Research Article Sensorless Speed Control of Permanent Magnet … · 2019. 7. 31. · Section introduces system description including PMSM modeling, neural network with LMS compensation

Research ArticleSensorless Speed Control of Permanent Magnet SynchronousMotors by Neural Network Algorithm

Ming-Shyan Wang, Ika Noer Syamsiana, and Feng-Chi Lin

Department of Electrical Engineering, Southern Taiwan University of Science and Technology, 1 Nan-Tai Street, Yung Kang District,Tainan City 710, Taiwan

Correspondence should be addressed to Ming-Shyan Wang; [email protected]

Received 20 August 2014; Accepted 8 September 2014; Published 25 September 2014

Academic Editor: Stephen D. Prior

Copyright © 2014 Ming-Shyan Wang et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

The slidingmode control has the merits with respect to the variation of the disturbance and robustness. In this paper, the sensorlesssliding-mode observer with least mean squared error approach for permanent magnet synchronous motor (PMSM) to detect therotor position by counter electromotive force and then compute motor speed is designed and implemented. In addition, the neuralnetwork control is also used to compensate the PI gain tuning to increase the speed accuracy without regarding the errors of thecurrent measurement and motor noise. In this paper, a digital signal processor TMS320F2812 utilizes its high-speed ADC moduleto get current feedback information and thus to estimate the rotor position and takes advantage of the built-in modules to achieveSVPWMcurrent control so that the senseless speed control will be accomplished.The correctness and effectiveness of the proposedcontrol system will be verified from the experimental results.

1. Introduction

Nowadays, the permanent magnet synchronous motor(PMSM) is more widely applied than before in the servocontrol systems. For servo control systems, their excellentperformance comes from using position sensors for feedbackcontrol. However, the disadvantages of shaft sensors limit theapplications, such as system cost increasing, motor size, andreliability decreasing in applications such as air conditionercompressors, where the environment is highly humid andhot. As a result, extensive research has been conducted onovercoming these difficulties by eliminating the positionsensors in servomotor systems [1].

Two kinds of sensorless control methods are popularlyused in servo control systems, fundamental model basedmethod and saliency based method. Fundamental modelbased method uses observers, such as back electromotiveforce (EMF) observer and flux linkage observer, to estimatethe rotor position. Meanwhile, the saliency based methodconsists of continuous signal injection and transient voltagevector injection [2]. Some authors proposed to estimate speed

and position of PMSM by back-EMF or flux linkage butit is hard at low speed operation and standstill becauseback EMF amplitude is approaching zero. Other referencescompared several methods and recommended continuoussignal injection method for low operating speed because ofits simple hardware configuration.However, the torque rippleand acoustic noise by continuous signal injection are largerthan other methods.

A flux linkage estimation method [3] is developed byfirst measuring the stator line-to-line voltages and statorphase current to obtain the back EMF space vector. Thisvector in turn is used to yield the angle of the flux linkagevector. However, it is affected by integrator drift in low speedand its accuracy is highly sensitive to parameter variation.Another observer basedmethod [4] is presented that removesthe dependency on mechanical parameters; however thereis still the need for an electrical model of the machine.The tracking control problem is addressed for a sensorlessPMSM with unknown constant load torque. Assuming thatonly stator currents and voltages are available for feedback,a novel sixth order nonlinear adaptive control algorithm is

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014, Article ID 321892, 7 pageshttp://dx.doi.org/10.1155/2014/321892

2 Mathematical Problems in Engineering

designed for the PMSM [5]. However, the proposed controlalgorithm is tested just by simulation. A high-speed sliding-mode observer [6] is proposed for PMSM, which estimatesthe rotor position and the angular velocity from the backEMF. Carrier-signal-injection-based control methods [7] areproposed for sensorless control. Fundamental pulse widthmodulation excitation is used to improve sensorless controlof a permanent magnet machine [8]. No additional signalinjection or separate test vectors are required. However,modification is needed when narrow PWM voltage vectorsoccur.

Recently, artificial neural networks (ANNs) haveattracted much attention to their possible use in a widerange of engineering applications like power electronics ormotor drives [9–15]. The use of ANNs is motivated by theiruseful features, like having a parallel distributed architecture,being able to identify nonlinear system dynamics, andhaving the ability to learn, generalize, and adapt. All of thesefeatures justify the use of ANNs for motor drive applications,including sensorless control.

This paper presents a neural network based approach tothe sensorless control of the PMSM.The basic premise of themethod is that an ANN provides a very efficient mappingstructure for the nonlinear PMSM. By measuring the phasecurrents and applying them as inputs to the estimator by leastmean squares, the rotor angle is estimated, thereby facilitatingthe elimination of the rotor position sensor. AnNNwith backpropagation algorithm is considered to compensate the PIgains for speed control.

The paper is organized as follows for further discussion.Section 2 introduces system description including PMSMmodeling, neural network with LMS compensation for rotorangle estimation, and speed control by ANN. Section 3consists of simulation by Matlab/Simulink and experiments.Finally, a conclusion is given in Section 4.

2. Servo System Design

There are three parts for the proposed servo control systemdesign, PMSMmodeling, sliding-mode observer (SMO)withLMS approach, and PI speed control compensated by neuralnetworks.

2.1. PMSM Modeling. By Park and Clarke transformations,the voltage equations of PMSM from the stationary a-b-cframe to the 𝛼-𝛽 frame and the rotating d-q frame will begiven as [9–15]

[

V𝛼

V𝛽

] =[

[

[

𝑅𝑠+

𝑑

𝑑𝑡

𝐿𝑠

0

0 𝑅𝑠+

𝑑

𝑑𝑡

𝐿𝑠

]

]

]

[

𝑖𝛼

𝑖𝛽

] + [

𝑒𝛼

𝑒𝛽

] ,

[

V𝑑

V𝑞

] =[

[

[

𝑅𝑠+

𝑑

𝑑𝑡

𝐿𝑠

−𝜔𝑟𝐿𝑠

𝜔𝑟𝐿𝑠

𝑅𝑠+

𝑑

𝑑𝑡

𝐿𝑠

]

]

]

[

𝑖𝑑

𝑖𝑞

] + [

0

𝜔𝑟𝜆𝑓

] ,

(1)

where V𝑑, V𝑞are d- and q-axis voltages; 𝑖

𝑑, 𝑖𝑞are d- and q-axis

currents; 𝜆𝑓is flux linkage due to the permanent magnets;

𝜔𝑟is the electric speed; and 𝑅

𝑠and 𝐿

𝑠are the resistance and

inductance. The 𝛼- and 𝛽-axis back EMFs are given as

𝑒𝛼= −𝜆𝑓𝜔𝑟sin 𝜃,

𝑒𝛽= 𝜆𝑓𝜔𝑟cos 𝜃.

(2)

The use of the Park transformation implies using therotor position. However, the actual rotor position is notknown in a sensorless application and needs to be estimated.Figure 1 shows the block diagramof sensorless PMSMcontrolsystem, which will be simulated by Matlab/Simulink andexperimented to verify the design.

2.2. Sliding-Mode Observer with LMS Approach. Controlsystems with sliding-mode control (SMC) may have betterperformance of smaller settling time, less or no overshoot,and faster tracking ability. In addition, sliding-mode observer(SMO) can provide information of rotor position and speedestimation. The dynamic equations of SMO are given asfollows:

𝑑

𝑑𝑡

��𝛼= −

𝑅𝑠

𝐿𝑠

��𝛼+

1

𝐿𝑠

]𝛼−

1

𝐿𝑠

𝑘 ∗ (��𝛼− 𝑖𝛼) ,

𝑑

𝑑𝑡

��𝛽= −

𝑅𝑠

𝐿𝑠

��𝛽+

1

𝐿𝑠

]𝛽−

1

𝐿𝑠

𝑘 ∗ (��𝛽− 𝑖𝛽) ,

(3)

where ��𝛼and ��𝛽are the estimated variables of 𝑖

𝛼and 𝑖𝛽and 𝑘

is observer gain. The sliding vector for the system is

𝑆𝑛= [𝑠𝛼, 𝑠𝛽]

𝑇

= [��𝛼− 𝑖𝛼, ��𝛽− 𝑖𝛽]

𝑇

, (4)

and the defined Lyapunov function is

𝑉 =

1

2

𝑆𝑇

𝑛𝑆𝑛=

1

2

(𝑠2

𝛼+ 𝑠2

𝛽) . (5)

The observer gain 𝑘 will be designed to satisfy Lyapunov’sstability theorem, �� < 0, as the system trajectory approachesto the sliding hyperplane, 𝑆

𝑛= 0. As a result, we have

𝑒𝛼= 𝑘 ∗ 𝑖

𝛼,

𝑒𝛽= 𝑘 ∗ 𝑖

𝛽

(6)

and the estimated rotor angle is

𝜃 = −tan−1 (

𝑒𝛼

𝑒𝛽

) . (7)

In order to compensate the rotor position estimationerror due to the process of motor speed tracking and noise,an adaptive linear element neural network (NN) structureshown in Figure 2 with least mean square approach isadopted. Artificial NNs are similar to biological NNs inthe sense that they are based on the same principle ofoperation based on highly parallel structure and acquiringknowledge through a learning process [16]. The buildingblocks of an ANN are simple computational nodes, called

Mathematical Problems in Engineering 3

NN

PI

PI

PI

i∗d

i∗q

id

iq

i

− −

−

∗𝜔

+

+

+

��V∗d

V∗q

Rotation/stationary

rotation

ADC

conversionStationary

PARK

Inverse PARK Inverse CLARK

SVPWM Inverter PMSM

Slidingmode

observerwith LMS

CLARKI𝛼 Iu

Iv

IwI𝛽

V∗𝛼

V∗𝛽

V∗u

V∗v

V∗w

��

3𝜙 → 2𝜙

2𝜙 → 3𝜙

Figure 1: Block diagram of the proposed control system.

neurons. They are connected into a network structure byweighted connections, much like the synaptic connectionsin the human brain. Although the components of an NNare simple and few, the structure and type of these networksvary greatly, determined by the ever increasing interest in thisresearch field.

In Figure 2, 𝑥1, 𝑥2, . . . , 𝑥

𝑛are input variables,

𝑤𝑘1, 𝑤𝑘2, . . . , 𝑤

𝑘𝑛are weights, 𝑏

𝑘is the bias, Δ𝑒 =

(𝑒1+ 𝑒2+ 𝑒3+ ⋅ ⋅ ⋅ + 𝑒

𝑛)/𝑛 is averaged error, and 𝑑(𝑘) is

the reference angle from the speed command, respectively.If the estimated error at time instant 𝑘 is e(k), by LMSapproach, we have the follow equations [9–16]:

𝜕𝑒2

(𝑘)

𝜕𝑤1,𝑗

= 2𝑒 (𝑘)

𝜕𝑒 (𝑘)

𝜕𝑤1,𝑗

𝑗 = 1, 2, . . . , 𝑛,

𝜕𝑒2

(𝑘)

𝜕𝑏𝑘

= 2𝑒 (𝑘)

𝜕𝑒 (𝑘)

𝜕𝑏𝑘

,

𝑤 (𝑘 + 1) − 𝑤 (𝑘) = Δ𝑤 = 2𝛼𝑒 (𝑘) 𝑥𝑛(𝑘) ,

𝑏 (𝑘 + 1) − 𝑏 (𝑘) = Δ𝑏 = 2𝛼𝑒 (𝑘) ,

𝑤 (𝑘 + 1) = 𝑤 (𝑘) + 2𝛼𝑒 (𝑘) 𝑥𝑛(𝑘) ,

𝑏 (𝑘 + 1) = 𝑏 (𝑘) + 2𝛼𝑒 (𝑘) , (8)

where 𝛼 is the learning rate.

wk2

wknxn

x2

x1

yk

ELMS algorithm

−+

+∑...

...

wk1bk

Δe

d(k)

Figure 2: Structure of adaptive linear element neural network.

2.3. PI Speed Control Compensated by Neural Networks. Theproportional-integral (PI) control is first considered in thesystem,

𝐺𝑠(𝑠) = 𝐾

𝑠𝑝+

𝐾𝑠𝑖

𝑠

, (9)

where 𝐾𝑠𝑝

and 𝐾𝑠𝑖are the proportional gain and integral

gain, respectively. PI controller is widely used in the industrialapplications. However, it cannot cope with the load variationor parameter variation well. In the paper, the ANN withback propagation algorithm is utilized to compensate the PIcontrol quantity as shown in Figure 1.


1

2

3

4

0

5

6

7

00 0.10.1 0.20.2 0.30.3 0.40.4 0.50.5 0.60.6 0.70.7 0.80.8 0.90.9 11

Figure 3: The estimated rotor angle with SMO at speed of 100 rpmby simulation.

00 0.10.1 0.20.2 0.30.3 0.40.4 0.50.5 0.60.6 0.70.7 0.80.8 0.90.9 11

1

2

3

4

0

5

6

7

Figure 4:The estimated rotor angle with SMO and LMS at speed of100 rpm by simulation.

The output of the jth neuron at the 𝑛th layer is calculatedas

𝑦𝑛

𝑗= 𝑓 (net𝑛

𝑗) ,

net𝑛𝑗= ∑

𝑖

𝑤𝑛

𝑗𝑖𝑦𝑛−1

𝑖+ 𝑏𝑛

𝑗.

(10)

The error function is defined as

𝐸 =

1

2

∑

𝑘

(𝑑𝑘− 𝑦𝑘)

2

. (11)

The conjugated gradient method is considered to find theminimum value of the error function (11).

3. Simulation and Experimental Results

The system simulation is programmed by Matlab/Simulink.The parameters of PMSM 8CB75 are listed in Table 1.After training, the chosen topology that gives good per-formance with minimal resources is a 2-hidden-neuronstructure for the speed estimating neural network. Theactivation functions in the hidden layers of the networksare hyperbolic tangent sigmoid functions and those of theoutput layer are purely linear transfer functions. The val-ues of these weights are given as input layer to hiddenlayer weights: {837.4172, −126.4659}, hidden layer to outputlayer weights: {−0.614, 0.6713}, hidden neurons’ thresholds:{12.5996, 8.3947}, and output neuron’s threshold: 0.6560.Thefinal mean squared error of 3.83267 ∗ 10

−17 is reached

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (s)

0

50

100

150

200

250

300

350

400

Estim

atio

n po

sitio

n (d

eg)

Figure 5: The real estimated rotor angle with SMO at speed of100 rpm.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (s)

0

50

100

150

200

250

300

350

400

Estim

atio

n po

sitio

n (d

eg)

Figure 6: The real estimated rotor angle with SMO and LMS atspeed of 100 rpm.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

50

100

150

200

250

Figure 7: The speed response of 200 rpm without compensation bysimulation.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

50

100

150

200

250

Figure 8:The speed response of 200 rpmwith NN compensation bysimulation.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (s)

Spee

d (r

pm)

Spee

d (r

pm)

00

5050

100100

150150

200200

250250

(a)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (s)

Spee

d (r

pm)

Spee

d (r

pm)

00

5050

100100

150150

200200

250250

(b)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (s)

Spee

d (r

pm)

0

50

100

150

200

−50

(c)

Figure 9: The no-load speed responses of 200 rpm without (a) andwith NN compensation (b) and the speed errors (c) (blue for nocompensation).

after 20 training epochs for the neural networks. The gainconstants of PI control are 𝐾

𝑠𝑝= 1.2 and 𝐾

𝑠𝑖= 1.5,

respectively. These parameters are applied to the simulationand experimentation.

Figures 3 and 4 display the rotor angle estimation withSMO and with SMO plus LMS at the motor speed of100 rpm, respectively. It is easy to find the accuracy oflittle difference by simulation. However, for experimentation,the great difference between the estimated values can beshown in Figures 5 and 6. One of the reasons is lack ofestimation of initial rotor position, which is our next researchtopic. As a result, there are no complete triangle positionwaveforms from zero degree to 360 degrees in the figures. Inaddition, the step speed responses of 200 rpm without andwith NN compensation are depicted in Figures 7 and 8. Thelatter has better performance of less overshoot and settlingtime. For experimentation, the no-load speed responses of200 rpm without (a) and with NN compensation (b) and thespeed errors (c) (blue for no compensation) are displayed

Spee

d (r

pm)

Spee

d (r

pm)

00

5050

100100

150150

200200

250250

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (s)

(a)

Spee

d (r

pm)

0

50

100

150

200

250

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (s)

(b)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (s)

Spee

d (r

pm)

0

50

100

150

200

−50

(c)

Figure 10: The speed responses of 200 rpm without (a) and withNN compensation (b) and the speed errors (c) (blue for nocompensation) under loading of 1 kg disc.

in Figure 9. Simultaneously, the step speed responses of200 rpmwith 1 kg disc load are shown in Figure 10.The speedresponses without compensation display both the computingerrors and the noise during motor rotation. The one by NNcontrol has almost no overshoot, very short settling time, andzero steady-state error. The speed step responses of 100-150-100 rpm without (a) and with NN compensation (b) underloading of 1 kg disc are shown in Figure 11. The effectivenessof the proposed algorithm shows more clearly.

4. Conclusions

This paper proposes a sensorless control system for PMSMby presenting an approach based on neural networks tocompensate both the estimated position error and PI controlgains. The suggested method is useful for applications toreduce cost. The simulation and experimental results showthat the controlled system is capable of estimating rotor


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Time (s)

Spee

d (r

pm)

0

50

100

150

200

250

(a)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Spee

d (r

pm)

Time (s)

0

50

100

150

200

250

(b)

Figure 11: The speed responses of 100-150-100 rpm without (a) andwith NN compensation (b) under loading of 1 kg disc.

Table 1: Parameters of PMSM Sinano 8CB75.

Parameters Unit Value𝑃 W 750𝑉 V 149.4𝑇 N⋅m 2.931𝐼 A 3.4𝑁 Rpm 3000𝐾 N⋅m/A 0.776𝐽 Kg⋅cm2 2.449𝑅 Ω 3.27𝐿 mH 10.2

angle and motor speed within acceptable limits for manyapplications.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

The authors would like to express their appreciation toMinistry of Science and Technology, Taiwan, under Contractno. NSC 100-2632-E-218-001-MY3 and MOST 103-2221-E-218-033- for their financial support.

References

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[2] J. M. Liu and Z. Q. Zhu, “Novel sensorless control strategywith injection of high frequency pulsating carrier signal intostationary reference frame,” IEEE Transactions on IndustryApplications, vol. 50, no. 4, pp. 2574–2583, 2013.

[3] R. Wu and G. R. Slemon, “A permanent magnet motor drivewithout a shaft sensor,” IEEE Transactions on Industry Applica-tions, vol. 27, no. 5, pp. 1005–1011, 1991.

[4] T. D. Batzel and K. Y. Lee, “Starting method for sensorless oper-ation of slotless permanent magnet synchronous machines,”in Proceedings of the IEEE Power Engineering Society SummerMeeting, pp. 1243–1247, Alberta, Canada, 1999.

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Research Article Sensorless Speed Control of Permanent Magnet … · 2019. 7. 31. · Section introduces system description including PMSM modeling, neural network with LMS compensation