Motor Control Basics

Modern EV motors don't just spin — they're precisely controlled to deliver exact torque at any speed. This lesson explains Field Oriented Control (FOC), the technique that makes electric motors feel responsive and smooth.

Why FOC?

The problem: AC motors have rotating magnetic fields. Unlike DC motors where torque control is simple (just control armature current), in AC motors the relationship between current and torque depends on the instantaneous rotor position. The solution: Transform the problem into a rotating reference frame where it looks like a DC motor problem.

Watch how 3-phase currents transform through Clarke and Park into clean d-q components.

The Transformation Chain

Step 1: Clarke Transform (abc → αβ)

Converts 3-phase currents (Ia, Ib, Ic) to 2-phase orthogonal (Iα, Iβ):

$$\begin{bmatrix} I_\alpha \\ I_\beta \end{bmatrix} = \frac{2}{3} \begin{bmatrix} 1 & -\frac{1}{2} & -\frac{1}{2} \\ 0 & \frac{\sqrt{3}}{2} & -\frac{\sqrt{3}}{2} \end{bmatrix} \begin{bmatrix} I_a \\ I_b \\ I_c \end{bmatrix}$$

Step 2: Park Transform (αβ → dq)

Converts stationary αβ frame to rotating dq frame:

$$\begin{bmatrix} I_d \\ I_q \end{bmatrix} = \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix} \begin{bmatrix} I_\alpha \\ I_\beta \end{bmatrix}$$

Where θ is the rotor electrical angle.

d-q Control Strategy

Torque Control via Iq

For a PMSM motor:

$$T = \frac{3}{2} \cdot p \cdot \lambda_m \cdot I_q$$

Where:

Flux Control via Id

In normal operation (below base speed):

Id = 0 (no demagnetizing current needed)
All current goes to Iq for maximum torque

In field weakening (above base speed):

Id < 0 (negative current to weaken field)
Reduces back-EMF, allows higher speed
Trades torque for speed

The FOC Control Loop

Torque Command → Iq* → PI Controller → Vq
                Id* = 0 → PI Controller → Vd
                              ↓
                    Inverse Park (dq → αβ)
                              ↓
                      SVPWM Generator
                              ↓
                     3-Phase Inverter
                              ↓
                         Motor

Space Vector PWM

Move the reference vector to see how PWM duty cycles change for each phase.

The Voltage Hexagon

The 3-phase inverter can produce 8 voltage states:

6 active vectors (V1-V6): At hexagon vertices
2 zero vectors (V0, V7): All switches high or all low

Each active vector corresponds to a switch state:

Vector	State	Switches ON
V1	100	A+, B-, C-
V2	110	A+, B+, C-
V3	010	A-, B+, C-
V4	011	A-, B+, C+
V5	001	A-, B-, C+
V6	101	A+, B-, C+

Synthesizing Any Voltage

To create a reference voltage Vref at angle θ:

Identify which sector (1-6) contains Vref
Calculate time spent on adjacent vectors
Fill remaining time with zero vectors

$$T_1 = \frac{\sqrt{3} \cdot T_s \cdot |V_{ref}|}{V_{dc}} \cdot \sin(60° - \alpha)$$

$$T_2 = \frac{\sqrt{3} \cdot T_s \cdot |V_{ref}|}{V_{dc}} \cdot \sin(\alpha)$$

$$T_0 = T_s - T_1 - T_2$$

Where α is the angle within the sector.

SVPWM vs Sinusoidal PWM

Feature	Sinusoidal PWM	SVPWM
Max voltage	0.866 × Vdc	1.0 × Vdc
DC bus utilization	86.6%	100%
THD	Higher	Lower
Switching losses	Similar	Similar
Implementation	Simple	Complex

SVPWM extracts ~15% more voltage from the same DC bus.

Position Sensing

FOC requires accurate rotor position (θ). Methods:

1. Resolver

Type: Analog position sensor Accuracy: ±0.1° Robustness: Very high (no magnets) Cost: Medium Used in: Most automotive EVs

2. Encoder

Type: Digital position sensor Accuracy: Depends on resolution (1000-10000 PPR) Robustness: Medium Cost: Low-Medium Used in: Industrial motors

3. Hall Sensors

Type: Discrete position (60° resolution) Accuracy: Low (±30° electrical) Robustness: Good Cost: Low Used in: BLDC commutation, startup

4. Sensorless

Type: Algorithm estimates position from currents Accuracy: Good at speed, poor at standstill Robustness: Depends on algorithm Cost: Zero (no sensor) Used in: Some two-wheelers, appliances

Control Bandwidth

Typical bandwidths for EV motor control:

Loop	Bandwidth	Sample Rate
Current (Id, Iq)	1-5 kHz	10-20 kHz
Speed	100-500 Hz	1-5 kHz
Position	10-50 Hz	100-500 Hz
Torque command	100-1000 Hz	From VCU

Why Fast Current Loop?

Motor electrical time constant: 0.5-2 ms
Must track rapidly changing torque commands
PWM frequency: 8-16 kHz
Current sampling: Every PWM cycle

Implementation Considerations

Fixed-Point vs Floating-Point

Fixed-point (Q15, Q31):

Faster on low-cost MCUs
More complex scaling
Used in: Cost-sensitive applications

Floating-point:

Easier development
Requires more powerful MCU
Used in: Automotive (Arm Cortex-M4F, M7)

Motor Parameter Identification

FOC requires accurate motor parameters:

Rs: Stator resistance
Ld, Lq: d-q inductances
λm: Magnet flux linkage

Methods:

Datasheet: Starting point
DC injection: Measure Rs
HF injection: Measure Ld, Lq
Auto-tuning: Run-time identification

Indian Context

Two-Wheeler Control Units

Ather 450X:

FOC with sensorless startup
6 kW peak power control
Custom inverter

Ola S1 Pro:

IPM motor control
8.5 kW peak
In-house motor controller

Passenger Vehicles

Tata Nexon EV:

PMSM with resolver feedback
105 kW inverter
CAN-based torque interface

Key Takeaways

FOC transforms the AC motor control problem into a DC-like problem
Clarke transform converts 3-phase to 2-phase stationary
Park transform converts to rotating dq frame
Iq controls torque, Id controls flux (field weakening)
SVPWM generates optimal voltage vectors with ~15% better utilization
Position feedback (resolver, encoder) is critical for accurate control

What's Next

In the next lesson, we'll explore Power Electronics — the inverters, DC-DC converters, and switching devices that convert battery DC into controlled AC for the motor.