Power Electronics & Motors Advanced 28 min

Field-Oriented Control (FOC) & Space Vector Modulation for BLDC Motors

Implement vector field-oriented control (FOC) using Clarke and Park transformations with Space Vector PWM (SVPWM) on an ARM Cortex-M4 microcontroller.

2. Prerequisites & Background Theory:

Electromagnetic vector theory, Clarke/Park coordinate transforms, Space Vector PWM, and timer dead-time generation.

STEP 1

Goal & Engineering Objectives

Achieve smooth, ripple-free torque and maximum torque-per-ampere (MTPA) control on a 3-phase BLDC motor by orienting stator current vector strictly orthogonal to rotor permanent magnet flux.

STEP 2

Governing Mathematical Formulation & Physics

                  Clarke Transform (3-Phase a,b,c to Stationary 2-Phase alpha,beta):
$$I_\alpha = I_a$$
$$I_\beta = \frac{1}{\sqrt{3}} I_a + \frac{2}{\sqrt{3}} I_b$$

Park Transform (Stationary alpha,beta to Synchronous Rotating d,q Frame):
$$I_d = I_\alpha \cos\theta_e + I_\beta \sin\theta_e$$
$$I_q = -I_\alpha \sin\theta_e + I_\beta \cos\theta_e$$

Torque Generation:
$$\tau_e = \frac{3}{2} p \cdot \lambda_m \cdot I_q$$
By driving direct-axis current Id to zero, all stator current is converted directly into electromagnetic torque without reactive winding loss.                

STEP 3

System Architecture & Block Flow Diagram

[Magnetic Encoder AS5600] --(SPI/ABZ 1kHz)--> [STM32F405 MCU (168MHz)]
                                                     |
[Inline Shunts + INA240] --(ADC DMA Dual Injected)---+  (Current Loop @ 20kHz)
                                                     |
                                         [Clarke / Park Transforms]
                                         [Dual PI Controllers (Id, Iq)]
                                         [Inverse Park + Space Vector PWM]
                                                     |
                                                     v
[DRV8302 Gate Driver] <--(TIM1 6-PWM Complementary w/ Deadtime)--+

STEP 4

Required Hardware Bill of Materials (BOM)

Hardware Component	Qty	Engineering Specification
STM32F405RG ARM Cortex-M4 MCU	1	168 MHz, Hardware FPU, 3x 12-bit ADCs
DRV8302 3-Phase Gate Driver IC	1	Integrated dual current-shunt amps, buck regulator
N-Channel MOSFETs (NVMFS5C604NL)	6	60V, 150A, 2.8mΩ RDS(on), SO-8FL
AS5600 12-bit On-Axis Magnetic Encoder	1	4096 counts/rev, diametric neodymium magnet
Tarot 4006 620KV Brushless DC Motor	1	14-pole pairs, 3-phase star wound
Low-Inductance Current Shunts	2	5 mΩ, 2W, 1% tolerance, 2512 package
Electrolytic DC-Link Capacitors	3	470µF 35V Low-ESR in parallel

Look up component pinouts in Components Catalog →

STEP 5

Wiring, Pinout & Schematics Mapping

                  • STM32 PA8, PA9, PA10 -> DRV8302 INH_A, INH_B, INH_C (High-side PWM)
• STM32 PB13, PB14, PB15 -> DRV8302 INL_A, INL_B, INL_C (Low-side PWM)
• STM32 PC0, PC1 (ADC1_IN10, ADC1_IN11) -> DRV8302 SO1, SO2 (Amplified shunt outputs)
• STM32 PA4, PA5, PA6, PA7 -> AS5600 CS, SCK, MISO, MOSI (High-speed SPI angle)
• Connect 3-phase motor leads (Phase A, B, C) to bridge half-bridge outputs.
• Connect 24V power supply across DC-link with common ground bonded to MCU.                

STEP 6

Firmware Implementation & Algorithms

// Vector FOC Core Math Kernel (ANSI C99 / CMSIS-DSP)
#include <math.h>

typedef struct {
    float id, iq;
    float vd, vq;
    float valpha, vbeta;
    float theta_elec;
    float pwm_a, pwm_b, pwm_c;
} FOCState;

void foc_park_inverse(FOCState *foc) {
    float s = sinf(foc->theta_elec);
    float c = cosf(foc->theta_elec);
    
    // Inverse Park: Convert Rotating d,q to Stationary alpha,beta
    foc->valpha = foc->vd * c - foc->vq * s;
    foc->vbeta  = foc->vd * s + foc->vq * c;
}

void foc_space_vector_modulate(FOCState *foc, float v_bus) {
    // Space Vector PWM: Centered Modulation
    float va = foc->valpha;
    float vb = -0.5f * foc->valpha + (sqrtf(3.0f) / 2.0f) * foc->vbeta;
    float vc = -0.5f * foc->valpha - (sqrtf(3.0f) / 2.0f) * foc->vbeta;
    
    // Zero-Sequence Voltage (SVM Center)
    float v_min = fminf(va, fminf(vb, vc));
    float v_max = fmaxf(va, fmaxf(vb, vc));
    float v_com = 0.5f * (v_min + v_max);
    
    // Calculate normalized duty cycles [0.0 .. 1.0]
    foc->pwm_a = 0.5f + (va - v_com) / v_bus;
    foc->pwm_b = 0.5f + (vb - v_com) / v_bus;
    foc->pwm_c = 0.5f + (vc - v_com) / v_bus;
}

Simulate and Edit in Coding Lab

STEP 7

Bench Testing & Waveform Verification

                  1. Spin rotor slowly by hand; confirm AS5600 encoder increments monotonically without missing angle codes.
2. Connect current probe to Phase A: Verify clean sinusoidal AC current waveforms without harmonic flat-topping.
3. Step Iq command from 0A to 5A: Verify instant torque response within 150 µs without acoustic resonance.                

STEP 8

Troubleshooting & Common Failure Modes

                  • Problem: Motor draws high current, vibrates violently, but does not rotate.
  Solution: Inverted electrical angle or wrong phase sequence. Swap Phase A and Phase B motor connections.
• Problem: Current feedback is noisy or drifts with temperature.
  Solution: Calibrate ADC zero-current voltage offsets while low-side MOSFETs are held continuously ON for 50 ms at boot.
• Problem: MCU resets during rapid motor reversal.
  Solution: Regenerative braking overvoltage. Install a braking chopper resistor and clamp circuit across the DC-link rail.                

STEP 9

Extensions & Undergraduate Research Challenges

                  1. Implement MTPA (Maximum Torque Per Ampere) lookup table for interior permanent magnet (IPM) motors.
2. Add sensorless Back-EMF Sliding Mode Observer (SMO) for high-speed operation if magnetic encoder fails.                