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_AtanYXShifted_FLT return; THETAADJ = THETAADJ + 360; end THETAADJ = THETAADJ/180; While applying the function, some general guidelines should be considered as stated below. At some values of the phase shift, and particularly at a phase shift approaching -180, 0 or 180 degrees, the algorithm may become numerically unstable, causing any error, contributed by input signal imperfections or through finite precision arithmetic, to be magnified significantly. Therefore, some care should be taken to avoid error wherever possible. The detailed error analysis of the algorithm is beyond the scope of this documentation, however, general guidelines are provided. There are several sources of error in the function: • error of the supplied signal values due to the finite resolution of the AD conversion • error contributed by higher order harmonics appearing in the input signals • computational error of the multiplication due to the finite length of registers • error of the phase shift Δθ representation in the finite precision arithmetic and in the values • error due to differences in signal amplitudes It should be noted that the function requires both signals to have the same amplitude. To minimize the output error, the amplitude of both signals should have the same amplitude. The function has been tested to be reliable at a phase shift in the range of [-179, -1] and [1, 179] degrees for perfectly sinusoidal input signals. Beyond this range, the function operates correctly, however, the output error can be beyond the guaranteed value. In a real application, an error, contributed by an AD conversion and by higher order harmonics of the input signals, should be also taken into account. Note The function calls the GFLIB_AtanYX_FLT function. The function accuracy is guaranteed for a phase shift in the range of [-179, -1] and [1, 179] degrees at perfect input signals. 4.39.5 Re-entrancy The function is re-entrant. Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0 266 Freescale Semiconductor, Inc.
4.39.6 Code Example #include "gflib.h" tFloat fltInY; tFloat fltInX; tFloat fltAng; GFLIB_ATANYXSHIFTED_T_FLT Param; void main(void) { //dtheta = 69.33deg, thetaoffset = 10deg //KY = 1/(2*cos((69.33/2)/180*pi))= 0.6079089139 //KX = 1/(2*sin((69.33/2)/180*pi))= 0.8790788409 } //THETAADJ = 10*pi/180 = 0.1745329252 Param.fltKy = (tFloat)(0.6079089139); Param.fltKx = (tFloat)(0.8790788409); Param.fltThetaAdj = (tFloat)(0.1745329252); // theta = 15 deg // Y = sin(theta) = 0.2588190 // X = sin(theta + dtheta) = 0.9951074 fltInY = (tFloat)(0.2588190); fltInX = (tFloat)(0.9951074); // Output angle should be 0.69228911 rad fltAng = GFLIB_AtanYXShifted_FLT (fltInY, fltInX, &Param); // Output angle should be 0.69228911 rad fltAng = GFLIB_AtanYXShifted (fltInY, fltInX, &Param, Define FLT); // ############################################################## // Available only if single precision floating point // implementation selected as default // ############################################################## // Output angle should be 0.69228911 rad fltAng = GFLIB_AtanYXShifted (fltInY, fltInX, &Param); 4.40 Function GFLIB_ControllerPIp_F32 This function calculates a parallel form of the Proportional-Integral controller, without integral anti-windup. 4.40.1 Declaration Chapter 4 API References tFrac32 GFLIB_ControllerPIp_F32(tFrac32 f32InErr, GFLIB_CONTROLLER_PI_P_T_F32 *const pParam); Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0 Freescale Semiconductor, Inc. 267
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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_
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
Page 245 and 246: Figure 4-24. atan(x) vs. GFLIB_Atan
Page 247 and 248: 4.34.2 Arguments Table 4-44. GFLIB_
Page 249 and 250: 4.35.1 Declaration tFrac16 GFLIB_At
Page 251 and 252: 4.36 Function GFLIB_AtanYX_FLT The
Page 253 and 254: 4.37.1 Declaration tFrac32 GFLIB_At
Page 255 and 256: The algorithm can be easily justifi
Page 257 and 258: The function has been tested to be
Page 259 and 260: where: Equation GFLIB_AtanYXShifted
Page 261 and 262: The function initialization paramet
Page 263 and 264: } Param.f16Kx = FRAC16 (0.879052013
Page 265: where: Equation GFLIB_AtanYXShifted
Page 269 and 270: Equation GFLIB_ControllerPIp_Eq1 ca
Page 271 and 272: • f32PropGain - is the scaled val
Page 273 and 274: where Equation GFLIB_ControllerPIp_
Page 275 and 276: and where Equation GFLIB_Controller
Page 277 and 278: Proportional-Integral (PI) algorith
Page 279 and 280: } // output should be 1.5e-2 fltOut
Page 281 and 282: where T s [sec] is the sampling tim
Page 283 and 284: The bounds are described by a limit
Page 285 and 286: (GFLIB_CONTROLLER_PIAW_P_T_F16). If
Page 287 and 288: The sum of the scaled proportional
Page 289 and 290: as default // #####################
Page 291 and 292: where T s [sec] is the sampling tim
Page 293 and 294: 4.46.2 Arguments Table 4-56. GFLIB_
Page 295 and 296: where Equation GFLIB_ControllerPIr_
Page 297 and 298: } // output should be 0x00A3D70A f3
Page 299 and 300: Equation GFLIB_ControllerPIr_Eq5 Th
Page 301 and 302: GFLIB_CONTROLLER_PI_R_T_F16 trMyPI
Page 303 and 304: Note All controller parameters and
Page 305 and 306: Equation GFLIB_ControllerPIrAW_Eq2
Page 307 and 308: The introduced scaling shift u16NSh
Page 309 and 310: 4.50 Function GFLIB_ControllerPIrAW
Page 311 and 312: Equation GFLIB_ControllerPIrAW_Eq5
Page 313 and 314: Note All controller parameters and
Page 315 and 316: Transforming equation GFLIB_Control
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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
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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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