Designing advanced DSP applications on the Kinetis Cortex-M4 MCU

To achieve the goal of the PM synchronous motor control, the algorithm uses feedback signals. The essential feedback signals are three-phase stator current and stator voltage. For correct operation, the presented control structure requires a speed feedback on the motor shaft. In the case of the presented algorithm, a sensorless algorithm is used, that estimates the angular speed and the rotor position.

Sensorless control of the PM synchronous motor

As described in previous section, the rotor position angle and angular speed need to be measured or estimated to implement the speed vector control. Different techniques can be used for the rotor position estimation:

• Utilization of magnetic saliency

• Calculating an appropriate motor model

• Combination of two sensorless algorithms

In the solution described in this article, the method based on the calculation of the motor model is used – Back-EMF observer. Because the sensorless technique based on back-EMF is proposed, the position can not be estimated at a zero or low speed. Therefore, the motor start-up is provided with a vector of constant current amplitude. Anyhow, there are applications, where this approach is not possible due to load characteristics.

The estimation method for the rotor position and angular speed is based on the motor mathematical model of interior PMSM motor with an extended electro-motive force function which is realized in estimated quasi synchronous reference frame γδ. The back-EMF observer detects the generated motor voltages induced by the permanent magnets.

A tracking observer uses the back-EMF signals to calculate the position and speed of the rotor. The transformed model is then derived as in the formula where RS = stator resistance; LD, LQ = D-axis and Q-axis inductance; ke = back-EMF constant; ωe = angular electrical speed; uD, uQ = stator voltages; ID, iQ = stator currents; s = operator of derivative; iq’ = first derivative of iq current.

The position estimation can now be performed by extracting the θerror term from the model.

Implementation of the FOC on Cortex-M4 processor and processor load

The algorithm was implemented on Cortex M4 using highly optimized intrinsic functions. All unimportant partial results were stored in registers instead of local variables.

Numbers representation and mathematical operations

Cortex-M4 uses integer, two’s-complement format. The positive number is represented as simply binary value and the negative number is represented by inverting all the bits of corresponding positive value and then adding 1.

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