Modern controllers for permanent magnet motors employ field‑oriented control (FOC) to decouple torque and flux regulation. The dq model allows use of independent PI controllers for the d and q currents.
Maximum torque per ampere (MTPA)
Given current limits, the MTPA trajectory defines the optimal combination of d‑ and q‑currents that maximizes torque production. For non‑salient machines ((L_d = L_q)), MTPA occurs at (i_d = 0). Salient machines benefit from negative d‑current.
Field‑weakening
Above base speed, the controller applies negative d‑current to reduce the effective flux linkage, keeping the back‑EMF within the DC bus voltage. This extends the speed range at the cost of reduced torque and efficiency.
Assumption
We assume ideal current regulators with infinite bandwidth. Real systems have finite dynamics which introduce phase lag and coupling.
Takeaways
- FOC enables independent control of torque and flux via dq currents.
- MTPA determines the optimal current vector below base speed.
- Field‑weakening trades off torque for speed, requiring careful thermal and voltage margin analysis.