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How Sensorless Brushless DC (BLDC) Motor Position Estimation Works

Last modified by Microchip on 2026/05/11 15:59

Introduction

Modern high‑performance Brushless DC (BLDC) motor drives—especially those using Field‑Oriented Control (FOC)—require accurate knowledge of the rotor position at all times. In sensorless systems, this position must be estimated rather than directly measured. This lesson explains how rotor position estimation is achieved using back Electromotive Force (back‑EMF) modeling, why traditional zero‑crossing techniques are not suitable for FOC, and how a Phase‑Locked Loop (PLL) estimator is used in Permanent Magnet Synchronous Motor (PMSM) control.

Microchip Technology addresses these challenges with dedicated motor‑control‑focused microcontrollers, optimized DSP architectures, and reference designs that help engineers implement robust sensorless BLDC motor systems efficiently.

Position Estimation in Sensorless BLDC and Permanent Magnet Synchronous Motor (PMSM) Drives

Position Estimation in Sensorless Brushless DC (BLDC) and Permanent Magnet Synchronous Motor (PMSM) Drives

In sensorless motor control, the rotor position is calculated using information derived from the motor’s electrical behavior rather than from physical sensors. One of the most important observable quantities is back‑EMF, which is the voltage generated in the stator windings due to the rotation of the rotor’s permanent magnets.

In traditional six‑step BLDC control, rotor position is often inferred by detecting back‑EMF zero crossings on the undriven motor phase. However, in FOC, all motor phases are continuously driven with PWM. Because there is no floating phase, zero‑crossing detection methods are not feasible. Instead, FOC relies on estimating the back‑EMF voltage using a mathematical model of the motor.

A PMSM has an electrical model that is fundamentally similar to both Brushed DC (BDC) and BLDC motors. Each phase can be represented by a resistance, an inductance, and a back‑EMF voltage source. This similarity allows proven modeling techniques to be reused across motor types.

Back-Electromotive Force (Back‑EMF) in the PMSM Electrical Model

Back Electromotive Force (EMF) in the Permanent Magnet Synchronous Motor (PMSM) Electrical Model

In the per‑phase electrical model of a PMSM, the phase voltage equation is typically written as:

\begin{equation} v = R * i + L * \frac {di}{dt} + e\end{equation}

where:
v is the phase voltage,
R is the phase resistance,
i is the phase current,
L is the phase inductance,
di / dt is the rate of change of current, and
e is the back electromotive force (back‑EMF).

The e represents the voltage induced in the stator winding by the rotating permanent magnet rotor. Physically, this voltage opposes the applied voltage and increases proportionally with rotor speed and magnetic field strength. Because back‑EMF is directly related to rotor motion, it is a key quantity for estimating rotor position and speed in sensorless control algorithms.

In FOC‑based systems, back‑EMF is not measured directly. Instead, it is estimated using measured phase currents, applied voltages, and known motor parameters (resistance and inductance). This estimated back‑EMF is then used to infer rotor position.

Microchip Technology’s dsPIC® Digital Signal Controllers (DSCs) are particularly well suited for this task, as they integrate high‑speed Analog‑to‑Digital Converters (ADCs) and a Digital Signal Processing (DSP) engine capable of executing these calculations in real time.

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Why Zero‑Crossing Detection Is Not Used in Field‑Oriented Control (FOC)

Zero‑crossing detection relies on observing the voltage of an unenergized motor phase. In six‑step BLDC control, one phase is always left floating, making this approach practical. In FOC, however, all three phases are actively driven throughout the electrical cycle to produce smooth sinusoidal currents. Because there is no undriven phase in FOC, back‑EMF zero‑crossing methods cannot be applied. Instead, back‑EMF voltage estimation is used in conjunction with a simplified motor model. This approach enables continuous rotor position estimation even while all phases are being actively controlled.

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PLL Estimator in BLDC and PMSM Motor Control

Phase-Lock Loop (PLL) Estimator in Brushless DC (BLDC) and Permanent Magnet Synchronous Motor (PMSM) Motor Control Block Diagram

Phase-Lock Loop (PLL) Estimator in Brushless DC (BLDC) and Permanent Magnet Synchronous Motor (PMSM) Motor Control Equations

A PLL is a control system that synchronizes an internal oscillator with the phase and frequency of an input signal. In motor control, a PLL estimator is used to lock onto the phase of the estimated back‑EMF, thereby tracking the rotor’s electrical angle and speed.

In a sensorless BLDC or PMSM system, the PLL continuously adjusts its estimated rotor angle so that the internally modeled back‑EMF aligns with the observed electrical behavior of the motor. The rate of change of the estimated angle provides rotor speed information, while the angle itself is used for commutation or FOC transformations.

PLL estimators are especially effective at medium to high speeds, where back‑EMF signals are strong and well defined. They also provide inherent filtering, improving robustness in electrically noisy environments. However, at very low speeds or at a standstill, back‑EMF is weak or nonexistent, which limits estimator accuracy and requires special startup strategies.

Microchip Technology provides proven PLL‑based sensorless control implementations through application notes such as "Sensorless Field Oriented Control (FOC) for a Permanent Magnet Synchronous Motor (PMSM) Using a PLL Estimator and Equation-based Flux Weakening (FW)" and through software frameworks like the Motor Control Application Framework (MCAF) and motorBench® Development Suite. These tools support dsPIC33 and selected 32‑bit microcontrollers, significantly reducing development time.

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Summary

Sensorless rotor position estimation is a cornerstone of modern BLDC and PMSM motor control, particularly for FOC. Because FOC drives all motor phases continuously, traditional back‑EMF zero‑crossing techniques are not applicable. Instead, back‑EMF is estimated using a simplified electrical model of the motor, and rotor position is derived using advanced algorithms such as PLL estimators. These techniques enable accurate, reliable motor control without physical position sensors. Microchip Technology supports these approaches with high‑performance dsPIC DSCs, optimized motor control libraries, and development tools that help engineers implement robust sensorless motor control systems efficiently.

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