A Controllability-Based Adaptive Field-Weakening Strategy for PMSM Drives Using Voltage-Angle Control

Field-weakening (FW) operation of permanent magnet synchronous motor (PMSM) drives is conventionally activated when the motor reaches a predefined base speed. Such an approach is convenient for implementation but does not represent a fundamental physical boundary of the drive. The actual onset of voltage limitation depends on machine parameters, operating current, load torque, DC-link voltage, and temperature, and therefore the effective field-weakening boundary may vary during operation. This paper proposes a controllability-based adaptive field-weakening strategy for PMSM drives using a voltage-angle-based field-oriented control formulation, referred to as θ-FOC. The proposed formulation represents the stator voltage vector in polar coordinates, using its magnitude and angular displacement with respect to the rotor-flux-oriented d-axis as control variables. In the voltage-unconstrained region, θ-FOC is mathematically equivalent to conventional current-oriented FOC and therefore preserves its current-control structure and dynamic properties. When the inverter voltage limit is reached, however, the voltage magnitude becomes constrained and the control problem can be reformulated in terms of the voltage angle. The paper shows analytically that, under voltage saturation, the sensitivity of the torque-producing current to the q-axis voltage progressively decreases with increasing electrical speed. This provides a physical interpretation of the loss of effective torque controllability in conventional current-based control. Based on this observation, the proposed strategy does not employ a predefined base-speed threshold. Instead, the transition to θ-based control is activated by the actual voltage saturation together with the saturation of the torque-producing current control action. In the voltage-limited region, the electromagnetic torque is described by a one-dimensional torque–voltage-angle relationship, allowing the control problem to be reduced from coupled current regulation to direct voltage-angle regulation. The proposed strategy is experimentally evaluated on a low-power PMSM drive under speed and load transients and for different thermal operating conditions. The results demonstrate smooth transition between current-controlled and voltage-angle-controlled operation, stable torque and speed regulation in the field-weakening region, and a continuous increase in the voltage angle above 90° during field weakening. The experimental results also demonstrate that the field-weakening boundary changes with motor temperature, supporting the proposed controllability-based approach over a fixed speed-threshold strategy.