Sensorless FOC System Loop Parameter Tuning Guide — Observer PLL

1. Position Observer Parameter Tuning

The position observer is the core algorithm of a sensorless FOC system. Common methods include Sliding Mode Observer (SMO), Luenberger observer, and flux linkage observer (Active Flux).

Sliding Mode Observer (SMO)

Sliding mode gain (Ksmo):

Excessive gain introduces high-frequency noise; insufficient gain slows convergence. Empirical value = 1.5–2 × back‑EMF amplitude. The SMO often works with a sensorless bldc controller implementation.

Low-pass filter cutoff frequency:

Must exceed the motor’s maximum electrical frequency but remain below half the switching frequency, especially in systems using a bldc foc controller.

New improved SMO:

The latest design removes the gain and low-pass filter entirely, significantly enhancing robustness in industrial dc motor controller systems.

Luenberger Observer

Observer gain matrix:

Configured via pole placement; poles should be 5–10× faster than the motor’s electrical dynamics in a brushless dc motor controller setup.

Model parameter sensitivity:

Sensitive to motor parameters (R, L), requiring online parameter identification often supported by a 3 phase bldc motor controller.

Combined with disturbance rejection characteristics:

Enhances robustness against parameter variations.

PLL Kp, Ki Parameter Tuning for the Observer

Tuning the observer PLL’s Kp and Ki parameters essentially reduces to tuning a first-order current loop and a second-order speed loop. We observe back‑EMF or flux linkage, for example:

The above formulas can be simplified, and the PLL control diagram in the observer can also be simplified to:

From this diagram, the closed-loop transfer function is:

Using control theory for second-order systems, tuning is performed accordingly:

Thus, PLL Kp and Ki are initially tuned using this theoretical approach. These values are approximate and require fine-tuning in practice. The damping ratio ζ should be ≥ 0.707, and natural bandwidth ωₙ is selected around 5 × mechanical speed.

Summary

Sensorless FOC parameter tuning must follow the principle: “inner loops first, then outer loops,” combining theoretical calculation with experimental adjustment. The current loop emphasizes fast response; the speed loop balances dynamic performance and disturbance rejection; the position observer depends on algorithm robustness. In practical tuning, use oscilloscopes, current probes, and other tools to gradually optimize parameters for stable and efficient control in systems using sensorless bldc controller, bldc foc controller, and industrial dc motor controller hardware.

Engineers systematically complete sensorless FOC parameter tuning to enhance performance and reliability, avoid blind trial-and-error, and simplify debugging. Once motor parameters are known, tunable settings include: current bandwidth (current loop), speed bandwidth and damping factor (speed loop), and PLL damping ratio and observer bandwidth in brushless dc motor controller and 3 phase bldc motor controller designs.