Performance improvement in a sensorless surface-mounted PMSM drive based on rotor flux observer

Control Engineering Practice 96 (2020) 104276

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Performance improvement in a sensorless surface-mounted PMSM drive based on rotor flux observer Mario Marchesoni a , Massimiliano Passalacqua a ,∗, Luis Vaccaro a , Marco Calvini b , Marco Venturini b a b

University of Genova, Department of Electrical, Electronic, Telecommunications Engineering and Naval Architecture, Via all’Opera Pia, 11A, Genova, 16145, Italy Phase Motion Control S.p.A Via Luigi Cibrario 4, Genova, 16154, Italy

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Keywords: Permanent magnet motors (PMSM) Rotor flux observer Sensorless control Speed control

ABSTRACT Permanent magnet synchronous motor sensorless algorithms for low speed region are usually based on rotor anisotropy. Although many studies showed a good behavior of this type of control, high frequency voltage injection is required, which causes loud acoustic noise in addition to electrical losses. On the other hand, methods based on back electromotive force or rotor flux observer, which guarantee high performance in the medium–high speed region, do not required voltage injection. In this paper, a rotor flux observer based algorithm performance is analyzed, in order to extend its use also in the low speed region. Behavior both with no-load, linear torque, quadratic torque, constant torque and compressor-load torque is tested, especially focusing on motor starting. Improvements to rotor flux observer algorithms available in the scientific literature are discussed and their effectiveness is verified by experimental results.

1. Introduction In last years permanent magnet synchronous motors (PMSMs) achieved a key role in low and medium power electrical drives. Compared to induction motors they are characterized by high power density, high torque-inertia ratio, high efficiency and they require low maintenance. However, in order to realize a proper control, rotor position measurement is necessary; for this purpose resolvers, encoders or effect Hall probes are usually employed. Nevertheless, in several industrial applications, the use of such transducers leads to disadvantages in terms of cost, sizing, reliability and noise immunity. For these reasons, a lot of studies focus on rotor position estimation methods, in order to remove the position sensor. Sensorless algorithms can be divided into three main categories: methods based on rotor anisotropy (Carpaneto, Maragliano, Marchesoni, & Vaccaro, 2009; Consoli, Scarcella, & Testa, 2001; Formentini, Maragliano, Marchesoni, & Vaccaro, 2012; Hosooka & Shinnaka, 2017; Ji-Hoon, Seung-Ki, JungIk, Ide, & Sawamura, 2002; Kim & Ha, 2008; Wang, Liu, Zhao, Ding, & Xu, 2018; Xu & Zhu, 2016a, 2016b; Zhang et al., 2018; Zhu & Gong, 2011), methods based on back-electromotive force (BEMF) (Baratieri & Pinheiro, 2016; Carpaneto, Fazio, Marchesoni, & Parodi, 2012; Chen, Li, Gao, & Chen, 2019; Chen, Luo, & Pi, 2015; Genduso, Miceli, Rando, & Galluzzo, 2010; Kim, Jeong, Nam, Yang, & Hwang, 2015; Li, Zhu, Howe, & Bingham, 2007; Morimoto, Kawamoto, Sanada, & Takeda, 2001; Paitandi & Sengupta, 2017; Yang & Chen, 2017; Ye, 2019;

Zhiqian, Tomita, Doki, & Okuma, 2003) and methods based on rotor flux observer (RFO) (Choi, Nam, Bobtsov, Pyrkin, & Ortega, 2017; Henwood, Malaizé, & Praly, 2012; Khlaief, Bendjedia, Boussak, & Gossa, 2012; Lee et al., 2010; Marchesoni, Passalacqua, Vaccaro, Calvini, & Venturini, 2019a; Xiao et al., 2017). In order to estimate rotor position exploiting rotor anisotropy, high frequency voltage components have to be injected. In surface-mounted PMSM (SPMSM) the saliency is low and therefore the amplitude of high frequency current to be injected is considerable. For this reason, even if these methods allow implementing both speed control and position control, they are characterized by additional losses and loud acoustic noise, therefore they are unsuitable for various applications. BEMF based methods do not require high frequency injection but their performance worsen in the low speed region, since BEMF tends to zero as speed approaches zero. The last category of sensorless algorithms, analogously to BEMF methods, do not require high frequency injection and rotor flux is constant even when speed tends to zero. For this reason RFO based methods performances at low speed are generally better than BEMF methods. In Xiao et al. (2017) the flux linkage is used as state variable and a high pass filter is designed in series with the integrator to eliminate DC offset. In Lee et al. (2010) a nonlinear observer is used which allows to obtain better performance in the low speed region with torque steps. The observer used in Lee et al. (2010) is combined with

∗ Corresponding author. E-mail addresses: [email protected] (M. Marchesoni), [email protected] (M. Passalacqua), [email protected] (L. Vaccaro), [email protected] (M. Calvini), [email protected] (M. Venturini).

https://doi.org/10.1016/j.conengprac.2019.104276 Received 15 May 2019; Received in revised form 7 October 2019; Accepted 6 December 2019 Available online xxxx 0967-0661/© 2019 Elsevier Ltd. All rights reserved.

M. Marchesoni, M. Passalacqua, L. Vaccaro et al.

Control Engineering Practice 96 (2020) 104276

the estimation of the flux linkage constant in Choi et al. (2017), which allows to significantly increase algorithm performance. A nonlinear flux observer is used for IPMSM in Khlaief et al. (2012). Some studies show the possibility of angle estimation without high frequency injection also in the low speed region using model predictive control (Nalakath, Sun, Preindl, & Emadi, 2018; Rovere, Formentini, Gaeta, Zanchetta, & Marchesoni, 2016), back-stepping strategy (Hamida, de Leon, & Glumineau, 2017) or methods which investigate the inductance variation measuring current derivatives (Jarzebowicz, Karwowski, & Kulesza, 2017); nevertheless, this techniques were used only for interior permanent magnet synchronous motors (IPMSMs), which are characterized by high motor anisotropy. Studies on RFO sensorless methods (Choi et al., 2017; Henwood et al., 2012; Khlaief et al., 2012; Lee et al., 2010; Xiao et al., 2017) do not deeply analyze algorithm behavior over different working conditions (i.e. different load torque and various reference speed). In particular, in Choi et al. (2017) motor starting in no-load condition is shown, but no works are known in the scientific literature showing the possibility of starting PMSMs with rated torque at zero speed using a RFO based method. In this paper, RFO based algorithm behavior with different loads is analyzed; in particular, SPMSM starting with rated torque at standstill is shown. Moreover, a method to avoid starting failure is presented and a new direct axis current reference management, aiming at transient performance improving, is pointed out. Finally, algorithm robustness towards motor parameter variation is investigated. RFO method is explained in Section 2, showing the starting failure avoidance technique and the direct axis current reference management; algorithm parameters used in this study are reported in this section. Experimental results are carried out on a 27 N m , 2000 rpm and on a 2.2 N m , 5000 rpm SPMSM; the test bench is shown in Section 3, whereas experimental results are reported in Section 4. Conclusions are pointed out in Section 5.

Being 𝜂 defined as: ⎧𝜂𝛼 = 𝜓̂ 𝑚 cos 𝜃0 [ ⎪ ⎪+ 1 𝑘2 2𝑎𝑠 𝑥𝛼 − 𝑎𝑠 𝑠+𝑎 ⎪ 𝑠 𝑠+𝑎 ⎨ 𝜂 = 𝜓 ̂ sin 𝜃 𝑚 0 ⎪ 𝛽 ⎪ [ ⎪+ 1 𝑘2 2𝑎𝑠 𝑥𝛽 − 𝑎𝑠 ⎩ 𝑠 𝑠+𝑎 𝑠+𝑎

(

(

) )] 2𝑎𝑠 ( 𝑥 𝜂 + 𝑥𝛽 𝜂𝛽 𝑥2𝛼 + 𝑥2𝛽 − 𝑠+𝑎 𝛼 𝛼

(5)

) )] 2𝑎𝑠 ( 𝑥 𝜂 + 𝑥𝛽 𝜂𝛽 𝑥2𝛼 + 𝑥2𝛽 − 𝑠+𝑎 𝛼 𝛼

where 𝜃0 is the initial rotor angle, 𝑘1 , 𝑘2 and 𝑎 are observer gains, 𝑑 is the differential operator and 𝜓̂ 𝑚 is the initial (rated) permanent 𝑠 ≡ 𝑑𝑡 magnet flux linkage constant. The observer rectifies this initial value, in order to meet the real value. The estimated rotor angle 𝜃̂𝑟 will be then calculated as: ) ( 𝑥𝛽 + 𝜂𝛽 (6) 𝜃̂𝑟 = tan−1 𝑥𝛼 + 𝜂𝛼 In this study initial rotor angle was unknown and thus was set to zero. Eqs. (1) to (6) are taken from Choi et al. (2017). To obtain rotor speed estimation, the PLL estimator depicted in Fig. 1 was used. The PLL input 𝜀 is clarified in Eq. (7): 𝜀 = sin(𝜃̃𝑟 ) cos(𝜃̂𝑟 ) − cos(𝜃̃𝑟 ) sin(𝜃̂𝑟 ) = sin(𝜃̃𝑟 − 𝜃̂𝑟 ) ≅ 𝜃̃𝑟 − 𝜃̂𝑟

(7)

The use of sin(𝜃̃𝑟 ) cos(𝜃̂𝑟 ) − cos(𝜃̃𝑟 ) sin(𝜃̂𝑟 ) as angle error instead of 𝜃̃𝑟 − 𝜃̂𝑟 highly reduces spikes during transition from −𝜋 to 𝜋. PLL output is then filtered with a first order low pass filter. The drive control scheme is shown in Fig. 2. 2.2. Starting failure avoidance Being the initial angle unknown and inestimable with RFO method, if rotor electrical position is around 90◦ with respect to the initial angle (which is set arbitrarily to zero), and the motor parameters are not correctly set, motor starting may fail. As a matter of fact Iq (quadratureaxis stator current) PI controller increases the reference value, but actually Id (direct-axis stator current) is growing due to angle error and no torque is provided. It is essential to notice that if estimated rotor angle is constant while motor is at standstill, speed is correctly estimated (i.e. estimated speed is zero), thus it is possible to detect the starting failure. If this situation occurs, integrators of Eqs. (5) are reset and initial angle is set to the estimated angle plus 𝜋∕2, as shown in Fig. 3. The starting failure can occur, in particular, if the value of the stator resistance in the observer is higher than the real one. Indeed it is interesting to note that if all parameters are correctly set, the starting failure does not occur. Please note that 𝜔𝑟𝑒𝑓 _𝑙𝑖𝑚𝑖𝑡𝑒𝑑 is the speed reference with derivative rate limitation. 𝜔𝑐ℎ𝑒𝑐𝑘_𝑠𝑡𝑎𝑟𝑡𝑖𝑛𝑔 and 𝜔𝑙𝑖𝑚𝑖𝑡_𝑠𝑡𝑎𝑟𝑡𝑖𝑛𝑔 are function of 𝜔𝑟𝑒𝑓 , i.e., the speed reference without derivative rate limitation, with the constraint of 𝜔𝑙𝑖𝑚𝑖𝑡_𝑠𝑡𝑎𝑟𝑡𝑖𝑛𝑔 < 𝜔𝑐ℎ𝑒𝑐𝑘_𝑠𝑡𝑎𝑟𝑡𝑖𝑛𝑔 . Value of above mentioned parameters are shown in Table 2 and interpolated for all speed range. The parameters are heuristically evaluated. 𝜔𝑐ℎ𝑒𝑐𝑘_𝑠𝑡𝑎𝑟𝑡𝑖𝑛𝑔 should be sufficiently high not to cause starting failure avoidance method improper intervention, but on the other hand should be sufficiently low not to delay to much the motor starting. 𝜔𝑙𝑖𝑚𝑖𝑡_𝑠𝑡𝑎𝑟𝑡𝑖𝑛𝑔 should be sufficiently high to neglect speed estimation error but significantly lower than 𝜔𝑐ℎ𝑒𝑐𝑘_𝑠𝑡𝑎𝑟𝑡𝑖𝑛𝑔 .

2. Sensorless algorithm based on rotor flux observer (RFO) 2.1. Angle observer and speed estimator Considering an isotropic motor (which is an adequate approximation for SPMSM) stator equations are: ⎧𝑣 = 𝑅𝑖 + 𝐿 𝑑𝑖𝑎 + 𝑑𝜓𝑎 𝑎 ⎪ 𝛼 𝑑𝑡 𝑑𝑡 (1) ⎨ 𝑑𝑖 𝑑𝜓 𝛽 𝛽 ⎪𝑣 = 𝑅𝑖 + 𝐿 + 𝛽 ⎩ 𝛽 𝑑𝑡 𝑑𝑡 𝑣𝛼 and 𝑣𝛽 are the stator voltages in the stationary axis reference frame, 𝑖𝛼 and 𝑖𝛽 are the stator currents in the stationary axis reference frame, R is the stator winding resistance, L is the stator winding inductance, 𝜓𝛼 and 𝜓𝛽 are the rotor flux components in the stationary reference frame, defined as: { 𝜓𝛼 = 𝜓𝑚 cos 𝜃𝑟 (2) 𝜓𝛽 = 𝜓𝑚 sin 𝜃𝑟 where 𝜃𝑟 is the rotor angle and 𝜓𝑚 is the permanent magnet flux linkage constant. From (1) one can obtain: ⎧ 𝑑𝜓𝛼 = 𝑣 − 𝑅𝑖 − 𝐿 𝑑𝑖𝛼 𝛼 𝛼 ⎪ 𝑑𝑡 𝑑𝑡 (3) ⎨ 𝑑𝜓 ⎪ 𝛽 = 𝑣 − 𝑅𝑖 − 𝐿 𝑑𝑖𝛽 𝛽 𝛽 ⎩ 𝑑𝑡 𝑑𝑡 Starting from Eqs. (3) one can define a state 𝑥 = [𝑥𝛼 , 𝑥𝛽 ]𝑇 with same dynamics as 𝜓 = [𝜓𝛼 , 𝜓𝛽 ]𝑇 but with different initial conditions; for this specific state it is possible to define an observer based on the descent gradient method (Choi et al., 2017): [ ] ⎧ 𝑑𝑥𝛼 = 𝑣 − 𝑅𝑖 − 𝐿 𝑑𝑖𝛼 + k 𝜂 (‖𝜂‖2 − 𝜓̂ 2 ) 𝛼 𝛼 1 𝛼 𝑚 ⎪ 𝑑𝑡 𝑑𝑡 ⎪ 𝑑𝑥 𝑑𝑖 (4) ⎨ 𝛽 = 𝑣 − 𝑅𝑖 − 𝐿 𝛽 + [k 𝜂 (‖𝜂‖2 − 𝜓̂ 2 )] 𝛽 𝛽 1 𝛽 𝑚 ⎪ 𝑑𝑡 𝑑𝑡 ⎪ ⎩𝑥𝛼 (0) = x𝛽 (0) = 0

2.3. Direct axis current (Id) reference management 𝑥𝛼 and 𝑥𝛽 derivatives, i.e. Eq. (4) left side, tend to zero at low speed, as a matter of fact 𝑥𝛼 and 𝑥𝛽 are quasi-sinusoidal quantities with almost constant peak values and frequency equal to motor electric frequency. Taking into account inverter nonlinearities, which are reported in Fig. 4 (Marchesoni, Passalacqua, Vaccaro, Calvini, & Venturini, 2019b), when currents approach zero, the inverter voltage drops change rapidly, therefore nonlinearities compensation is less precise; 2

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Control Engineering Practice 96 (2020) 104276

Fig. 1. PLL speed estimator.

Fig. 2. Drive control scheme.

Table 1 Observer and speed loop parameters. Symbol

Quantity

27 N m PMSM

2.2 N m PMSM Compressor coupling

2.2 N m PMSM Motor coupling

𝑘1

Observer gain 1

0.05 (low speed) 0.005 (high speed)

0.05 (low speed) 0.005 (high speed)

0.25

𝑘2

Observer gain 2

0.1 (low speed) 0.01 (high speed)

0.1 (low speed) 0.01 (high speed)

0.25

a 𝑘𝑖

Observer time constant PLL integral gain

500 10 000

500 10 000

500 10 000

𝑘𝑝

PLL proportional gain

800

300

800

𝑓 𝑟1

PLL filter cutoff frequency

22 Hz

22 Hz

22 Hz

Vd P Vq P

Direct and quadrature axis voltage proportional gain

10

10

5

Vd I Vq I

Direct and quadrature axis voltage integral gain

15

15

7

Iq P

Quadrature axis current proportional gain

0.8

0.5 (transients and high speed) 0.8 (constant low speed)

0.5

Iq I

Quadrature axis current integral gain

0.9

0.9

3

Iq lim

Quadrature axis current limit

[−25 A;25 A]

[−8 A;8 A] (transients and high speed) [−12 A;12 A] (constant low speed)

[−8 A; 8 A]

𝐴𝑐𝑐𝑙𝑖𝑚

Acceleration limit

150 rad/s∧ 2 (speed < 30 rad/s) 1000 rad/s∧ 2 (speed > 30 rad/s)

150 rad/s∧ 2 (speed < 70 rad/s) 1000 rad/s∧ 2 (speed > 70 rad/s)

150 rad/s∧ 2 (speed < 70 rad/s, braking) 1000 rad/s∧ 2 (speed > 70 rad/s and acceleration)

if also voltage tends to zero (i.e. low speed), the influence of voltage

medium-high speed to low speed; indeed, voltages and currents approach rapidly zero, starting from high values. A heuristic method was implemented to improve algorithm performance during transients. Id reference, which is normally zero in order to minimize losses, is set to

drop on voltage estimation becomes significant and the estimation worsen. This condition is particularly critical during transition from 3

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Control Engineering Practice 96 (2020) 104276

Fig. 3. Starting failure avoidance method.

Fig. 5. Id reference management during transient.

Table 3 ID reference management parameters. 27 N m PMSM

2.2 N m PMSM

𝜔𝑙𝑖𝑚 𝐼𝑑

50 rad/s 2 A

50 rad/s 2 A

Table 4 Motors and inverter parameters.

Fig. 4. Inverter voltage drop (𝛥V) as a function of motor current (I).

Table 2 Starting failure avoidance parameters. 𝜔𝑟𝑒𝑓 _𝑙𝑖𝑚𝑖𝑡𝑒𝑑

𝜔𝑐ℎ𝑒𝑐𝑘_𝑠𝑡𝑎𝑟𝑡𝑖𝑛𝑔

𝜔𝑙𝑖𝑚𝑖𝑡_𝑠𝑡𝑎𝑟𝑡𝑖𝑛𝑔

5 rad/s 50 rad/s 100 rad/s 209 rad/s (27 N m PMSM) 520 rad/s (2.2 N m PMSM)

4.9 rad/s 45 rad/s 50 rad/s

0.5 rad/s 2.5 rad/s 5 rad/s

50 rad/s

5 rad/s

a positive value during transients. In this way, the current is different from zero and the inverter works in the region where the voltage drop is almost constant and therefore nonlinearities compensation is more efficient. This aspect is confirmed by the fact that the current amplitude which should be injected is almost independent from motor sizing but depends on inverter features (dead times, parasitic capacitance etc.). In SPMSM 𝐿𝑑 ≅ 𝐿𝑞 and therefore electromagnetic torque is almost directly proportional to Iq; for this reason the injection of a constant d-axis current does not produce electromagnetic torque. In addition to that, defining Idreal and Iqreal as the 𝑑-axis and 𝑞-axis current in the real synchronous reference (reference with 𝜃𝑟 ), the relation between currents and estimated angle error 𝛥𝜃 (defined in Eq. (8)) is given by Eqs. (9) and (10), where Iqref is the Iq reference value. Therefore, the torque produced by Iqreal contributes to 𝛥𝜃 reduction (since the additional term to Iqref accelerates the motor if the estimated angle is lower than the real angle and vice versa). Id reference management flowchart is shown in Fig. 5, whereas parameter values are reported in Table 3. Please note that 𝜔𝑙𝑖𝑚 has to be considered as speed absolute value; indeed the algorithm works both with positive and negative speed. The values in Table 3 were evaluated experimentally; 𝐼𝑑 and 𝜔𝑙𝑖𝑚 are the lower values that guarantee a proper behavior of the sensorless control. 𝛥𝜃 = 𝜃𝑟 − 𝜃̂𝑟

Symbol

Symbol

Quantity

27 N m PMSM

2.2 N m PMSM

𝑉𝑟𝑎𝑡𝑒𝑑 𝐼𝑟𝑎𝑡𝑒𝑑 𝑇𝑟𝑎𝑡𝑒𝑑 𝜔𝑟𝑎𝑡𝑒𝑑 P 𝑅𝑠 L 𝜓𝑚 𝑓𝑠𝑤 𝑓𝑠𝑎𝑚𝑝𝑙𝑒 𝑉𝐷𝐶 𝑡𝑑𝑒𝑎𝑑

Phase-to-phase rated voltage Rated current Rated torque Rated speed Poles pair Winding resistance Winding inductance Magnet flux linkage Switching frequency Sampling frequency DC voltage Dead time

380 V 11.9 A 27 N m 209 rad/s 4 0.68 Ω 5.0 mH 0.335 Wb 5 kHz 5 kHz 520 V 4 μs

380 V 2.2 A 2.2 N m 520 rad/s 4 1.65 Ω 6.2 mH 0.125 Wb 5 kHz 5 kHz 520 V 4 μs

in Fig. 6. One of them (27 N m , 209 rad/s, 11.9 A motor) is used in sensored mode to realize the appropriate load thanks to the use on an optical encoder; both a twin 27 N m motor and a 2.2 N m , 520 rad/s, 2.2 A motor were tested in this configuration. This configuration was used to simulate no-load condition, linear, quadratic torque load (typical load profile of pumps and fans) and constant torque (feeders and conveyors), as well as load steps and speed inversion. In the second test bench the 2.2 N m motor was coupled with an air compressor as shown in Fig. 7. Compressor-load is characterized by highly intermittent torque, with constant and high peak values, equal to the rated one, even near zero-speed, therefore is a demanding load for sensorless algorithms. Moreover, in the configuration shown in this paper, the motor was overloaded; as a consequence, the test on the compressor was highly critical for the sensorless algorithm. Both 27 N m and 2.2 N m motors were equipped with resolvers in order to evaluate speed and angle error. Control algorithm was implemented on a Dspace DS1103 controller board and a prototype inverter was used, as shown in Fig. 7. Motors and inverter parameters, as well as their rated values, are reported in Table 4.

(8)

4. Experimental results 𝐼𝑑𝑟𝑒𝑎𝑙 = 𝐼𝑑 ⋅ cos(𝛥𝜃)

𝐼𝑞𝑟𝑒𝑎𝑙 = 𝐼𝑞𝑟𝑒𝑓 + 𝐼𝑑 ⋅ sin(𝛥𝜃)

(9)

A large number of tests, under different conditions, was carried out and in this section the most interesting results are shown. At first, results of speed reference step variation between 180 rad/s and −180 rad/s with linear torque and from 180 rad/s to 5 rad/s with no-load are reported, in order to illustrate Id reference management technique performance improvement during transients. After, the results showing the starting failure avoidance technique effectiveness are illustrated. Moreover, motor starting under linear torque is reported. All these tests were performed using the 27 N m motor coupled with

(10)

3. Test bench Experimental results were obtained using two different configurations. The first test bench consists of two coupled motors, as shown 4

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Control Engineering Practice 96 (2020) 104276

Fig. 6. Coupled motors. 27 N m motor (left), 2.2 N m (right).

Fig. 7. Compressor test bench, Dspace, prototype inverter.

Fig. 9. Id and Iq without Id reference management technique (speed step from 180 rad/s to −180 rad/s).

Fig. 8. Reference, measured and estimated speed without Id reference management technic (speed step from 180 rad/s to −180 rad/s).

the twin motor. After, results at low speed with no-load, quadratic torque and constant torque are shown. For this tests the 2.2 N m motor was used coupled with the 27 N m motor. Finally, motor starting with compressor-load is analyzed and steady-state speed ripple in sensorless mode is compared with sensored operation. Measured and estimated speed during reference variation between 180 rad/s and −180 rad/s with linear torque (Eq. (11)) are shown in Fig. 8; the test is performed with Id reference set to zero (i.e. without Id reference management technique). During zero crossing, angle reference is lost, as it can be noted also from Figs. 9–11, where currents and angle error are plotted; as a consequence of angle reference loss, high frequency current peaks occur. Please note that Id and Iq maximum values correspond to phase current maximum value (i.e. root-meansquare value multiply by root of two); as a consequence Iq rated value is 16.8 A. 𝑇 [N m] =

27 [N m ] 𝜔 [rad∕s] 180 [rad∕s]

Fig. 10. Id and Iq without Id reference management technique (speed step from 180 rad/s to −180 rad/s), enlargement between 5.9 and 6.2 s.

(11) Measured and estimated speed are plotted in Fig. 12, whereas

The same test was performed with the proposed Id reference management, which avoids angle and speed reference loss.

currents are shown in Fig. 13. 5

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Fig. 11. Angle error without Id reference management technique (speed step from 180 rad/s to −180 rad/s), enlargement between 5.9 and 6.2 s. Fig. 14. Reference, measured and estimated speed without Id reference management technique (speed step from 180 rad/s to 5 rad/s).

Fig. 12. Reference, measured and estimated speed with Id reference management technique (speed step from 180 rad/s to −180 rad/s).

Fig. 15. Reference, measured and estimated speed with Id reference management technic (speed step from 180 rad/s to 5 rad/s).

Fig. 13. Id and Iq with Id reference management technique (speed step from 180 rad/s to −180 rad/s).

Fig. 16. Reference and speed profile during motor starting with linear torque.

Benefits of the proposed algorithm can be noticed also in speed reference step variation between 180 rad/s and 5 rad/s with no-load. Using Id reference management technique, speed reference is correctly followed, as it can be noticed from Fig. 15; instead, Fig. 14 shows a worse response without the proposed method, with motor stops in various occasions. Motor starting is an essential issue for industrial applications and the test was performed at first with a linear torque load. Speed profile is shown in Fig. 15; only measured speed is reported, being speed error negligible. As aforementioned, initial angle at standstill is unknown, therefore in some occasions motor can start moving in the opposite

way, as it can be noticed from negative speed spikes in Fig. 16 (red circles). Nevertheless, observing electrical angle plotting enlargement during the worst situation in Fig. 17, about one electrical radian movement (which corresponds to about 15 mechanical degree) is performed in wrong direction and then speed reference is correctly followed. A motor starting with about 90◦ initial error and stator resistance set at 2.5 the rated value is reported in Fig. 18; during first 200 ms starting is failing, then the proposed method intervenes, according to 6

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the reference speed values shown in Table 2, preventing efficaciously starting failure. The sensorless control was tested in the low speed region and compared with a traditional back-EMF. One has to note that setting the observer gains k1 and k2 to zero, a traditional back-EMF observer is obtained. Result for no-load condition (both with RFO and BackEMF control) for 1.9%, 3.8% and 5.7% of rated speed are reported in Fig. 19., whereas results for constant load with same speed reference are reported in Fig. 20. As it can be noticed from the results, the performance of a traditional back-EMF technique are significantly worse and speed cannot be commanded at very low speed. Constant load is defined in Eq. (12). Results with quadratic torque are reported in Fig. 21. Quadratic torque is defined in Eq. (13). Fig. 17. Electrical angle enlargement during motor starting.

𝑇[N

m]

= 𝑠𝑖𝑔𝑛(𝜔) ⋅ T𝑟𝑎𝑡𝑒𝑑[N

𝑇 [N m] =

m]

2.2 [N m] 2 𝜔 [rad∕s] 1802 [rad∕s]

(12)

(13)

Along with linear, quadratic and constant torque, compressor torque is a typical industrial load; therefore the second test bench (i.e. the motor coupled to the air compressor) was used. Speed profile during motor starting is shown in Fig. 22. The proposed algorithm allows motor starting despite the critical load. The critical issue is that the compressor is characterized by high and irregular torque at zero speed, as it can be noted from Iq plotting in Fig. 23. Moreover, in this configuration, motor is overloaded (indeed rated Iq is 3.1 A), which is an additional demanding condition. Being the torque irregular, a significant speed ripple occurs. In order to verify sensorless control effectiveness, it is interesting to investigate if the speed ripple is caused by a reduction of bandwidth caused by the sensorless algorithm or if the motor has the same ripple also in sensored mode. Speed ripple was evaluated at relatively low speed (50 rad/s).

Fig. 18. Speed during starting failure avoidance technique intervention.

Fig. 19. Reference and measured speed with no-load. RFO (left), Back-EMF (right).

Fig. 20. Reference and measured speed with constant torque. RFO (left), Back-EMF (right).

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Fig. 21. Reference and measured speed with quadratic torque. Fig. 24. Measured speed in sensored mode with compressor-load.

Fig. 25. Id and Iq in sensored mode with compressor-load.

Fig. 22. Reference and estimated and measured speed, motor starting with compressor-load.

Fig. 26. Measured speed in sensorless mode with compressor load. Fig. 23. Id and Iq, motor starting with compressor-load.

In order to reduce speed ripple Iq proportional gain must be increased, compatibly with system stability; it was set at 0.8 in sensorless mode at low speed (as reported in Table 1). In sensored mode it was possible to increase proportional gain at 0.8 also during transient, but in steady state 0.8 was the optimal value too (i.e. the maximum value until which ripple decreases and for which the system keeps stable). In Figs. 24 and 25 speed and currents in sensored mode are plotted, whereas in Figs. 26 and 27 same quantities are plotted in sensorless operation. As it can be noticed from the reported results, speed ripple remains almost constant moving from sensored to sensorless mode and there are not significant changes in axis currents. All in all, even if sensored mode shows advantages during transients, steady state improvements are negligible.

Fig. 27. Id and Iq in sensorless mode with compressor load.

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Fig. 28. Id and Iq in sensorless mode with compressor load.

References

One of the main critical issues of sensorless algorithms is the sensitiveness towards motor parameter variations. Since the algorithm proposed in this paper has an online estimation of flux linkage, this parameter is not critical and only an approximated value should be given to 𝜓̂ 𝑚 . Analogously, the control is low sensitive to stator resistance (an error of about 50% is highly tolerable). The most critical parameter is the stator inductance; for this reason a sensitiveness analysis for this parameter was carried out. In Fig. 28, for six different working conditions and for both motors, the range of inductance values for which the control can properly work is shown by the gray bar. As it can be noticed from the plot, the maximum allowed error for which the motor can operate properly is always above 9%. Indeed the most critical operating condition is the starting of 27 N m motor at 10 rad/s with no-load. All the other working conditions have a significantly higher robustness towards inductance change.

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5. Conclusions In this paper a sensorless algorithm, working both in the low and high speed region, was presented. The algorithm is based on a rotor flux observer and no voltage injection is required. Improvements with respect to the algorithm available in literature are shown and experimental results prove their effectiveness. These improvements regard performance increase during transients from high to low speed and starting failure avoidance. Various tests have been performed in different working condition and with different test bench set up. No-load linear torque, quadratic torque, constant torque and compressor-load torque were considered, which are the typical load of industrial applications. Motor starting was possible with all type of torque and the motor can work with a reference speed from about 2% to 100% of rated speed. Moreover no significant differences in terms of speed ripple in steady state were noticed comparing sensorless operations with sensored ones. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. 9

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