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 Vector Clarke Transform CMSIS-DSP: Vector Clarke Transform
CMSIS-DSP  Version 1.7.0
CMSIS DSP Software Library

Functions

__STATIC_FORCEINLINE void arm_clarke_f32 (float32_t Ia, float32_t Ib, float32_t *pIalpha, float32_t *pIbeta)
Floating-point Clarke transform. More...

__STATIC_FORCEINLINE void arm_clarke_q31 (q31_t Ia, q31_t Ib, q31_t *pIalpha, q31_t *pIbeta)
Clarke transform for Q31 version. More...

Description

Forward Clarke transform converts the instantaneous stator phases into a two-coordinate time invariant vector. Generally the Clarke transform uses three-phase currents Ia, Ib and Ic to calculate currents in the two-phase orthogonal stator axis Ialpha and Ibeta. When Ialpha is superposed with Ia as shown in the figure below

Stator current space vector and its components in (a,b).

and Ia + Ib + Ic = 0, in this condition Ialpha and Ibeta can be calculated using only Ia and Ib.

The function operates on a single sample of data and each call to the function returns the processed output. The library provides separate functions for Q31 and floating-point data types.

Algorithm
where Ia and Ib are the instantaneous stator phases and pIalpha and pIbeta are the two coordinates of time invariant vector.
Fixed-Point Behavior
Care must be taken when using the Q31 version of the Clarke transform. In particular, the overflow and saturation behavior of the accumulator used must be considered. Refer to the function specific documentation below for usage guidelines.

Function Documentation

__STATIC_FORCEINLINE void arm_clarke_f32 ( float32_t  Ia,
float32_t  Ib,
float32_t pIalpha,
float32_t pIbeta
)
Parameters
[in]Iainput three-phase coordinate a
[in]Ibinput three-phase coordinate b
[out]pIalphapoints to output two-phase orthogonal vector axis alpha
[out]pIbetapoints to output two-phase orthogonal vector axis beta
Returns
none
__STATIC_FORCEINLINE void arm_clarke_q31 ( q31_t  Ia,
q31_t  Ib,
q31_t pIalpha,
q31_t pIbeta
)
Parameters
[in]Iainput three-phase coordinate a
[in]Ibinput three-phase coordinate b
[out]pIalphapoints to output two-phase orthogonal vector axis alpha
[out]pIbetapoints to output two-phase orthogonal vector axis beta
Returns
none
Scaling and Overflow Behavior
The function is implemented using an internal 32-bit accumulator. The accumulator maintains 1.31 format by truncating lower 31 bits of the intermediate multiplication in 2.62 format. There is saturation on the addition, hence there is no risk of overflow.