Classic Application of the ‘Three-Stage’ Algorithm in Sensorless Control

Initial Positioning → IF Start → Switch to Sliding Mode Observer after Speed Criteria Met

1.Overall Logical Framework

The core contradiction of sensorless control is: weak back electromotive force (EMF) at low speed/stationary state makes observation impossible, while at high speed, dynamic response and robustness must be balanced. The three-stage strategy resolves this contradiction through a “phased switching algorithm,” as follows: stationary state → initial positioning (forced alignment) → IF start (constant current acceleration) → speed criteria met → sliding mode observer (high-precision closed-loop). Each stage has clear objectives: – Initial positioning: establish the rotor’s initial position to avoid reverse startup; – IF start: provide sufficient torque to accelerate until back EMF can be observed; – Sliding mode switching: achieve high-precision position/velocity estimation at high speed, ensuring steady-state performance.

2.Detailed Expansion of Each Stage

Stage 1: Initial Position Estimation

1.Core Objective

When stationary, the motor’s back EMF is 0, making it impossible to estimate position through the observer. Initial positioning must actively apply a specific current/voltage vector to “force align” the rotor to a known angle, providing a reference for subsequent startup.

2.Common Methods (Classic Solutions)

(1)DC Bias Positioning Method (most commonly used)– Principle: Apply DC current in a fixed direction (e.g., α-axis) to the stator, using the stator’s magnetic force and the rotor’s permanent magnet attraction to align the rotor in that direction.

Key Parameters:a.Positioning current: must be sufficiently large (usually 30%~60% of rated current) to ensure the generated magnetic force overcomes static friction;b.but should not be too large to avoid overheating or magnetic saturation of the stator.– Positioning time: must exceed the rotor’s mechanical response time (the heavier the load, the longer the time), generally taken as over 200ms.

(2)Pulsed Voltage Positioning Method (Fast Positioning)– Principle: Apply short pulse voltages to stator windings at different angles, detecting the current response under each pulse; the direction with the highest current indicates the rotor’s magnetic pole direction (as this direction has the least magnetic resistance). Example angle sequence: 0°→ 90°→ 180°→ 270°, applying a 10ms pulse each time and detecting the current peak; the angle with the highest peak is the initial position. Advantages: short positioning time (only a few tens of milliseconds), suitable for rapid startup scenarios; Disadvantages: high current detection accuracy required, need to filter pulse current spikes.

(3)Engineering Considerations– Consequences of positioning failure: rotor reverse, jitter, or inability to rotate during startup; – Solutions: – Apply “pre-excitation” (small current) before positioning to eliminate the effect of rotor remanence; – Delay 100ms after positioning before entering the startup phase to ensure rotor stability; – If positioning fails multiple times (e.g., no current response), increase the positioning current or extend the time.

Stage 2: IF Start (Current/Frequency Start)

1.Core Objective

After initial positioning, the motor remains stationary. IF start gradually increases the stator magnetic field speed through **constant current + linear frequency increase**, driving the rotor to rotate synchronously (similar to “soft start” of an asynchronous motor) until the speed reaches the “minimum operating speed” of the sliding mode observer.

2.Principle and Control Logic

Control Strategy:– Current loop: maintain constant d/q axis current (q axis current constant, d axis current is 0 or a small value), ensuring stable output torque; – Frequency loop: the stator magnetic field electrical angular speed rises linearly from 0 to the target switching angular speed (corresponding to mechanical speed).

3.Key Parameter Design

(1) Frequency Ramp Rate – Definition: Increment of electrical angular speed per unit time (determines startup acceleration); – Design Principles: – If the ramp rate is too high: insufficient startup torque, rotor cannot keep up with the stator magnetic field (loss of synchronization), resulting in motor jitter and sudden current increase; – If the ramp rate is too low: startup time is too long, efficiency is low; – Empirical value: design based on motor inertia and load torque, generally taken as 50~200 rad/s² (corresponding to mechanical acceleration ~500 rpm/s).Can be calibrated based on actual project conditions.

(2) Switching Angular Speed – Definition: Electrical angular speed at which the switch from IF phase to sliding mode observer occurs; – Core Constraint: must ensure that back EMF is sufficiently large during switching (to allow the sliding mode observer to accurately estimate position); – Empirical value: – For surface-mounted permanent magnet synchronous motors (SPMSM), switching electrical angular speed ≥50~100 rad/s (corresponding to mechanical speed ≥500~1000 rpm, depending on the number of motor pole pairs); – If the motor’s back EMF coefficient is large, the switching speed can be appropriately reduced.

(3) IF Phase Current – – q axis current: provides auxiliary torque to accelerate the rotor synchronously, usually taken as 0.1~0.3 times the rated current (should not be too large to avoid magnetic field distortion).

4.Common Issues and Solutions

Loss of Synchronization Issue:

Phenomenon: motor jitter, sudden current increase, speed does not rise;

Cause: frequency ramping too fast, insufficient current, excessive load;

Solution: reduce frequency ramp rate, increase IF phase current, optimize load matching.

Switching Impact:

Phenomenon: speed fluctuation and current impact at the moment of switching;

Cause: large deviation between the observer’s initial position and the actual position during switching;

Solution: add “position synchronization” logic before switching (e.g., use the estimated position from the IF phase as the initial value for the sliding mode observer).

Stage 3: Sliding Mode Observer Switching (SMO)

1.Core Objective

Once the speed reaches the switching threshold, the back EMF is sufficiently strong, allowing the sliding mode observer to accurately estimate rotor position and speed through back EMF detection, achieving **high-precision closed-loop control** (fast dynamic response, strong robustness)..

2.Sliding Mode Observer Principle (Simplified Version)

– Core Idea: Construct a “virtual motor model,” comparing the current error between the virtual model and the actual motor, using “sliding mode control law” to force the error to converge to 0, thereby estimating back EMF and rotor position. – Simplified Logic: 1. Establish a current model for the virtual motor, input actual voltage, output estimated current; 2. Calculate the error between actual current and estimated current, generating a “sliding surface” through the sign function; 3. Estimate back EMF based on the sliding surface, then calculate rotor position using the arctan2 function.

3.Key Parameter Design

(1) Sliding Mode Gain – Function: determines the error convergence speed and observer robustness; – Design Principles: – If the gain is too high: observer output jitters (high-frequency spikes), affecting position estimation accuracy; – If the gain is too low: slow error convergence, poor dynamic response, prone to loss of accuracy at low speeds; – Empirical value: adjust based on motor parameters (stator inductance Ls, stator resistance Rs), generally taken as 10~50 (requires actual debugging and optimization).

(2) Low-Pass Filter (LPF) Parameters – Necessity: the sign function of the sliding mode observer introduces high-frequency noise, requiring filtering of back EMF through LPF; – Design Principles: – Cutoff frequency must be higher than 1.5 times the motor’s highest operating frequency (to avoid filtering out useful signals); – Empirical value: 100~500 Hz (adjust based on motor speed range).

4.Switching Logic and Smooth Transition

– Hard switching issue: directly switching from IF to sliding mode may cause sudden position changes and current spikes;

– Smooth switching scheme: 1. Position synchronization: before switching, use the “open-loop position” from the IF phase (obtained by integrating electrical angular speed) as the initial position for the sliding mode observer; 2. Speed synchronization: at the moment of switching, force the estimated speed of the sliding mode observer to equal the electrical angular speed of the IF phase, then gradually release; 3. Current transition: within 10~20ms after switching, keep the d/q axis current commands unchanged, and restore normal current commands after the observer stabilizes.

3.Engineering Debugging Process for the Three-Stage Strategy

1.Debugging Sequence (from simple to complex)

Initial Positioning Debugging: – Disconnect the motor load and test the positioning function alone; – Use an oscilloscope to observe the current during the positioning phase, confirming current stability; – Manually rotate the rotor; after positioning, it should be able to “hold” the rotor (unable to rotate easily).

IF Start Debugging: – In no-load condition, set a small frequency ramp rate; – Observe the speed rise curve (should be linear and smooth, without jitter); – Gradually increase the frequency ramp rate, testing the maximum non-loss-of-synchronization ramp rate.

Sliding Mode Switching Debugging: – First fix the switching speed and adjust the sliding mode gain; – Use an oscilloscope to observe current and speed fluctuations at the moment of switching (fluctuations should be less than 10% of the rated value); – Gradually lower the switching speed, testing the minimum stable switching speed.

2.Key Indicator Verification – Startup success rate: 100 consecutive startups without reverse or jitter; – Switching impact: current fluctuation at the moment of switching <15% of rated current, speed fluctuation <10% of switching speed; – Steady-state accuracy: under sliding mode, position estimation error <5° electrical angle, speed fluctuation <5% of rated speed.

4.Application Scenarios and Limitations

1.Applicable Scenarios

Medium and small power permanent magnet synchronous motors (PMSM): such as household appliance motors (air conditioning compressors, washing machines), industrial servo motors (power < 10kW); drones; electric fans, etc.

2.Limitations

Limited low-speed performance: the sliding mode observer has weak back EMF at low speeds (<500 rpm), leading to decreased estimation accuracy;

Sensitive to motor parameters: stator inductance and resistance vary with temperature and load, affecting observer performance (requires parameter self-tuning compensation);

Longer startup time: the IF frequency ramp phase requires a certain time to reach the switching speed (compared to starting with an encoder, startup time increases by 50~100ms).

Reduced motor capability: reduces the motor’s ability to reach peak torque and power

Dynamic conditions prone to loss of control: when operating conditions change dramatically, limited observer bandwidth may lead to loss of control.

5.Optimization Directions

Parameter self-tuning: obtain motor parameters through offline identification or online adaptive adjustment;

Hybrid observer: use “Extended Kalman Filter (EKF)” for low speed and sliding mode observer for high speed, balancing low-speed accuracy and high-speed robustness;

No-switching strategy: adopt “full sliding mode observer,” optimizing initial conditions (e.g., pre-positioning + adaptive startup) to avoid the IF phase (suitable for high-speed motors).

Improve anti-interference capability and reliability.