This page describes some details of sensorless method used in PMC. Also look into porting guide.
ADC is sampled at the begin of PWM period. The values obtained are processed by software. The new value of duty cycle is loaded to the hardware timer. This value is used at next PWM period. ADC samples are made using two ADCs in order shown in the diagram.
// Control loop diagram //
|<--------------------- dT ---------------------->|
| |
| TIM update +----+---+----+ PWM |
| / | | | | <-- waveforms |
|/ | | | | |
---*--*--*-----------------------------+-------------*---
| | | | |
iA uS uB preload DC |
iB uA uC to hw timer --> TIM
\ /
pm_feedback() /
p_set_DC(xA, xB, xC)
We need about 3 us before ADC samples to be clean. If MOSFET switching occurs at this time then the result is not used.
Now consider the internals of the pm_feedback procedure. At simplest view it is state observer. We use the following state vector X[5]:
X[0] (iD) current on D axis [A]
X[1] (iQ) current on Q axis [A]
X[2] DQ frame cosine
X[3] DQ frame sine (so atan(X[3] / X[2]) gives a rotor angle)
X[4] (wS) electrical speed [radian/s]
Also there is drift_Q variable that in fact is a part of state vector. The observer procedure consists of the following steps:
- Get corrected terminal voltages (uXY) from the measurements (uA, uB, uC). It corresponds to the previous PWM period.
- Update X using the corrected uXY. Thus we have done the propagation step on previous PWM period.
- Update X using current measurement (iA, iB).
- Propagate X to the next PMW period with supposed terminal voltages (uXY).
Note that 1,2 are performed if voltage correction conditions are met, 3 is performed if current measurement is recognized as reliable, 4 is performed always.
After that we have state vector estimation to the moment of next PWM period begins. This state vector goes into the current control loop and then into voltage control procedure. As a result we get the duty cycle (xA, xB, xC) to the next PWM period. Then it transferred to the hardware timer.
+----+ +-------+ +-----+ +-----+
iD ---X----->| PI |-+---->| DQ /| | |--->| |
| +----+ | -->| / |-+--->| PWM |--->| VSI |
+----+ | +----+ | / |/ XY |---+->| |--->| |
| PI |---|--X-->| PI |--- +-------+ | | +-----+ +-----+
+----+ | | +----+ | ^ | | | | |
^ | | | | | | +-----------+ | | uA
| +--|------+ | | | | | +---------|-+ | uB
wS -->X | | | | | | | | | +-------|-|-+ uC
| | | +-----------+ | | | | | | | | |
| | | | HF |----/ v v v v v | | |
\------|--|---| injection | | +------------+ | | |
| | | +-----------+ +---| FLUX |<----+ | | iA
| | | | | observer |<----|-+ | iB
| | | +--< residue +------------+ | | |
| | | | | | | | |
| +-----------------------------+ | | iD | | |
| +-----------------------------+ | iQ -----
+------------------------------------------+ wS / \
Motor
\ /
// Block diagram // -----
The main sensorless method is a flux linkage observer. It is based on BEMF induced in stator windings when rotor flux is moving. This method works well when the value of BEMF is greater that voltage distortion (dUDT). Look at the synchronous machine equations:
iD
-- * Ld = uD - iD * R + fluxQ * wS
dT
iQ
-- * Lq = uQ - iQ * R - fluxD * wS + drift_Q
dT
Where uD uQ is voltages applied from VSI, fluxD fluxQ is a flux linkage.
uD = X[2] * uX + X[3] * uY
uQ = X[2] * uY - X[3] * uX
fluxD = Ld * iD + E
fluxQ = Lq * iQ
To implement an observer we need to know Ld Lq R E parameters. At the propagation step we solve this equations in pm_solve_2 procedure.