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_Atan_F32 4.31.1 Declaration tFrac32 GFLIB_Atan_F32(tFrac32 f32In, const GFLIB_ATAN_T_F32 *const pParam); 4.31.2 Arguments Table 4-38. GFLIB_Atan_F32 arguments Type Name Direction Description tFrac32 f32In input Input argument is a 32-bit number between [-1,1). const GFLIB_ATAN_T_F32 *const 4.31.3 Return pParam input Pointer to an array of minimax approximation coefficients. The function returns the atan of the input argument as a fixed point 32-bit number that contains the angle in radians between [- π/4, π/4), normalized between [-0.25,0.25). 4.31.4 Description The GFLIB_Atan_F32 function provides a computational method for calculation of a standard trigonometric arctangent function arctan(x), using the piece-wise minimax polynomial approximation. Function arctan(x) takes a ratio and returns the angle of two sides of a right-angled triangle. The ratio is the length of the side opposite the angle divided by the length of the side adjacent to the angle. The graph of arctan(x) is shown in Figure 4-19. Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0 234 Freescale Semiconductor, Inc.
Figure 4-19. Course of the function GFLIB_Atan The GFLIB_Atan_F32 function is implemented with consideration to fixed point fractional arithmetic. As can be further seen from Figure 4-19, the arctangent values are identical for the input ranges [-1, 0) and [0, 1). Moreover, it can be observed from Figure 4-19 that the course of the arctan(x) function output for a ratio in interval 1. is identical, but with the opposite sign, to the output for a ratio in interval 2. Therefore, the approximation of the arctangent function over the entire defined range of input ratios can be simplified to the approximation for a ratio in range [0, 1), and then, depending on the input ratio, the result will be negated. In order to increase the accuracy of approximation without the need for a higher order polynomial, the interval [0, 1) is further divided into eight equally spaced sub intervals, and minimax polynomial approximation is done for each interval respectively. Such a division results in eight sets of polynomial coefficients. Moreover, it allows using a polynomial of only the 3rd order to achieve an accuracy of less than 0.5LSB (on the upper 16 bits of 32-bit results) across the entire range of input ratios. The GFLIB_Atan_F32 function uses fixed point fractional arithmetic, so to cast the fractional value of the output angle [-0.25, 0.25) into the correct range [- π/4, π/4), the fixed point output angle can be multiplied by π for an angle in radians. Then, the fixed point fractional implementation of the minimax approximation polynomial, used for calculation of each sub sector, is defined as follows: Equation GFLIB_Atan_Eq1 Embedded Software and Motor Control Libraries for PXR40xx, Rev. 1.0 Chapter 4 API References Freescale Semiconductor, Inc. 235
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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 = (
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 and 194: 4.18.2 Arguments Table 4-18. GDFLIB
Page 195 and 196: eplaced by output from the previous
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 229 and 230: 4.29.5 Re-entrancy The function is
Page 231 and 232: The computation algorithm for arcsi
Page 233: 4.30.5 Re-entrancy The function is
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 and 266: where: Equation GFLIB_AtanYXShifted
Page 267 and 268: 4.39.6 Code Example #include "gflib
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
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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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4.46.2 Arguments Table 4-56. GFLIB_
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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
Page 517 and 518:
Page 519 and 520:
Page 521 and 522:
Page 523 and 524:
For the determination of auxiliary
Page 525 and 526:
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
Page 721 and 722:
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
Page 783 and 784:
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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