-19. Course of the function
Page 237 and 238: Figure 4-20 depicts a floating poin
Page 239 and 240: 4.32.4 Description The GFLIB_Atan_F
Page 241 and 242: Figure 4-22. atan(x) vs. GFLIB_Atan
Page 243 and 244: Table 4-42. GFLIB_Atan_FLT argument
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Figure 4-24. atan(x) vs. GFLIB_Atan
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4.34.2 Arguments Table 4-44. GFLIB_
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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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4.52.5 Re-entrancy The function is
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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 4-44. Course of the function
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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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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
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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
Page 825 and 826:
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
Page 837 and 838:
8.154 Define GFLIB_LIMIT_DEFAULT_F3
Page 839 and 840:
8.159 Define GFLIB_LOWERLIMIT_T #in
Page 841 and 842:
Definition of GFLIB_LOWERLIMIT_DEFA
Page 843 and 844:
Page 845 and 846:
Page 847 and 848:
8.176 Define GFLIB_LUT1D_DEFAULT_FL
Page 849 and 850:
Page 851 and 852:
8.184.2 Description Default value f
Page 853 and 854:
Page 855 and 856:
Page 857 and 858:
8.198.2 Description This function i
Page 859 and 860:
Definition of GFLIB_SIN_DEFAULT as
Page 861 and 862:
Page 863 and 864:
Page 865 and 866:
Page 867 and 868:
Page 869 and 870:
8.225 Define GFLIB_UPPERLIMIT_DEFAU
Page 871 and 872:
8.229 Define GFLIB_UPPERLIMIT_DEFAU
Page 873 and 874:
Page 875 and 876:
8.237 Define GFLIB_VECTORLIMIT_DEFA
Page 877 and 878:
8.242.1 Macro Definition #define GM
Page 879 and 880:
8.246 Define GMCLIB_DECOUPLINGPMSM_
Page 881 and 882:
8.249.2 Description Default value f
Page 883 and 884:
Page 885 and 886:
Definition of GMCLIB_ELIMDCBUSRIP_D
Page 887 and 888:
Page 889 and 890:
8.267.2 Description This function r
Page 891 and 892:
8.273 Define MLIB_Mac #include 8.2
Page 893 and 894:
8.278.1 Macro Definition #define ML
Page 895 and 896:
8.283.2 Description This function s
Page 897 and 898:
8.289 Define MCLIB_VERSION #include
Page 899 and 900:
8.294.2 Description 8.295 Define MC
Page 901 and 902:
8.300.1 Macro Definition #define MC
Page 903 and 904:
8.305.2 Description Constant repres
Page 905 and 906:
8.310.2 Description Value 0.25 in 3
Page 907 and 908:
8.316 Define FLOAT_MIN #include 8.
Page 909 and 910:
8.321.1 Macro Definition #define IN
Page 911 and 912:
8.326.2 Description Type casting -
Page 913 and 914:
8.332 Define INT16TOF32 #include 8
Page 915 and 916:
8.337.1 Macro Definition #define F1
Page 917 and 918:
8.342.1 Macro Definition #define F3
Page 919 and 920:
8.347.1 Macro Definition #define FL
Page 921 and 922:
8.352.2 Description Double to singl
Page 923 and 924:
8.358 Define FLOAT_MINUS_1 #include
Page 925 and 926:
8.363.2 Description Library identif
Page 927:
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Embedded Software and Motor Control Libraries for PXR40xx

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