Introduction
This article describes the full-speed-range vector control process for permanent magnet synchronous motors (PMSMs): how motor speed increases from zero to its limit, how current-loop currents are designed to produce constant torque, and how speed stability is maintained. Understanding this process helps deepen comprehension of motor control. The article explains three basic vector control methods:
1) Field-oriented control 
2) Maximum torque per ampere control (MTPA)
3) Field-weakening control
Background
The motor topic involves extensive background knowledge. This section lists the required facts; during analysis you may treat these as conclusions without fully understanding their derivation.
PMSM control strategies include direct torque control and vector control. This article discusses speed control under vector control only.
Vector control decouples three-phase stator currents into orthogonal d- and q-axis components. Basic vector control methods include field-oriented control, MTPA, and field-weakening control.
Key Equations
Torque equations:
Voltage equation:
Where:
Theoretical Analysis
Overall, the speed-increase process can be summarized in three stages:
- When motor speed is within the rated speed, the motor operates under maximum torque per ampere control (MTPA).
- As speed increases further, voltage limitations force the motor into field-weakening operation to maintain torque.
- With further speed increase, current limits are reached and the motor operates under constant-power conditions; output torque decreases as speed increases.
Step-by-step analysis of the above conclusions:
First, understand the concepts of current constraint and voltage constraint. A motor's available energy is finite and it cannot reach infinite speed. The stator current vector Is and the stator voltage vector Us are subject to the following constraints:
Surface-mounted PMSM: Full-speed-range Vector Control
Surface-mounted PMSMs differ structurally from interior-mounted PMSMs. This section analyzes speed control for a surface-mounted PMSM.
For surface-mounted PMSMs, d-axis and q-axis inductances are equal, Ld = Lq, so the torque equation simplifies to:
Interior-mounted PMSM: Full-speed-range Vector Control
The speed control process for interior-mounted PMSMs can be fully characterized in Figure:
Figure. Current variation over the full speed range for an interior-mounted PMSM
Summary
To recap the three stages of motor speed increase from zero to the limit:
- Within rated speed, the motor uses MTPA control.
- With higher speed, voltage limits lead to field-weakening to maintain torque.
- At even higher speed, current limits impose constant-power operation and output torque decreases as speed increases.
