# DSP-Based Drive For Sensorless Vector Control Of PMSM

### Abstract

Methods for adjustment of drive parameters during the change of control modes is presented. The methods are applied to Permanent Magnet Synchronous Motor (PMSM) sensorless control with Sliding Mode Observer (SMO). The phase compensation was proposed to optimize rotor position in the speed control mode. This technique is based on the measurement of control current with constant load torque. The validity of the proposed methods is verified experimentally.

### INTRODUCTION

Permanent Magnet Synchronous Motors (PMSM) with Field Oriented Control drives are widely used in various industrial applications due to their high-power factor, high-torque density, high efficiency and small size. For effective application of vector-control algorithms, it is necessary to know the rotor position. Encoders or revolvers have been used for sensing the rotor position. However, the position sensor increases the cost and decreases reliability and noise immunity of the PMSM drive system. Therefore, vector-control methods, in the absence of any shaft sensors, have been investigated by many researchers.

Sensorless control in field-oriented PMSM relies on dependency of the rotor position upon the back electromotive force (back-EMF) induced in the stator windings [10, 11]. The estimation of the rotor position and speed (state variables) requires the use of a relatively accurate motor model, the knowledge of the feeding voltages (system input) and the measurement of motor currents (system output) with waveforms proportional to back-EMF.

Several estimated methods were covered in literature, which base on state observers [1, 2, 3, 4], extended Kalman filters [5, 6] and sliding mode observer [5, 7, 8].

Among the various approaches, the Sliding Mode Observer (SMO) represents an attractive proposal because it is robust to measurement noise, parameter deviations and the inherent high gain structure [11]. This method doesn't require high computational charge (as in the case of Kalman Filter) and may be effectively implemented in low-cost controllers. However, SMO introduces time-delay in the rotor position estimation due to the use of the low-pass filter to extract rotor position angle from back-EMF signal. Meanwhile, this low-pass filter leads to unavoidable and unwanted phase lag in the rotor-angle estimation. Various sensorless control schemes were proposed to improve the accuracy of the rotor position estimation [8, 12, 13]. For variable speed drive, the speed and frequency of back-EMF are not constant. Thus, a compensation method that can accommodate this situation is needed. Theoretically, the compensation angle can be obtained directly by the phase/frequency response of the adopted low-pass filter. In fact, a further correction is needed due to various deviations of motor parameters, measurement errors, calculation delay, etc.

This research presents one method to compensate phase lag in SMO for the PMSM drive with close-loop velocity control. Practical recommendations were made to change control mode in real time from starting open-loop to close-loop speed control.

### CONTROL SCHEME

A standard digital vector control scheme is shown in Fig. 1. It is known that SMO does not operate normally at a very low speed and standstill. To reach the speed set-point, the whole start-up procedure was implemented by sequential switching of the three control modes in the following order:

- open-loop V/f speed control (switches 1 and 2 are set in position 1);
- inner-loop vector current control (switch 1 is turned into position 2 and switch 2 continues to be set in position 1);
- outer-loop speed control (switches 1 and 2 are set in position 2).

The similar start-up operation for sensorless speed control was described in [15] for Kalman filter estimator. In this paper the adjustable SMO was used to manage the start-up transient without brutal state change during the mode switching.

As a result of the first step, a rotating-stator field is generated with angular velocity wop given by the derivative of the reference angle Qop in the space-vector pulse width modulation (SVPWM), and with amplitude depending on the current value iq,op. The rotor begins to move due to the attracting torque between the rotor magnets and rotating field. SMO falls into a correct estimation mode. However, the estimated rotor position Q always differs from the generated stator reference angle Qop. To avoid a sharp angle change, the estimated rotor angle Q* in the output of SMO must be forced (DQstart) to the reference angle Qop before the second control mode switching.

In the second control mode PMSM reaches the certain speed which depends on the current value iq,op and the load torque in the motor rotor. To prepare the smooth switching of the third control mode, the PID output current in the point 2 must be adjusted so that it would be equal to the value iq,op.

In the closed-loop it is necessary to adjust the SMO parameters to improve control characteristics. We propose the phase correction of the estimated rotor angle to achieve the best relation between the real motor torque (T) and current value (iq,*).

The field-oriented control of PMSM is based on the interaction between two orthogonal frames: a stationary reference stator frame a,b and a synchronously rotating reference rotor frame d,q. The theoretical and real transformations of a stationary model a,b to a synchronously rotating d,q frame are represented in Fig. 2.

The control strategy of the drive (Fig. 1) in d,q coordinates becomes very simple. The currents are compared with the reference values and updated by two separate proportional-integral (PI) controllers that independently control id to zero and iq to produce the required torque.

The electric torque of PMSM can be described by the interaction between the rotor currents and the flux wave resulting from the stator currents induction. The theoretical motor torque (T), in an ideal rotation system coordinates d,q, becomes

Due to the error of the rotor position estimating DQ, the estimated rotor current iq* is not alined with the rotor coordinates d,q resulting in reduction of the real torque. The real motor torque T* depends on the value of DQ in accordance with Fig. 2:

The load motor with the constant load torque (Tl = T* = const.) is used to compensate the phase lag DQ in the rotor position coordinates d*,q*. The rotor speed w is held stable by the certain value of the current iq,* in the outer control loop. Considering T*=const in (5), it is possible to adjust the rotor angle phase DQ by measuring the control current iq*. The optimal estimation of the rotor angle corresponds to the minimum value of the measuring current iq*.

### EXPERIMENTAL RESULTS

The universal motor drive platform, based on the DSK eZdspTM LF2407, was used to test the proposed control solutions [16]. The Permanent Magnet Synchronous Motor of 250 W with three-pole pairs was loaded by the DC motor of 500 W to produce a constant torque as is shown in Fig. 3.

The proposed control algorithm was implemented in the DSK software. Fig. 4 shows the principal waveforms in the real-time experience.

The proposed control algorithm was implemented in the DSK software. Fig. 4 shows the principal waveforms in the real-time experience.

The rotor reaches the speed set-point for w = 153 rad/sec in t1 = 13,5 sec after beginning of the start-up procedure. The second mode is switched in t1 with the adjusted rotor angle DQstart. During any PWM cycles, the control software introduces the initial state into integral path to make equal the output PID current with iq,op. The closed-loop control is switched automatically and the speed control mode begins. The control current iq* changes to one nonoptimal value after the transient to the right of t1. The optimization of DQ begins in t2 = 24,5 sec. Measuring iq* and adjusting DQ , the control software achieves the minimum value of the quadrature current iq*min in the time point t3 = 35 sec. The increasing of the rotor speed is explained by change of DQ during the optimization process.

### CONCLUSION

In this work a complete start-up procedure for the sensorless PMSM drive with SMO has been examined. It was shown how the drive parameters can be adjusted to avoid brutal state change during the mode switching. The phase correction method was proposed to compensate the estimation errors of the rotor position in SMO. This method is based on minimization of the control current while the rotor speed and load torque are constant. The experimental results prove the correct operation of the sensorless motor drive in every control mode.

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