PMSM Field-Oriented Control Example¶

Permanent magnet synchronous motor with vector control.

Overview¶

Field-Oriented Control (FOC) provides: - Torque and flux decoupling - Maximum torque per ampere - Smooth low-speed operation - Four-quadrant operation

Specifications¶

Circuit Files¶

• pmsm_foc_basic.ipes - Basic FOC implementation
• pmsm_foc_mtpa.ipes - Maximum torque per ampere
• pmsm_sensorless.ipes - Sensorless FOC

Theory¶

dq Reference Frame¶

Transform abc quantities to rotating dq frame:

Clarke Transform (abc → αβ): $\(\begin{bmatrix} i_\alpha \\ i_\beta \end{bmatrix} = \frac{2}{3}\begin{bmatrix} 1 & -1/2 & -1/2 \\ 0 & \sqrt{3}/2 & -\sqrt{3}/2 \end{bmatrix}\begin{bmatrix} i_a \\ i_b \\ i_c \end{bmatrix}\)$

Park Transform (αβ → dq): $\(\begin{bmatrix} i_d \\ i_q \end{bmatrix} = \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}\begin{bmatrix} i_\alpha \\ i_\beta \end{bmatrix}\)$

Motor Equations (dq Frame)¶

Torque Equation¶

For surface PM (Ld = Lq): τe = (3/2)p·ψm·iq

Control Structure¶

                    ┌──────────────┐
Speed Ref ─────────►│   Speed PI   │
                    │   Controller │
Speed fb ──────────►│              │
                    └──────┬───────┘
                           │ iq*
              id*=0        ▼
                ├─────────────────────┐
                ▼                     ▼
         ┌──────────┐          ┌──────────┐
         │ id PI    │          │ iq PI    │
         │ Control  │          │ Control  │
         └────┬─────┘          └────┬─────┘
              │ vd*                 │ vq*
              └──────────┬─────────┘
                         ▼
                   ┌──────────┐
                   │ Inverse  │
                   │ Park/SVM │
                   └────┬─────┘
                        ▼
                   ┌──────────┐
                   │ Inverter │
                   └────┬─────┘
                        ▼
                   ┌──────────┐
                   │  PMSM    │
                   └──────────┘

Current Controller Tuning¶

PI Gains¶

d-axis: $\(K_{p,d} = L_d \cdot \omega_c, \quad K_{i,d} = R_s \cdot \omega_c\)$

q-axis: $\(K_{p,q} = L_q \cdot \omega_c, \quad K_{i,q} = R_s \cdot \omega_c\)$

Where ωc is desired current loop bandwidth.

Decoupling¶

Add feedforward terms: - ωe·Lq·iq to d-axis - ωe·Ld·id + ωe·ψm to q-axis

Exercises¶

1. Basic FOC: Implement current loops, verify iq tracking
2. Speed Loop: Add speed controller, tune response
3. MTPA: Implement id* curve for IPM motor
4. Field Weakening: Extend speed range above base speed

Related Resources¶

• BLDC Control
• 904 - Mechanical Systems