Sensorless Field Oriented Control (FOC) for a Permanent Magnet Synchronous Motor (PMSM) Using a PLL Estimator and Field Weakening (FW)

Author: Mihai Cheles, Microchip Technology Inc.

INTRODUCTION

Current industry trends favor Permanent Magnet Synchronous Motors (PMSM) for motor control applications due to their high power density, fast dynamic response, high efficiency, reduced manufacturing costs, and improved magnetic properties. Microchip Technology offers a range of Digital Signal Controllers (DSCs) and reference designs to facilitate efficient, robust, and versatile motor control, shortening the development cycle for new products.

FIELD ORIENTED CONTROL (FOC)

For PMSM motors, the rotor field speed must be synchronized with the stator (armature) field speed. Loss of synchronization causes the motor to halt. Field Oriented Control (FOC) is a method that uses one flux (rotor, stator, or air gap) as a reference frame to decouple the torque and flux-producing components of the stator current. This allows for simpler control of three-phase motors, similar to DC motors, where armature current controls torque and excitation current controls flux. This application note uses the rotor flux as the reference frame.

Several Microchip application notes, such as AN1078 and AN908, provide details on FOC principles. This document focuses on a new implementation using the dsPICDEM™ MCLV Development Board (DM330021), which supports PMSM control without additional hardware. The control scheme is similar to AN1162 for AC Induction Motors, with specific adjustments for PMSM and estimator particulars.

FOC PHASOR DIAGRAM (BASE SPEED)

The d-axis current reference (Idref), corresponding to the armature reaction flux, is set to zero in PMSM FOC. The rotor's permanent magnets generate the rotor flux linkage (ΨPM). The air gap flux is the sum of the rotor's flux linkage and the armature reaction flux linkage from the stator current. In constant torque mode, the d-axis air gap flux equals ΨPM, with zero d-axis armature reaction flux. In constant power operation, the d-axis current (Id) is used for field weakening to achieve higher speeds.

FOC PHASOR DIAGRAM (HIGH SPEED - FW)

During field weakening, the d-axis current is made negative to weaken the air gap flux linkage. This allows for higher speeds. However, for surface-mounted PMSM, the large air gap results in weak armature reaction flux, limiting the achievable speed increase. The maximum speed achieved in this mode is typically double the base speed.

SURFACE MOUNTED PM PMSM TRANSVERSAL SECTION

The document describes a surface-mounted permanent magnet synchronous motor (PMSM) which offers advantages like low torque ripple and lower cost. This motor type has a smooth air gap flux, resulting in sinusoidal Back Electromotive Force (BEMF). The larger air gap in these motors leads to smaller inductance, simplifying the motor's mathematical model for speed and position estimation.

The FOC maximum torque per ampere is achieved by maintaining the motor's rotor flux linkage 90 degrees behind the armature generated flux linkage.

PLL TYPE ESTIMATOR

The estimator used in this application note is adapted from AN1162 and is based on the principle that the d-component of the Back Electromotive Force (BEMF) should be zero at steady state. The estimator uses a Phase-Locked Loop (PLL) structure. The estimated speed (ωrestim) is integrated to obtain the estimated angle (θestim). The estimated speed is derived from the q-component of the BEMF and the voltage constant (Kφ).

The BEMF d-q components are filtered after Park transformation. The stator circuit equations are represented, considering phase inductance (Ls) and resistance (Rs). These parameters are normalized for computation. The derivative of current is filtered to reduce noise. The BEMF values are transformed into the rotor flux reference frame (Eq, Ed) using the Park transform and the estimated angle.

ELECTRICAL CIRCUIT MODEL FOR PLL ESTIMATOR

The voltages (Va, Vβ) used in the estimator's equations are previous cycle calculations from the FOC. The phase currents (IA, Iβ, Ic) are obtained from the shunts. The stator inductance (Ls) and resistance (Rs) are normalized. The derivative of current is limited to manage noise. The BEMF values are transformed into the rotating reference frame (Eq, Ed) using the Park transform. The estimated electrical speed (ωrestim) provides the rotor flux angle. The normalized voltage constant (Kφ) is used in the electrical speed computation.

The software implementation involves calculating the derivative of current to time, which can be noisy. A limiting value for current variation per estimator execution loop is introduced. The BEMF d-q components are filtered. The estimated electrical speed is used to calculate the rotor flux angle.

TUNING AND EXPERIMENTAL RESULTS

Algorithm tuning is straightforward for speeds below the base speed where maximum torque is applied. Motor parameters are entered into a support file (tuning_params.xls) and then normalized for the estimator. Tuning involves measuring the rotor's resistance (Rs), inductance (Ls), and voltage constant (Kφ).

The stator resistance and inductance can be measured at the motor terminals. The voltage constant (Kφ) can be measured by rotating the rotor at a constant speed and measuring the output voltage. Table 1 provides experimental data for a Hurst Motor DMB00224C10002, including connection type, resistance, inductance, voltage constant, and ambient temperature.

Field weakening tuning is more complex due to system non-linearity. The goal is to achieve a nominal speed doubling. Caution is advised during field weakening to prevent motor damage or demagnetization. Loss of FOC at high speeds can damage the inverter. The tuning process involves iterative coefficient corrections. The d-axis current component is adjusted via a lookup table to control air gap flux density. Inductance variation is also managed with a lookup table.

For loaded tests, the initial d-axis current reference (which equals the nominal current for field weakening) is adjusted based on the load torque-speed characteristic. The ratio between power for field weakening and torque generation depends on this characteristic.

Figure 8 shows the d-axis current and the inverse of the voltage constant (1/Kφ) as a function of speed for both initial and fine tuning. Table 2 presents experimental results with load, showing achieved speed, torque, and RMS phase current at various speeds.

Voltage limitation of the inverter in field weakening mode affects the d-q current components. The q-component of the current prioritizes the d-component for field weakening. Figure 9 illustrates the dynamic voltage adjustment block schematic.

SOFTWARE RESOURCES AND EXECUTION TIME

The sensorless FOC algorithm, developed for a dsPIC33FJ32MC204 using -03 level optimization, requires specific program memory (Flash) and data memory (RAM). The execution time for the ADC interrupt, with and without field weakening code, is measured in microseconds. The ADC interrupt is triggered every PWM period.

CONCLUSION

This application note provides a method for flux angle and speed estimation for PMSM motors, successfully applied in Field Weakening mode to expand application possibilities. It discusses the theoretical basis of the estimator, tuning directions, and the use of support files for adaptation to different motors. Utilizing Microchip's development hardware platform can significantly reduce time-to-market.

REFERENCES

The following application notes are referenced and available for download from the Microchip website (www.microchip.com):

AN908 “Using the dsPIC30F for Vector Control of an ACIM"
AN1078 "Sensorless Field Oriented Control of PMSM Motors using dsPIC30F or dsPIC33F Digital Signal Controllers"
AN1162 "Sensorless Field Oriented Control (FOC) of an AC Induction Motor (ACIM)"

APPENDIX A: SOURCE CODE

The software is supplied under a license agreement and is protected by copyright laws. Microchip makes no warranties regarding the software. The software is available as a single WinZip archive file, downloadable from the Microchip corporate website.

APPENDIX B: REVISION HISTORY

Revision A (September 2009): This is the initial released version of this document.

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