# Sensorless control of permanent magnet drives

Synchronous machines with permanent magnet excitation, also refered to as PMSMs, have a smaller inertia, higher efficiency and a higher torque to volume ratio compared to asynchronous machines. These advantages have resulted in an increased application of the PMSM in hybrid vehicles, ships, windmills, pumps, compressors and HVAC devices. As a high performance and a high-dynamical behaviour are of importance, advanced control techniques are developed at our laboratorium.

In this research, particular interest is given to sensorless control. To obtain a stable PMSM drive through closed-loop control, motion-state sensors are mounted on the shaft or placed inside the machine. However, as these devices are installed close to the machine, they are subjected to temperature variations and mechanical vibrations. This can result in a malfunction of the sensor. For this reason, a replacement of mechanical motion-state sensors by estimators is strongly desired. A drive equiped with a motion-state estimator instead of a sensor is frequently referred to as a sensorless or self-sensing drive.

Today, some commercial sensorless asynchronous and synchronous drives are available. Most of these drives are based on the speed induced voltage or back-emf which works well above 30-100 tpm. However, at a lower speed range, more advanced control methods are required as the signal to noise ratio of the back-emf will be insufficient to control the PMSM in a stable manner. What's more, at standstill, the back-emf is no longer available to detect the rotor position.

Our research to sensorless control is focussed on the estimation of the rotor angle and flux position at low speed. In this speed range, high-frequency signals are injected additionally to the fundamental voltages and currents which are required for normal operation. As the phase inductances in PMSMs vary with the rotor angle and flux position, the high-frequency response will depend on these motion states. Proper conditioning of this response will result in an estimation of the motion states required for the torque or speed control of the PMSM.

## Applications

**Sensorless control of a permanent-magnet synchronous machine with buried magnets.**

The permanent-magnet synchronous machine with buried magnets or interior PMSM (IPMSM, Fig. 1) has several extra advantages such as high-flux concentration, a passive shielding of the burried magnets from high-frequency signals and robustness against centrifugal forces at high speeds. Moreover, the additional reluctance torque, generated by field-weakening, allows to drive the machine in a very large speed range. Furthermore, as the saliency for an IPMSM is very large, the phase inductances strongly vary with the rotor angle. As a result, accurate estimation of the rotor angle by using high-frequency signals can be obtained.

Various high-frequency techniques can be applied to estimate the motion states. They differ in signal generator, type of waveform, frequency, amplitude, reference frame and signal conditioning. Each of these methods gives accurate results at low loads. However, by applying a load, magnetic saturation occurs and an estimation error is observed.

Indeed, at no load, extrema in the amplitude of the high-frequency current response have been measured for high-frequency voltage vectors alligned along one of the orthogonal magnetic axes (fig 2.a). From these measurements, an accurate estimation of the rotor position can be made. Even a distinction between the permanent magnetic north and south pole can be made as the machine is magnetically non-linear. An increase of the permanent magnetic field due to the stator current results in a reduction of the inductance whereas field-weakening increases the inductance along the magnet direction.

At load, a stator current is applied and a second mmf is generated perpendicular to the permanent-magnet mmf. As the machine is magnetic nonlinear, an important magnetic interaction exists between the two magnetic axes. As a result the inductances of direct and quadrature axes are a function of both components of the stator current.

The magnetic interaction is observed at standstill by performing measurements of the direct inductance for different stator current components, Fig. 3. As a result of the magnetic interaction, measurements confirm that the loci of extrema in the high-frequency current response differ from the loci of extrema in the permanent-magnet field, as is shown in Fig. 2.b. As a consequence, a motion-state estimation for a loaded machine will be more difficult than for the unloaded case.

To develop advanced sensorless drives, the conventional Park model which neglects the magnetic interaction has to be adapted. An enhanced analytical model is developed which includes the magnetic interaction. Identification and validation of the novel model is done by using various tests such as synchronizing the PMSM to the electrical grid, applying DC-decay tests, multisinus test signals, short circuit tests and tests at load. Measurements are performed by using a VXI data-acquisition system. Based on the novel model, improvements are made to the high-frequency signal based sensorless control methods in order to obtain accurate measurements for a loaded machine.

## Relevant Publications

- Frederik De Belie, “Vector control of synchronous permanent-magnet machines without mechanical position sensor”, Ph.D.-dissertation, Ghent University, Faculty of Engineering, Gent, Belgium, 31 March 2010. (received the Biennial 2010 Iwan Akerman Award from Atlas Copco and the FWO-Flanders)
- Frederik De Belie and Jan Melkbeek, “Sensorless Control of Salient-Pole Machines”, WO/2009/103662A1, EP2258043A1 and US20100327789A1.
- Sergeant, P., De Belie, F. & Melkebeek, J. (2011). Rotor Geometry Design of Interior PMSMs with and without Flux Barriers for More Accurate Sensorless Control. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, 2011, IF 4,678 (in press DOI 10.1109/TIE.2011.2116763).
- De Belie, F., Sergeant, P. & Melkebeek J. (2010). A sensorless PMSM drive using modified high-frequency test pulse sequences for the purpose of a discrete-time current controller with fixed sampling frequency. MATHEMATICS AND COMPUTERS IN SIMULATION, 81(2), pp. 367-381, IF 0,946.
- De Belie, F., Sergeant, P. & Melkebeek, J. (2010). A Sensorless Drive by Applying Test Pulses Without Affecting the Average-Current Samples. IEEE TRANSACTIONS ON POWER ELECTRONICS, 25(4) 875-888, IF 2,929.
- Sergeant, P., De Belie, F., Dupré, L. & Melkebeek, J. (2010). Losses in sensorless controlled permanent-magnet synchronous machines. IEEE TRANSACTIONS ON MAGNETICS, 46(2) 590-593, IF 1,061.
- Sergeant, P., De Belie, F. & Melkebeek, J. (2009). Effect of rotor geometry and magnetic saturation in sensorless control of PM synchronous machines. IEEE TRANSACTIONS ON MAGNETICS, 45(3) 1756-1759, IF 1,061.
- De Belie, F., Melkebeek, J., Vandevelde, L., Geldhof, K. & Boel, R. (2006). A discrete-time model including cross-saturation for surface permanent-magnet synchronous machines. COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING, 25(4) 766-778, IF 0,274.