Vector Park Transform

Functions
void	arm_park_f32 (float32_t Ialpha, float32_t Ibeta, float32_t *pId, float32_t *pIq, float32_t sinVal, float32_t cosVal)
	Floating-point Park transform.
void	arm_park_q31 (q31_t Ialpha, q31_t Ibeta, q31_t *pId, q31_t *pIq, q31_t sinVal, q31_t cosVal)
	Park transform for Q31 version.

Description

Forward Park transform converts the input two-coordinate vector to flux and torque components. The Park transform can be used to realize the transformation of the Ialpha and the Ibeta currents from the stationary to the moving reference frame and control the spatial relationship between the stator vector current and rotor flux vector. If we consider the d axis aligned with the rotor flux, the diagram below shows the current vector and the relationship from the two reference frames:

Stator current space vector and its component in (a,b) and in the d,q rotating reference frame

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 Ialpha and Ibeta are the stator vector components, pId and pIq are rotor vector components and cosVal and sinVal are the cosine and sine values of theta (rotor flux position).

Fixed-Point Behavior

Care must be taken when using the Q31 version of the Park 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

arm_park_f32()

void arm_park_f32	(	float32_t	Ialpha,
		float32_t	Ibeta,
		float32_t *	pId,
		float32_t *	pIq,
		float32_t	sinVal,
		float32_t	cosVal
	)

Floating-point Park transform.

Parameters

[in]	Ialpha	input two-phase vector coordinate alpha
[in]	Ibeta	input two-phase vector coordinate beta
[out]	pId	points to output rotor reference frame d
[out]	pIq	points to output rotor reference frame q
[in]	sinVal	sine value of rotation angle theta
[in]	cosVal	cosine value of rotation angle theta

The function implements the forward Park transform.

arm_park_q31()

void arm_park_q31	(	q31_t	Ialpha,
		q31_t	Ibeta,
		q31_t *	pId,
		q31_t *	pIq,
		q31_t	sinVal,
		q31_t	cosVal
	)

Park transform for Q31 version.

Parameters

[in]	Ialpha	input two-phase vector coordinate alpha
[in]	Ibeta	input two-phase vector coordinate beta
[out]	pId	points to output rotor reference frame d
[out]	pIq	points to output rotor reference frame q
[in]	sinVal	sine value of rotation angle theta
[in]	cosVal	cosine value of rotation angle theta

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 and subtraction, hence there is no risk of overflow.