Sliding Mode Control Based DTC of Sensorless Parallel ... · PDF fileFive-Phase PMSM Drive System ... The resulting DTC-SVM approach substitutes the ... phase was done on induction

J Electr Eng Technol.2018; 13(?): 1921-718 http://doi.org/10.???/JEET.2018.13.2.1921

1921Copyright The Korean Institute of Electrical Engineers

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Sliding Mode Control Based DTC of Sensorless Parallel-Connected Two Five-Phase PMSM Drive System

Tounsi Kamel*, Djahbar Abdelkader*, Barkat Said**, M. Al-Hitmi*** and Atif Iqbal†

Abstract – This paper presents a sensorless direct torque control (DTC) combined with sliding mode approach (SM) and space vector modulation (SVM) to achieve mainly a high performance and reduce torque and flux ripples of a parallel-connected two five-phase permanent magnet synchronous machine (PMSM) drive system. In order to increase the proposed drive robustness and decrease its complexity and cost, the rotor speeds, rotor positions, fluxes as well as torques are estimated by using a sliding mode observer (SMO) scheme. The effectiveness of the proposed sliding mode observer in conjunction with the sliding mode control based DTC is confirmed through the application of different load torques for wide speed range operation. Comparison between sliding mode control and proportional integral (PI) control based DTC of the proposed two-motor drive is provided. The obtained speeds, torques and fluxes responses follow their references; even in low and reverse speed operations, load torques changes, and machines parameters variations. Simulation results confirm also that, the ripples of the torques and fluxes are reduced more than 3.33% and 16.66 %, respectively, and the speed overshoots and speed drops are reduced about 99.85% and 92.24%, respectively.

Keywords: Five-phase permanent magnet synchronous machine; Direct torque control; Sliding mode control; Sliding mode observer

1. Introduction

Recently, the use of high power semiconductor devices has opened the door to new scopes in electrical drives. The five-phase PMSM may be is one of the newest ideas in this field. This has led to an increasing interest in multiphase (greater than three phases) drives. Here and now, in some industrial applications such as high power ship propulsion, electric aircraft, electric traction, the use of this kind of drives is very suitable due to their tangible benefits over the conventional three-phase drives. Their advantages include reducing the amplitude of torque and current pulsations, increasing the frequency of torque pulsations, reducing the stator current per phase without increasing the stator voltage per phase, lowering the DC link current harmonics, higher reliability, and fault tolerance capability [1-3].

Different control algorithms of the PMSM were proposed in the literature [4-8]. Among all these control methods, the DTC is one of the effective control techniques adopted to control torque and flux linkage. The DTC is considered particularly interesting being less parameters dependency; making the system more robust, fast dynamic response,

and a pretty simple control [9]. Furthermore, the DTC avoids the need to the internal current loops, coordinate transformations, and the modulator block; hence the delay caused by current regulator is eliminated. It directly selects voltage vectors according to the error between the reference and the estimated values of the torque and flux [10]. However, the main disadvantages of using hysteresis controllers are: difficulty to control flux and torque at low speed, unfixed switching frequency which changes with rotor speed and load torque [9], a high sampling frequency needed for digital implementation of hysteresis controllers, and high torque ripple responsible for noises and vibrations generation [11]. In order to handle the above-mentioned problems, several researchers have proposed many approaches to overcome the drawbacks of the basic DTC. A space vector modulation was implemented to replace the switching table and provide a constant inverter switching frequency [12-13]. The resulting DTC-SVM approach substitutes the hysteresis controllers by two PI controllers to generate the direct and quadrature voltage components in synchronous frame. This scheme reduces torque and flux ripples as stated in [14-15].

However, some factors such as neglected dynamics, parameter variations, friction forces, and load disturbances are the main disturbances and uncertainties that can affect the effective functioning of the drive system. So, it will be very difficult to limit these disturbances effectively if linear control methods like PI controllers are adopted [11, 16]. To overcome this problems, especially to enhance stability and robustness of the DTC scheme other advanced

† Corresponding Author: Dept. of Electrical Engineering, Qatar University, Qatar. ([email protected])

* Dept. of Electrical Engineering, Chlef University, Algeria.([email protected], [email protected])

** Dept. of Electrical Engineering, M’sila University, Algeria. ([email protected])

*** Dept. of Electrical Engineering, Qatar University, Qatar ([email protected])

Received: January 20, 2016; Accepted: November 4, 2017

ISSN(Print) 1975-0102 ISSN(Online) 2093-7423

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1922 J Electr Eng Technol.2018; 13(2): 1921-718

methods have been proposed [4, 15, 17-18]. These approaches include among others the sliding mode control. The SMC is a nonlinear control method known to have robust control characteristics under restricted disturbance conditions or when there are limited internal parameter modeling errors as well as when there are some nonlinear behaviors [10, 11, 20-21]. The robustness of the SMC is guaranteed usually by using a switching control law. Unfortunately, this switching strategy often leads to a chattering phenomenon. In order to mitigate the chattering phenomenon, a common method is to use the smooth function instead of the switching function [16, 22-23].

The parallel/series-connected multi-machine systems fed by a single supply become strongly suggested due to the following benefits: low cost drive, compactness, and lightness [24-25]. In the series-connected system, both beginnings and ending of each phase should be brought out to the terminal box of each multiphase machine, these results in system complexity and poor efficiency due to higher losses. As a suitable alternative, the parallel connection of multiphase machines has been suggested in [26]. In multiphase machine there are more than direct and quadrature current components. Actually, to control the torque and flux of any multiphase only direct and quadrature current components are used, the remaining components can be used to control the others machines which are fed by a single multi-leg inverter [27].

It is well established that the PMSM can be efficiently controlled only if the position of the rotor is accurately known. Generally, the rotor position is obtained using some sensors types such as an optical encoder or resolver connected to the rotor shaft [24, 28]. However, the use of these sensors will increase the cost and reduce the reliability of the drive, and may suffer from some restrictions such as temperature, humidity, and vibration. These problems can be solved by using the well-known sensorless control technology. Various methods of sensorless control have been proposed by several researchers [29-31]. These estimation techniques are based mainly on the measurement of the machine currents and voltages. However, few applications deal with sensorless control of multiphase machines such as, model reference system [32], Kalman filtering technique [33] and sliding mode observer of five-phase PMSM [34,35]. Unlike the other approaches, the SMO is more attractive due to its robustness against the system parameters variations, disturbances, and noises [36]. This type of observer is based on the system model and the use of a high frequency switch to force the estimated variables trajectories to remain on the sliding surface. A low pass filter is used to reduce the chattering caused by sign function. However, the adding of this filter generates phase delay. Thus, the resulting SMO cannot improve the control in high performance applications [37]. Indeed, there were several researches that proposed another SMO as alternative to remove low-pass filter and phase delay in

[34, 36]. In conventional sensorless DTC scheme, one possible

solution is to combine a current observer and flux estimator [8, 12, 29] to perform the sensorless task, which increases the system complexity and reduce the accuracy of the estimation. To solve this problem, a SMO is proposed in this paper to improve the sensorless control of each five-phase PMSM by using its flux model in the stationary reference frame. Similar to the SMC, in the SMO algorithm the conventional switch function is replaced also by a smooth function to reduce the chattering phenomenon.

Most of the previous works on parallel connected multi-phase was done on induction motor drive systems using indirect vector control based on PI controllers to control each motor independently [24, 26]. However, the uncertainties and parameters disturbances can strongly influence the decoupling between the two motor [4]. In addition, all of these research works used sensors to measure the rotors positions, which increase the cost and the complexity of the system.

The purpose of this paper is to study a sensorless DTC sliding mode control scheme (DTC-SMC) equipped with a sliding mode observer for parallel connected two five-phase PMSMs fed by a single five-leg inverter. To obtain the desired characteristics, the SMC is implemented for speeds, fluxes and electromagnetic torques control and the SMO is used for sensorless operation purposes. The developed control scheme combines the features of the robust control and the robust estimation to enhance the performances of the proposed two-machine drive. So, the proposed nonlinear sensorless DTC-SMC based on SMO is attended to minimize the torque and stator flux ripples which are the main disadvantage of the classical DTC.

The performance of the estimation and control scheme is tested with challenging variations of the load torque and speed reference. The obtained results prove that the two machines are totally decoupled under large speeds and loads variations, although they are connected in parallel and supplied by a single inverter. In addition to that, a comparison between SMC, the traditional PI based DTC, and conventional DTC for sensorless operation is also provided.

2. Drive System Description and Modeling The two-machine drive system under consideration is

shown in Fig. 1. It consists of a five-leg inverter feeding two five-phase PMSMs. It can be seen from Fig. 1 that the phase transposition rules of parallel-connected two five-phase PMSMs system are as follows: as1-as2, bs1-cs2, cs1-es2, ds1-bs2, es1-ds2 [24]; where indices 1 and 2 identify the two machines as indicated in Fig. 1. According to this, the relationships between voltages and currents are given as:

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Tounsi Kamel, Djahbar Abdelkader, Barkat Said, M. Al-Hitmi and Atif Iqbal

http://www.jeet.or.kr 1923

Stator of PMSM1

Stator of PMSM2

Fig. 1. A parallel connected five-phase two-motor drive

1 2 1 2

1 2 1 2

1 2 1 2

1 2 1 2

1 2 1

;

inv inva aas as as asinv invb bbs cs bs csinv inv

abcde c cs es abcde c cs esinv inv

ds bs ds bsd dinv inves ds ese e

v iv v i iv iv v i i

v v v v i i i iv v i iv iv v i iv i

é ù é ù= +é ùê ú ê úê ú= +ê ú ê úê úê ú ê ú= = = = = +ê úê ú ê ú= +ê úê ú ê úê ú= +ê ú ê úë û

ë û ë û2ds

é ùê úê úê úê úê úë û

(1)

where , , , ,inv inv inv inv inva b c d ev v v v v and , , , ,inv inv inv inv inv

a b c d ei i i i i are the inverter voltages and currents, 1,2 1,2 1,2, , ,as bs csv v v 1,2 ,dsv

1,2esv and 1,2 1,2 1,2 1,2 1,2, , , ,as bs cs ds esi i i i i are the voltages and currents of the two machines.

The main five dimensional systems can be decomposed into five dimensional uncoupled subsystems (α-β-x-y-0). The correlation between the original phase variables and the new (α-β -x- y-0) variables is given by xyo abcdef Cfab = , where C is the following transformation matrix [24]:

1 cos(2 5) cos(4 5) cos(6 5) cos(8 5)0 sin(2 5) sin(4 5) sin(6 5) sin(8 5)

2[ ] 1 cos(6 5) cos(2 5) cos(8 5) cos(4 5)5 0 sin(6 5) sin(2 5) sin(8 5) sin(4 5)

1/ 2 1/ 2 1/ 2 1/ 2 1/ 2

C

p p p pp p p pp p p pp p p p

é ùê úê ú

= ê úê úê úë û

(2) By applying the transformation matrix (2) on equation

(1), the voltage and current components of the five-phase inverter become:

1 2

1 2

1 2

1 2

0

1 2

1 2

1 2

1

0

[ ] ,

0

[ ]

invs xsinvs ys

inv invx abcde xs sinv

ys syinv

invs xsinvs ys

inv invx abcde xs sinv

ysyinv

v v vv v vv C v v v

v vvv

i i ii i ii C i i i

i iii

a ab b

a

b

a ab b

a

é ù =é ùê úê ú= -ê úê úê ú = = =ê úê ú

=ê úê úê úê ú ë ûê úë û

é ù +ê ú+ê ú

ê ú = = +ê ú

+ê úê úê úë û

20

sb

é ùê úê úê úê úê úë û

(3)

where Lsj, Llsj are the inductances in the rotating frame and rsj is the stator resistance; fjF is the magnet flux; jw and

jq are electrical speed and rotor position, respectively. Where 0, , , ,inv inv inv inv inv

x yv v v v va b and 0, , , ,inv inv inv inv invx yi i i i ia b

are the inverter voltages and currents in the α, β, x, y, 0 axes, respectively. , , ,sj sj xsj ysjv v v va b and , , ,sj sj xsj ysji i i ia b (j=1,2) are the stator voltages and currents in the α, β, x, y axes, respectively.

The model of each five-phase PMSM (j=1, 2) is presented in a rotating α-β -x-y frame is given as:

( sin( ) ) /

( cos( ) ) /

( ) /

( ) /

sjsj sj j fj j sj sj

sjsj sj j fj j sj sj

xsjsj xsj xsj lsj

ysjsj ysj ysj lsj

dir i v L

dtdi

r i v Ldt

dir i v L

dtdi

r i v Ldt

aa a

bb b

w q

w q

= - + F +

= - - F +

= - +

= - +

(4)

The stator flux linkage components of each machine are

given by:

sjsj sj sj

sjsj sj sj

xsjsj xsj xsj

ysjsj xsj xsj

dr i v

dtd

r i vdt

dr i v

dtd

r i vdt

aa a

bb b

F= - +

F=- +

F= - +

F= - +

(5)

where , , ,sj sj xsj ysja bF F F F are the flux linkage in the αβxy frame.

The torques equations for the first and the second machines are given by:

11

22

5( )

25

( )2

em s s s s

em xs ys ys xs

pT i i

pT i i

a b b a= F -F

= F -F (6)

where p1, p2 are the pole pairs.

The proposed sensorless DTC-SMC of the parallel-connected two five-phase permanent magnet synchronous machines is presented in Fig. 2, where the two main parts SMC and SMO are considered. The SMO has been proved being strong robust and accurate with a fast convergence and having a good estimation performance over full speed rang [34, 37]. The SMO is designed to estimate the rotor position, speed, torque and flux of each machine by using voltages and currents measurements. The actual speed, estimated speed and load torques are the inputs of the

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speeds SMCs to determine the torques references. The estimated flux and torque are processed in DTC-SMCs to obtain as outputs the α-β-x-y axes reference voltages components. These reference voltages become the input signals to the SVM blocks. The SVM transmits the gating signals to the five-leg inverter to drive the two five-phase PMSMs connected in parallel.

3. Sliding Mode Control The design of a sliding mode controller requires mainly

two stages. The first stage is choosing an appropriate sliding surface. The second stage is designing a control law, which will drive the state variables to the sliding surface and will keep them there.

3.1 Sliding surfaces choice

In order to prescribe the desired dynamic characteristics

of the controlled system, the following general form of sliding surface can be adopted [38].

1( ) ( ) ( )rdS x e xdt

l -= + (7)

with ( ) refe x x x= - , l is a positive coefficient, and r is the relative degree, which is the number of times required to differentiate the surface before the input appears explicitly. 3.2 Controller design

In order to drive the state variables to the sliding surface,

the following control law is adopted:

eqc dicu u u= + (8) The equivalent control eqcu is capable to keep the state

variables on the switching surface, once they reach it, and to achieve the desired performance under nominal model. It is derived as the solution of the following equation:

( ) ( ) 0S x S x= =& (9)

Switching Signals Slection

SVM

SVM

SMC

abcdeto

αβxySMO1

PMSM1

PMSM2

abcdeto

αβxy

SMC

SMO2

DTC-

SMC2

DTC-

SMC1

SVM of five-phase parallel-connected two-motor drive

Fig. 2. Sensorless DTC-SMC of a parallel-connected two five-phase PMSMs drive system

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The discontinuous control dicu is needed to assure the convergence of the system states to sliding surfaces in nite time, and it should be designed to eliminate the effect of any unpredictable perturbation. The discontinuous control input can be determined with the help of the following Lyapunov function candidate:

21 ( )2

V S x= (10)

The control stability is ensured under the following two

conditions: - The Lyapunov function V is positive definite. - The derivative of the Lyapunov function should be negative ( ) ( ) 0 ( )TV S x S x S= < "&& .

The so-called reaching stability condition . .

( 0)V S S= < is fulfilled using the following discontinuous control:

( ( ))dicu k sign S x= (11)

where k is a control gain.

In order to reduce the chattering phenomenon, a saturation function instead of the switching one can be used. The saturation function is expressed as follows:

sgn( ( )) ( )

( ( )) ( ) ( )

S x if S xsat S x S x if S x

d

dd

ì >ï= í<ïî

(12)

with d is the boundary layer width.

4. Sliding Mode Control of the Five-Phase Two-

Machine Drive

4.1 Speed SMC design The sliding mode speed controller for each five-phase

PMSM is designed by selecting the suitable sliding surfaces ( )jS W . Since the relative degree is one, the following sliding surfaces are adopted:

( ) , 1, 2j refj jS jW = W -W = (13)

By taking the derivative of the sliding surfaces given by

(13) with respect to time and using the machines motion equations, it yields:

1

2

1 1 1 11 1 1

1 1 1

2 2 2 22 2 2

2 2 2

5( )

25

( )2

f lref qs

f lref ys

p T fS iJ J J

p T fS iJ J J

F WW = W - + +

F WW = W - + +

& &

& & (14)

where , andj j ljJ f T are the moment of inertia, damping

coefficient, and load torque of each machine, respectively. The currents controls 1qsi and 2ysi are defined by:

1 1 1

2 2 2

qs qseqc qsdic

ys yseqc ysdic

i i ii i i

= += + (15)

where:

1 1 1 1 11 1 1 1

1 1

2 2 2 2 22 2 2 2

2 2

, and ( ( ))52

, and ( ( ))52

ref lqseqc qsdic

f

ref lyseqc ysdic

f

J T fi i k sat S

p

J T fi i k sat S

p

W

W

W + + W= - = W

F

W + + W= - = W

F

&

&

1kW and 2kW are positive constants. The reference torques are computed as:

11 1 1

22 2 2

52

52

emref f qs

emref f ys

pT i

pT i

= F

= F (16)

4.2 Stability analysis

During the convergence mode, the condition ( ) ( ) ( ) 0 ( ( ))TV x S x S x S x= < "&& must be verified. Indeed,

by replacing (15) into (14), one gets:

1

2

11 1 1

1

22 2 2

2

5( ) ( ) 0

25

( ) ( ) 02

fT

fT

pV S k sat

Jp

V S k satJ

W

W

FW = - W <

FW = - W <

&

& (17)

From (17) the derivatives are negative, which means that

the stability condition is ensured.

4.3 Torques and fluxes SMCs design The DTC-SMC is designed to generate the stator voltage

command from the torque and flux errors to track the electromagnetic torque and flux by controlling the input voltage of the motor.

The electromagnetic torque and stator flux linkage squared are given by:

2 2 2

5( )

2j

emj sj sj sj sj

sj sj sj

pT i ia b b a

a b

= F -F

F = F +F (18)

The control objectives are to track the desired torques

and fluxes trajectories. So, the sliding surfaces can be

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calculated as follows:

*

*2 2

( )( )

emj emj emj

sjsj sj

T T S TS

Sé ù- é ùê ú= = ê úFF +Fê ú ë ûë û

(19)

Using (4) and (5), the time derivative of (19) can be

rewritten as:

1 2 2 1

1 1 2 2

2 12 1 1

21 2

5 5( ) ( sin( )) ( cos( ))2 2

( ) 2 2

5 5( ) ( )

2 2

2 2

j jemj sj h s j fj j h s sj h s j fj j h s

sj sj h s h s sj h sj h s

j h sj j h sh s h s h s

sj sjh s

h s h s

p pS T r i r iS r i r i

p pi i v

L Lv

w q w q- -é ùé ù - F F + F Fê úê ú = ê úê úF - F - Fë û ê úë û

- F -é ùF- - é ùê ú

+ ê úê úë ûê ú- F - Fë û

&

&

(20)

with h1=α, x and h2=β, y. So, the equation (20) can be expressed in the following

matrix form:

S F DU= +& (21)

with:

( )( )

emj

sj

S TS

S

é ù= ê ú

Fê úë û

&&

&

1 2 2 1

1 1 2 2

5 5( sin( )) ( cos( ))

2 22 2

j jsj h s j fj j h s sj h s j fj j h s

sj h s h s sj h s h s

p pr i r iF

r i r i

w q w q- -é ù

- F F + F Fê ú= ê ú- F - Fê úë û

2 12 1

1 2

1

2

5 5( ) ( )

2 22 2

j jh s h sh s h s

sj sj

h s h s

h s

h s

p pi i

D L L

vU

v

- -é ùF F- -ê ú= ê ú

ê ú- F - Fë ûé ù= ê úë û

So, it is possible to choose the control laws for stator

voltages as follows:

1 1 1

2 2 2

h s h seqc h sdic

h s h seqc h sdic

v v vv v v

= += + (22)

where

1 1 1

2 2

FF

h seqc

h seqc

vD

v-é ù é ù= -ê ú ê úë ûë û

11

2

k sat(T )k sat( )

Temj emjh sdic

h sdic j sj

vD

v-

F

é ùé ù = - ê úê ú Fë û ë û

with kTemj, k sjF are positive gains.

4.4 Stability analysis During the convergence mode, the condition ( )V x =& ( ) ( ) 0 ( ( ))TS x S x S x< "& must be verified. Indeed, by

replacing (22) into (21), one gets:

k (T )

( ) 0sat( )j

sj

Tem emjT

sj

satV S S

k F

é ù= - <ê úFê úë û

& (23)

From (23) it is obvious that the system is globally stable,

S and S& will be forced to zero in a definite period, which also means that the torque and flux of the five-phase PMSM will follow their reference values.

5. SVM Technique Based DTC-SMC Hysteresis controllers used in the conventional DTC

generate a variable switching frequency, causing electro-magnetic torque ripples [2, 15]. In order to overcome this problem, the adopted solution consists in replacing the hysteresis controllers and the switching table by two SMC controllers and a space vector modulator.

The five-phase inverter has totally thirty-two space voltage vectors, thirty non-zero voltage vectors and two zero voltage vectors. Each voltage vector can be mapped by (24) onto the α-β subspace and x-y subspace as shown in

9v 16v 25v26v

29v24v

20v13v

10v

22v

5v11v 18v

21v27v

1v23v

2v

15v

4v30v 8v

6v

7v

3v 19v

17v

28v12v

14v

v b

v a

0v

31v

6v 16v 22v19v

30v18v

24v14v

3v

25v12v

7v 17v28v

23v

4v29v

1v

15v

8v27v 2v

9v

13v

5v 21v

20v

26v10v

11v

xv

yv

0v

31v

Fig. 3. Space vectors of a five-phase inverter in two 2-D

subspaces

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Fig. 3. [27]:

2 3 4

2 4 6 8

2 ( )52 ( )5

inv inv inv j inv j inv j inv ja b c d e

inv inv inv j inv j inv j inv jxy a b c d e

v v v e v e v e v e

v v v e v e v e v e

a a a aab

a a a a

= + + + +

= + + + + (24)

where 2

5pa = .

From Fig. 3 the space vectors are divided into three groups in accordance with their magnitudes: small, medium and large space vector groups. The magnitudes are identified with indices s, m, and l, and are given as:

( ) 4 5cos 2 5s dcV vp= , 2 5m dcV v= , and ( ) 4 5cos 5l dcV vp= , respectively [27, 39]. It can be

observed from Fig. 3 that medium length space vectors of the α-β plane are mapped into medium length vectors in the x-y plane, and large vectors of the α-β plane are mapped into small vectors in the x-y plane, and vice-versa.

The reference voltage can be obtained by averaging a certain number of active space vectors for adequate time intervals, without saturating the VSI. Four active space vectors are required to reconstruct the reference voltage vector [27, 40].

6. Sliding Mode Observer Based Speed Estimator for Parallel-Connected Two-Motor Drive

Normally, speed observers used for three-phase machines

can be easily extended to multi-phase multi-machine drives. For each machine the speed estimator requires only stator voltages and currents components. In the five-phase PMSM control case, α, β, x, y currents and voltages are measured.

In this section, a sliding mode observer based on flux model is presented to estimate directly the flux and speed as well as the electromagnetic torque by using stator voltages and currents as inputs. Using the flux model of the five-phase PMSM and based on the sliding-mode variable structure theory, the proposed sliding mode observer for each five-phase PMSM is designed as:

ˆ

ˆˆ( / ) cos( ) ( )

ˆˆˆ( / ) sin( ) ( )

ˆˆ( / ) ( )

ˆˆ( / ) ( )

ˆ 52

sjsj sj sj sj sj fj j sj

sjsj sj sj sj sj fj j sj

xsjxsj sj lsj xsj xsj

ysjysj sj lsj ysj ysj

j j

dv r L r ksat

dtd

v r L r ksatdt

dv r L ksat

dtd

v r L ksatdt

d pdt J

aa a a

bb b b

q

q

F= - F + F + F

F= - F - F + F

F= - F + F

F= - F + F

W= ˆ ˆˆ ˆ( )[ cos( ) sin( )]fj

sj j sj jj sjL b aq qF

F -F

1 11ˆ ( ) ( )lj sj sj

j j

f T k sat k satJ J a b- W- + F + F

ˆˆj

jddtq

= W (25)

with ˆ

sj sj sja a aF = F -F , ˆsj sj sjb b bF = F -F , xsjF =

ˆxsj xsjF -F and ˆ

sj ysj ysjbF = F -F are the sliding surfaces, and k, k1 are the observer gains. ˆ ˆ ˆ ˆ

sj sj xsj ysja bF F F F are the estimated stator flux linkage components. ˆ

jW and ˆjq are

the estimated mechanical speed and rotor position, respectively.

The actual flux components can be obtained from:

ˆcos( )ˆsin( )

sj sj sj fj j

sj sj sj fj j

xsj lsj xsj

ysj lsj xsj

L i

L iL iL i

a a

b b

q

q

F = +F

F = +FF =F =

(26)

6.1 Stability analysis

The estimation errors dynamics are:

( / )

ˆ( / ) (cos( ) cos( )) ( )

( / )

ˆ( / ) (sin( ) sin( )) ( )

( / ) ( )

( / ) ( )

sjsj sj sj

sj sj fj j j sj

sjsj sj sj

sj sj fj j j sj

xsjsj lsj xsj xsj

ysjsj lsj ysj ysj

j

dr L

dtr L ksat

dr L

dtr L ksat

dr L ksat

dtd

r L ksatdt

dd

aa

a

bb

b

q q

q q

F= - F

+ F - - F

F= - F

+ F - - F

F= - F - F

F= - F - F

W

1 1

5 ˆˆ( ) [ cos( ) cos( ))2

ˆˆ( sin( ) sin( ))]1ˆ ( ) ( )

j fjsj j sj j

j sj

sj j sj j

lj sj sjj j

pt J L

f T k sat k satJ J

b b

a a

a b

q q

q q

F= F -F

- F -F

- W- - F - F

jj

ddtq

= W (27)

with ˆ

j j jW = W -W and ˆj j jq q q= - .

In order to demonstrate the stability of the proposed sliding mode observer, the following Lyapunov function candidate is adopted:

2 2 2 2 2 21 ( )2 sj sj xsj ysj j jV a b q= F +F +F +F +W + (28)

Its time derivative is:

Proofreading



. ..

... .

.2

2

2

ˆ( / ) ( / ) (cos( ) cos( ))

( ) ( / )ˆ( / ) (sin( ) sin( )) ( )

( / )

sj sjsj sj

xsj ysjxsj ysj

sj sj sj sj sj sj fj j j

sj sj sj sj sj

sj sj sj fj j j sj sj

sj lsj xsj

V

V r L r L

ksat r L

r L ksat

r L

a ba b

a a

a a b

b b b

q q

q q

q q

= F F +F F

+F F +F F +W W+

= - F +F F -

-F F - F

+F F - -F F

- F -2

( )

( / ) ( )5 ˆˆ( )[ cos( ) cos( ))2

1ˆˆ( sin( ) sin( ))]

xsj xsj

sj lsj ysj ysj ysj

j fjsj j sj j

j sj

sj j sj j j j lj j

ksat

r L ksatpJ L

f TJ J

b b

a a

q q

q q

F F

- F -F FF

F -F

- F -F W - W - W

1 1( ) ( ) 0j sj j sj j jk sat k sata b q-W F -W F +W < (29) To force the observer to converge to its sliding surfaces,

the observer gains must be chosen to fulfill the following conditions:

max

1 max max

2

2

s fjj

sj

fjj

j sj

rk p

L

k pJ L

F> W

F> F W

(30)

7. Simulation Results

In order to verify the feasibility of the proposed control

scheme for the two-machine drive system presented in Fig. 2, a series of simulations is performed using two identical five-phase PMSM. The parameters of each machine are listed in Table 1. The performance of the SMC controller is compared with that of the PI controller and conventional DTC. The tuning parameters for the SMC and SMO are also given in Table 2. The switching frequency of the five-phase inverter is set at 10 kHz.

Simulations results are obtained for both controllers under the same conditions (same DC-link voltage, same switching frequency). Different operation modes of the proposed multiphase drive have been presented such as no

load starting up, load torque application, speed direction reversing, low-speed operation and robustness test. In every test, speeds, estimation errors, torques, stator fluxes and their circular trajectories will be presented.

Case 1: Two motors operating in the same direction

Fig. 4 shows the operation of the two-machine drive

system for many different speeds references with no load at starting up phase. At steady state condition, the two machines are loaded simultaneously or not by their nominal loads. At the beginning, the first machine is running at 60 rad/s; at t=0.25 s, it is accelerated to 100 rad/s, after that, its direction of rotation is reversed to -80 rad/s at t=0.5 s and then to -40 at t=0.75 s. For the second machine the speed reference is set at 40 rad/s, 80 rad/s, -100 rad/s, and -60 rad/s at t=0 s, 0.25 s, 0.5 s, 0.75 s, respectively. From Figs. 4(a), it can be seen that using DTC-SMC approach the two machines reach their speed references rapidly at starting phase without overshoots compared to the DTC-PI and conventional DTC approach. The load variations have not any tangible effects on the speeds responses contrary to DTC-PI and conventional DTC where drops and rises are observed during the same variations instants. Furthermore, faster dynamic and better reference tracking during the speed reversing operation are observed when the proposed DTC-SMC is used.

The estimations errors are illustrated in Figs. 4(b). From these figures, the speed estimation errors converge toward zero in steady state, which means that the SMO shows good speed estimation, and the load does not have a significant effect on the tracking performance. Indeed, the maximum speeds estimation errors in DTC-SMC scheme are less than 0.08% (Fig. 4(b) (DTC-SMC)), but for the DTC-PI and conventional DTC schemes, they are less than 0.11%, Fig. 4(b) (DTC-PI) with noticeable ripples in case of conventional DTC.

The electromagnetic torques, generated by the two machines during the simulated speed step response, are shown in Figs. 4(c). Compared to DTC-PI and conventional DTC controllers, the proposed DTC-SMC controller shows a significant improvement in torque response time as well as in the overshoots and undershoots magnitudes. It can also be seen that DTC-SMC has a better dynamic and faster torque response during the startup and direction reversing states. In addition, it can be seen that the torque ripple in conventional DTC is greater than DTC-PI and DTC-CMC.

Figs. 4(d) show the stator flux magnitudes using the proposed DTC-SMC, DTC-PI, and conventional DTC, respectively. In case of DTC-SMC controller, it can be observed that the stator flux ripples in steady state are less than those obtained by DTC-PI and conventional DTC.

Figs. 4(e) describe the stator flux trajectories in αβ and xy plane. The αβ trajectories are almost circular but the xy trajectories are closed to zero. In these figures, it can be

Table 1. Five-phase PMSM parameters

pj Lsj fjF

Jj rsj fj srefjF

2 5.6mH 0.2444 Wb 0.00174 kg.m2 1.4 W 0 0.3 Wb

Table 2. SMC and SMO parameters

Speed controller

Torque controller

Flux controller SMC

4jkW = 9000Temjk = 9000jGF = SMO k=99000, k1=300

Proofreading



seen again that DTC-SMC controller offers the better and fast response without overshoot and less ripple compared to the DTC-PI and conventional DTC.

Case 2: Two motors operating in the opposite directions

The effect of the speed rotation reversion of one

machine on the other machine performance is investigated in Fig. 5. In the stating phase, the first machine is rotating

at +100 rad/s; the other is running at the opposite speed. After that

Ω1 is kept at standstill, while Ω2 is reversed from -100 to +100 rad/s at t=0.4 s, and it is returned to zero at t=0.6 s. At the subsequent test, the speed Ω2 is held at zero, while Ω1 is set at -100 rad/s at 0.7s.

Compared with DTC-PI and conventional DTC, the DTC-SMC shows again no overshoots and no significant influence of the load application. Furthermore the results

a

b

c

d

e

a

b

c

d

e

0 0.2 0.4 0.6 0.8 1-100

-50

0

50

100

Time (s)

Spee

ds (r

ad/s

)

W1W1estW1refW2W2estW2ref

0.01 0.02 0.03 0.040

20

40

60

0 0.2 0.4 0.6 0.8 1-0.1

-0.05

0

0.05

0.1

Time (s)

Spee

ds e

rror

(rad

/s)

estimation error1estimation error2

0 0.2 0.4 0.6 0.8 1-40

-20

0

20

40

Time (s)

Torq

ues

(N.m

)

Tem1Tem2

0.05 0.1 0.15

-1

0

1

0 0.2 0.4 0.6 0.8 1

-0.1

-0.05

0

0.05

Time (s)

Spee

ds e

rror

(rad

/s)


0 0.2 0.4 0.6 0.8 1-40

-20

0

20

40

Time (s)

Torq

ues

(N.m

)

Tem1Tem2

0.05 0.1 0.15

-1

0

1

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

Time (s)

Fs1

,2 (W

b)

Fs1Fs2

-0.4 -0.2 0 0.2 0.4-0.4

-0.2

0

0.2

0.4

Fa (Wb)

Fb (W

b)

Fab1

Fab2

Fxy 1,2

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

Time (s)

Fs1

,2 (W

b)

Fs1Fs2

-0.4 -0.2 0 0.2 0.4-0.4

-0.2

0

0.2

0.4

Fa (Wb)

Fb (W

b)

Fab1

Fab2

Fxy 1,2

0 0.2 0.4 0.6 0.8 1-0.1

-0.05

0

0.05

0.1

Time(s)

Spee

ds e

rror

(rad

/s)


-0.4 -0.2 0 0.2 0.4-0.4

-0.2

0

0.2

0.4

Fa (Wb)

Fb (

Wb)

Fab1

Fab2

21,Fxy

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

Time(s)

Fs F

s1,2

(Wb)

(Wb)

Fs1Fs2

0 0.2 0.4 0.6 0.8 1-150

-100

-50

0

50

100

Time(s)

Spee

ds (r

ad/s

)

W1West1W ref1W2West2W ref2

0 0.02 0.040

204060

0 0.2 0.4 0.6 0.8 1-40

-20

0

20

40

Time(s)To

rque

s (N

.m)

0.05 0.1 0.15

-202

Tem1Tem2

0 0.2 0.4 0.6 0.8 1-200

-100

0

100

200

Time (s)

Spee

ds (r

ad/s

)

0 0.02 0.040

20

40

60


a

b

c

d

e

(DTC-SMC) (DTC-PI) ( DTC-switching up-table)

Fig. 4. Dynamic responses of parallel-connected two five-phase PMSMs system controlled by SMC, PI based DTC, and conventional DTC and operating at different reference speeds values: (a) Reference, actual and estimated speeds, (b) Speed estimation errors, (c) Electromagnetic torques, (d) Stator fluxes magnitudes, (e) Stator fluxes trajectories

Proofreading



illustrated in Fig. 5 show once more that the control of the two machines is completely decoupled. Indeed, the speed of one machine and its electromagnetic torque remain completely undisturbed during the reversion of the other machine, indicating a complete decoupling of the control.

So, there is hardly any evidence of torque disturbance of one machine during the reversal of the other one. As shown from Figs. 5(a), the starting and reversing transients of one machine do not have any tangible consequence on the operation of the second machine. The decoupled control is

a

b

c

d

e

a

b

c

d

e

0 0.2 0.4 0.6 0.8 1-200

-100

0

100

200

Time (s)

Spee

ds (r

ad/s

)


0 0.2 0.4 0.6 0.8 1-40

-20

0

20

40

Time (s)

Torq

ues

(N.m

)

Tem1Tem2

0 0.2 0.4 0.6 0.8 1-100

-50

0

50

100

Time (s)

Spee

ds (r

ad/s

)


0 0.2 0.4 0.6 0.8 1-0.1

-0.05

0

0.05

0.1

Time (s)

Spee

ds e

rror

(rad

/s)


0 0.2 0.4 0.6 0.8 1

-20

-10

0

10

20

Time (s)

Torq

ues

(N.m

)

Tem1Tem2

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

Time (s)

Fs1

,2 (W

b)

F

s1F

s2

-0.4 -0.2 0 0.2 0.4-0.4

-0.2

0

0.2

0.4

Fa (Wb)

Fb (W

b)

Fab1

Fab2

Fxy 1,2

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

Time (s)

Fs1

,2 (W

b)

Fs1Fs2

-0.4 -0.2 0 0.2 0.4-0.4

-0.2

0

0.2

0.4

Fa (Wb)

Fb (W

b)

Fab1

Fab2

Fxy 1,2

0 0.2 0.4 0.6 0.8 1

-100

0

100

200

Time (s)

Spee

ds (r

ad/s

)


0 0.2 0.4 0.6 0.8 1-0.1

-0.05

0

0.05

0.1

Time(s)

Spee

ds e

rror

(rad

/s)

estimation error1

estimation error2

0 0.2 0.4 0.6 0.8 1-40

-20

0

20

40

Time(s)

Torq

ues

(N.m

)

Tem1

Tem2

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

Time(s)

Fs1

2(Wb)

Fs1Fs2

-0.4 -0.2 0 0.2 0.4-0.4

-0.2

0

0.2

0.4

Fa(Wb)

Fb (W

b)

Fab1

Fab2

2Fxy 1,

a

b

c

d

e

0 0.2 0.4 0.6 0.8 1-0.15

-0.1

-0.05

0

0.05

0.1

Time (s)

Spee

ds e

rror

(rad

/s)

estimation error1

estimation error2

(DTC-SMC) (DTC-PI) ( DTC-switching up-table)

Fig. 5. Dynamic responses of parallel-connected two five-phase PMSMs system controlled by SMC, PI based DTC, and conventional DTC: when the two motors are operating in the opposite directions: (a) Reference, actual and estimated speeds, (b) Speed estimation errors, (c) Electromagnetic torques, (d) Stator fluxes magnitudes, (e) Stator fluxes trajectories

Proofreading



preserved and the characteristics of both machines are unaffected.

Case 3: Operation at different loading conditions

Fig. 6 shows the performance of the two-machine drive

controlled by DTC-SMC, DTC-PI, and conventional DTC

controllers under load torques variations condition. The reference of the first speed is set at 100 rad/s, while the speed reference of the second machine is set at 50 rad/s. A set of load torques from 5 Nm to 2.5 Nm are applied on the two machines shafts in different times. It is clear from Fig. 6 that when one machine is either loaded or unloaded, the

a

b

c

d

e

a

b

c

d

e

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

Time (s)

Spee

ds (r

ad/s

)

W 1 W est1 W ref1 W 2 W est2 W ref2

0 0.2 0.4 0.6 0.8 1-0.04

-0.02

0

0.02

0.04

0.06

Time (s)

Spe

eds

erro

e (r

ad/s

)


0 0.2 0.4 0.6 0.8 1

0

5

10

15

20

Time (s)

Torq

ues

(N.m

)

Tem1Tem2

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

Time (s)

Spee

ds (r

ad/s

)


0 0.2 0.4 0.6 0.8 1-0.05

0

0.05

0.1

0.15

Time (s)

Spee

ds e

rror

(rad

/s)


0 0.2 0.4 0.6 0.8 1-10

0

10

20

30

40

Time (s)

Torq

ues

(N.m

)

Tem1Tem2

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

Time (s)

Fs1

,2 (W

b)

F

s1F

s2

-0.4 -0.2 0 0.2 0.4-0.4

-0.2

0

0.2

0.4

Fa (Wb)

Fb (W

b)

Fab1

Fab2

Fxy 1,2

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

Time (s)

Fs1

,2 (W

b)

Fs1Fs2

-0.4 -0.2 0 0.2 0.4-0.4

-0.2

0

0.2

0.4

Fa(Wb)

Fb (W

b)

Fab1

Fab2

Fxy 1,2

0 0.2 0.4 0.6 0.8 1-0.05

0

0.05

0.1

0.15

Time(s)

Spee

ds e

rror

(rad

/s)


0 0.2 0.4 0.6 0.8 1-10

0

10

20

30

Time(s)

Torq

ues

(N.m

)

Tem1Tem2

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

Time (s)

Fs1

2 (Wb)

Fs1Fs2

-0.4 -0.2 0 0.2 0.4-0.4

-0.2

0

0.2

0.4

Fa (Wb)

Fb (W

b)

Fxy1,2

Fab1

Fab2

0 0.2 0.4 0.6 0.8 10

20

40

60

80

100

120

Time(s)

Spee

ds(r

ad/s

)


a

b

c

d

e

(DTC-SMC) (DTC-PI) (DTC-switching up-table) Fig. 6. Dynamic responses of parallel-connected two five-phase PMSMs system controlled by SMC, PI based DTC ,and

conventional DTC and operating at different loading conditions: (a) Reference, actual and estimated speeds, (b) Speed estimation errors, (c) Electromagnetic torques, (d) Stator fluxes magnitudes, (e) Stator fluxes trajectories

Proofreading



second machine performance is unaffected; which proves once again that both motors connected in parallel are totally decoupled. In case of sliding mode control, no variation whatsoever can be observed in the speeds responses of the both machines during these transients. It is

worth noticing that there is no impact on the speed and electromagnetic torque of one machine when the speed or the load of the other machine in parallel-connected system changes. Thus, through proper phase transformation rules, the decoupled control of two five-phase PMSMs connected

a

b

c

d

e

a

b

c

d

e

0 0.2 0.4 0.6 0.8 1-10

-5

0

5

10

Time (s)

Spe

eds

(rad

/s)

W

1

West1

Wref1

W2

West2

Wref2

0 0.2 0.4 0.6 0.8 1-0.1

-0.05

0

0.05

0.1

Time (s)

Spe

eds

erro

r (r

ad/s

)

estimation error

1estimation error

2

0 0.2 0.4 0.6 0.8 1-10

-5

0

5

10

Time (s)

Spe

eds

(rad

/s)

W

1

West1

Wref1

W2

West2

Wref2

0 0.2 0.4 0.6 0.8 1-0.03

-0.02

-0.01

0

0.01

Time (s)

Spee

ds e

rror

(rad

/s)

estimation error

1estimation error

2

0 0.2 0.4 0.6 0.8 1-5

0

5

10

Time (s)

Torq

ues

(N.m

)

T

em1T

em2

0 0.2 0.4 0.6 0.8 1-20

-10

0

10

20

Time (s)

Torq

ues

(N.m

)

T

em1T

em2

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

Time (s)

Fs1

,2 (W

b)

Fs1

Fs2

-0.4 -0.2 0 0.2 0.4-0.4

-0.2

0

0.2

0.4

Fa (Wb)

Fb (W

b)

Fab1

Fab2

Fxy 1,2

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

Time (s)

Fs1

,2 (W

b)

Fs1

Fs2

-0.4 -0.2 0 0.2 0.4-0.4

-0.2

0

0.2

0.4

Fa (Wb)

Fb (W

b)

Fab1

Fab2

Fxy 1,2

0 0.2 0.4 0.6 0.8 1-10

-5

0

5

10

Time (s)

Spe

eds

(rad

/s)

W1

West1

Wref1

W2

West2

Wref2

0 0.2 0.4 0.6 0.8 1-0.03

-0.02

-0.01

0

0.01

Time(s)

Spe

eds

erro

r (r

ad/s

)

estimation error

1estimation error

2

0 0.2 0.4 0.6 0.8 1-5

0

5

10

Time(s)

Torq

ues

(N.m

)

T

em1T

em2

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

Time(s)

Fs1

2(Wb)

F

s1F

s2

-0.4 -0.2 0 0.2 0.4-0.4

-0.2

0

0.2

0.4

Fa (Wb)

Fb (W

b)

1,2Fxy

Fab1

Fab2

a

b

c

d

e

(DTC-SMC) (DTC-PI) DTC-switching up-table)

Fig. 7. Dynamic responses of parallel-connected two five-phase PMSMs system controlled by SMC, PI based DTC, and conventional DTC and operating at low speed conditions: (a) Reference, actual and estimated speeds, (b) Speed estimation errors, (c) Electromagnetic torques, (d) Stator fluxes magnitudes, (e) Stator fluxes trajectories

Proofreading



in parallel can be achieved with a single supply from a five-phase voltage source inverter. Furthermore, measured and estimated speeds are in excellent agreement in both steady state and transient operations.

Case 4: Low speed operation

Fig. 7 shows the performance of the senseorless feedback control under low speed condition. The speed reference of the first machine is set to 7 rad/s, -3 rad/s, 4

a

b

c

d

e

a

b

c

d

e

0 0.2 0.4 0.6 0.8 1-100

-50

0

50

100

Time (s)

Spe

eds

(rad

/s)

W

1W

est1W

ref1W

2W

est2W

ref2

0 0.2 0.4 0.6 0.8 1-0.1

-0.05

0

0.05

0.1

Time (s)

Spe

eds

erro

r (r

ad/s

)

estamation error

1estamation error

2

0 0.2 0.4 0.6 0.8 1-20

-10

0

10

20

30

Time (s)

Torq

ues

(N.m

)

T

em1T

em2

0 0.2 0.4 0.6 0.8 1-200

-100

0

100

200

Time (s)

Spe

eds

(rad

/s)

W

1W

est1W

ref1W

2W

est2W

ref2

0 0.2 0.4 0.6 0.8 1-0.15

-0.1

-0.05

0

0.05

0.1

Time (s)

Spe

eds

erro

r (r

ad/s

)

estimation error

1estimation error

2

0 0.2 0.4 0.6 0.8 1-40

-20

0

20

40

Time (s)

Torq

ues

(N.m

)

T

em1T

em2

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

Time(s)

Fs1,

2 (W

b)

F

s1F

s2

-0.4 -0.2 0 0.2 0.4-0.4

-0.2

0

0.2

0.4

Fa (Wb)

Fb (W

b)

Fab1

Fab2

Fxy 1,2

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

Time (s)

Fs1

,2 (W

b)

F

s1F

s2

-0.4 -0.2 0 0.2 0.4-0.4

-0.2

0

0.2

0.4

Fa(Wb)

Fb (W

b)

Fab1

Fab2

Fxy 1,2

0 0.2 0.4 0.6 0.8 1-200

-100

0

100

200

Time (s)

Spe

eds

(rad

/s)

W

1W

est1W

ref1W

2W

est2W

ref2

0 0.2 0.4 0.6 0.8 1-0.1

-0.05

0

0.05

0.1

Time(s)

Spe

eds

erro

r (r

ad/s

)

estimation error

1estimation error

2

0 0.2 0.4 0.6 0.8 1-40

-20

0

20

40

Time(s)

Torq

ues

(N.m

)

T

em1T

em2

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

Time (s)

Fs1

,2 (W

b)

F

s1F

s2

-0.4 -0.2 0 0.2 0.4-0.4

-0.2

0

0.2

0.4

Fa (Wb)

Fb (W

b)

Fxy 21,

Fab1

Fab2

a

b

c

d

e

(DTC-SMC) (DTC-PI) (DTC-switching up-table)

Fig. 8. Dynamic responses of parallel-connected two five-phase PMSMs system controlled by SMC, PI based DTC, and conventional DTC and operating at stator resistance variations: (a) Reference, actual and estimated speeds, (b) Speed estimation errors, (c) Electromagnetic torques, (d) Stator fluxes magnitudes, (e) Stator fluxes trajectories

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rad/s and -5 rad/s at t=0s, 0.3s, 0.55s, 0.8s, respectively. For the second machine, the speed reference is set to 5 rad/s, -4 rad/s, 5 rad/s, and-7 rad/s at the same times as previous one. A torque of 5 Nm was applied on the shafts of the first and second machines at the instants t = 0.1 s and 0.2 s, respectively. In case of the DTC-PI and conventional DTC controls, the application of the load torque causes a noticeable speed drop up to -5 rad/s. The speed controller compensates this drop after a necessary recovery time, and it is clear that the conventional DTC suffers during low speed operation. However, with the DTC-SMC control, this influence is reduced and better reference tracking during the speed reversing are observed. Furthermore, it can be seen that in case of DTC-SMC control the estimation using the SMO is more robust during low speed operations.

Case 5: Parameters variations

In this test, the influence of the variation of the stator

resistance on the decoupling between the flux and the torque and the speed regulation performance is studied. For that end, the resistance of the first machine is increased by +100% at t=0.2 s, whereas the resistance of the second machine is increased by the same rate at 0.3 s.

Fig. 8 shows the responses of the five-phase machines under a sudden change in load torque from 0 Nm to 5 Nm at t = 0.2 s and 0.3s, respectively. In this test, the reference speed is step changed from 100 rad/s to -90 rad/s at t=0.5 s for the first machine and from 70 rad/s to -100 rad/s at t=0.6 s for the second one. From this figure, this parameter variation has no influence on the decoupling between the flux and the torque, but its influence on the decoupling between the two machines and the estimation errors is not so considerable and has been recovered quickly thanks to of the robustness of the SMO.

A general comparison between DTC-SMC, DTC-PI and conventional DTC is given in Table 3. Compared to the DTC-PI and conventional DTC controllers, the DTC-SMC shows superiority in terms of settling time and overshoot magnitude.

8. Conclusion In this paper, a sliding mode control and sliding mode

observer are combined to enhance the direct torque control of a parallel-connected two five-phase PMSMs drive system fed by a single five-leg inverter. The resulting control system has been developed using Lyapunov theory in order to guarantee the system stability. The SMC is adopted to control torques, fluxes and speeds, due its inherent advantages such as, robustness, high precision, stability and simplicity. The same quantities are estimated by using a sliding mode observer based on a flux model of the five-phase PMSM. The effectiveness of the proposed control approach has been verified through extensive computer simulations and compared with PI controller and conventional DTC as well.

Simulation results have demonstrated not only truly decoupled operation between the two machines but also many improvements on the dynamic response as well as the steady state performance, in terms of speed response, accuracy, and ripple reduction. The main improvements brought by the proposed DTC-SMC compared to the DTC-PI and conventional DTC have been summarized in Table 3, and they are listed below:

- Faster rise time. - Good speed tracking without overshoots or drops. - Reduction in the torque and flux ripples. The added value of the SMO based sensorless control is

the amelioration in the system dynamics through the accuracy in speeds, fluxes, and torques estimation. Indeed, the obtained simulation results show better speed tracking performance at both dynamic and steady state, acceptable estimations errors, robustness in different tests including speed variation, load application, low speed operation, and stator resistance variation. So, these results affirm the ability of the proposed observer to guarantee good estimations in steady state and transients as well.

However, the lack of load torque estimator and more developed technique dealing with chattering phenomenon is the main drawback of the proposed control approach.

Table 3. Comparison between SMC and PI based DTC

Reduction rate (%) Controlled variable Comparison criterion DTC-SMC DTC-PI Conventional

DTC DTC-PI Conventional DTC

Rotor speed

Settling time (s) Overshoot (rad/s) Speeds drops (%)

Recovery time (at abrupt load) (s) Overshoot in reversal mode (%)

The maximum speed estimation error (%)

0.01 0.02 0.9

0.01 0

0.04

0.09 13.63 11.6 0.08 48 0.1

0.09 13.63 11.6 0.08 61

0.09

88.88 99.85 92.24 87.5 100 60

88.88 99.85 92.24 87.5 100

55.55

Electromagnetic torque

Settling time (s) Overshoot (rad/s)

Ripple (N.m)

0.009 2.5

1.16

0.07 1.6 1.2

0.07 10.9 3.5

87.71 36(increase)

3.33

87.71 77.06 66.85

Stator flux Settling time (s)

Overshoot (rad/s) Overshoot in reversal mode (%)

Ripple (N.m)

0.002 0 0

0.007

0.0046 0.034 0.016

0.0084

0.004 0 0

0.28

56.52 100 100

16.66

50 0 0

97.5

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References

[1] M. Bermudez, I. Gonzalez-Prieto, F. Barrero, H. Guzman, M. J. Duran, and X. Kestelyn, “Open-Phase Fault-Tolerant Direct Torque Control Technique for Five-Phase Induction Motor Drives,” IEEE Transactions on Industrial Electronics, vol. 64, no. 2, pp. 902-911, 2017.

[2] S. Payami, R. K. Behera, X. Yu, and M. Gao, “An Improved DTC Technique for Low Speed Operation of a Five-Phase Induction Motor,” IEEE Transactions on Industrial Electronics, vol. 64, no. 5, pp. 3513-3523, 2017.

[3] B. Tian, Q.-T. An, J.-D. Duan, D.-Y. Sun, L. Sun, and D. Semenov, “Decoupled Modeling and Nonlinear Speed Control for Five-Phase PM Motor under Single Phase Open Fault,” IEEE Transactions on Industrial Electronics, vol. 32, no. 7, pp. 5473-5486, 2017.

[4] N. R. Abjadi, “Sliding-Mode Control of a Six-phase Series/Parallel Connected Two Induction Motors Drive,” ISA Transactions, vol. 53, no. 6, pp. 1847-1856, 2014.

[5] H. H. Chen and C.-X. Su, “Current Control for Single-Inverter Fed Series-Connected Five-Phase PMSMS,” IEEE International Symposium on Industrial Electronics, Taipei, Taiwan, pp.1-6, 28-31May, 2013.

[6 ] L. Gao and J. E. Fletcher, “A Space Vector Switching Strategy for Three-Level Five-Phase Inverter Drives, “IEEE Transactions on Industrial Electronics, vol. 57, no. 7, pp. 2332-2343, July 2010.

[7] L. Yuan, M.-L. Chen, J.-Q. Shen, and F. Xiao, “Current Harmonics Elimination Control Method for Six-Phase PM Synchronous Motor Drives,” ISA Transactions, vol. 59, pp. 443-449, November 2015.

[8] L. Parsa and H. A. Toliyat, “Sensorless Direct Torque Control of Five-Phase Interior Permanent-Magnet Motor Drives,” IEEE Transactions on Industry Applications, vol. 43, no. 4, pp. 952-959, July/August 2007.

[9] Y. N. Tatte and M. V. Aware, “Torque Ripple and Harmonic Current Reduction in Three-Level Inverter Fed Direct Torque Controlled Five-Phase Induction Motor,” IEEE Transactions on Industrial Electronics, vol. 64, no. 7, pp. 5265-5275, 2017.

[10] A. Ammar, A. Bourek, and A. Benakcha, “Robust SVM-Direct Torque Control of Induction Motor Based on Sliding Mode Controller and Sliding Mode Observer,” Frontiers in Energy, pp. 1-14, 2017.

[11] B. Ning, S. Cheng and Y. Qin, “Direct Torque Control of PMSM Using Sliding Mode Backstepping Control with Extended State Observer,” Journal of Vibration and Control, pp. 1-14, 2016.

[12] B. S. Khaldi, H. Abu-Rub, A. Iqba, R. Kennel, O. Mahmoudi, and D. Boukhetala,”Sensorless Direct

Torque Control of Five-Phase Induction Motors Drives,” IECON 2011, 37th Annual Conference on IEEE Industrial Electronics Society, Melbourne, VIC, pp. 3501-3506, 7-10 November 2011.

[13] M. H. Vafaie, B. M. Dehkordi, P. Moallem, and A. Kiyoumarsi, “A New Predictive Direct Torque Control Method for Improving Both Steady-State and Transient-State Operations of the PMSM,” IEEE Transactions on Power Electronics, vol. 31, no. 5, pp. 3738-3753, May 2016.

[14] F. Ben Salem and N. Derbel, “Second-Order Sliding-mode Control Approaches to Improve Low-speed Operation of Induction Machine under Direct Torque Control,” Electric Power Components and Systems, vol. 44, no. 17, pp. 1969-1980, June 2016.

[15] A. Ammar, A. Bourek, and A. Benakcha, “Nonlinear SVM-DTC for Induction Motor Drive Using Input-Output Feedback Linearization and High Order Sliding Mode Control,” ISA Transactions, vol. 67, pp. 428-442, 2017.

[16] X. Zhang, L. Sun, K. Zhao, and L. Sun, “Nonlinear Speed Control for PMSM System Using Sliding-Mode Control and Disturbance Compensation Techniques,” IEEE Transactions on Power Elec-tronics, vol. 28, no. 3, pp. 1358-1365, March 2013.

[17] S. M. J. R. Fatemi, N. R. Abjadi, J. Soltani, and S. Abazari, “Speed Sensorless Control of a Six-Phase Induction Motor Drive Using Backstepping Control,” IET Power Electron., vol. 7, no. 1, pp. 114-123, January 2014.

[18] A. Hosseyni, R. Trabelsi, A. Iqbal, and M. F. Mimouni, “Backstepping Control for a Five-Phase Permanent Magnet Synchronous Motor Drive,” International Journal of Power Electronics and Drive System(IJPEDS), vol. 6, no. 4, pp. 842-852, December 2015.

[19] M. Ahmed, F. M. Karim, M. Abdelkader, and B. Abdelber, “Input Output Linearization and Sliding Mode Control of a Permanent Magnet Synchronous Machine Fed by a Three Levels Inverter,” Journal of Electrical Engineering, vol. 57, no. 4, pp. 205-210, 2006.

[20] L.-B. Li, L.-L. Sun, S.-Z. Zhang, and Q.-Q. Yang, “PMSM Speed Tracking and Synchronization of Multiple Motors Using Ring Coupling Control and Adaptive Sliding Mode Control,” ISA Transactions, vol. 58, pp. 635-649, September 2015.

[21] C. Lascu and A. M. Trzynadlowski, “Combining the Principles of Sliding Mode, Direct Torque Control and Space-Vector Modulation in a High-Performance Sensorless AC Drive,” IEEE Transactions on Industry Applications, vol. 40, no. 1, January/ February 2004.

[22] S F.-J. Lin, Y.-C. Hung, and M.-T. Tsai, “Fault-Tolerant Control for Six-Phase PMSM Drive System Via Intelligent Complementary Sliding Mode

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Control Using TSKFNN-AMF,” IEEE Transactions on Industrial Electronics, vol. 60, no. 12, pp. 5747-5762, December 2013.

[23] S. Chen, Y. Luo, and Y. Pi, “PMSM Sensorless Control with Separate Control Strategies and Smooth Switch From Low Speed to High Speed,” ISA Transactions, vol. 58, pp. 650-658, September 2015.

[24] M. Jones, S. N. Vukosavic, and E. Levi, “Parallel-Connected Multiphase Multidrive Systems with Single Inverter Supply,” IEEE Transactions on Industrial Electronics, vol. 56, no. 6, pp. 2047-2057, June 2009.

[25] H. Zhang, S. Luo, Y. Yu, and L. Liu, “Study on Series Control Method for Dual Three-Phase PMSM Based on Space Vector Pulse Width Modulation,” International Journal of Control and Automation, vol. 8, no. 1, pp. 197-210, 2015.

[26] M. Jones, E. Levi, and S. N. Vukosavic, “Independent Control of Two Five-Phase Induction Machines Connected in Parallel to a Single Inverter Supply,” IEEE Industrial Electronics Conference, Paris, France, pp. 1257-1262, 6-10 November 2006.

[27] D. Dujic, G. Grandi, M. Jones, and E. Levi, “A Space Vector PWM Scheme for Multi Frequency Output Voltage Generation With Multiphase Voltage-Source Inverters,” IEEE Transactions on Industrial Electronics, vol. 55, no. 5, pp. 1943-1955, May 2008.

[28] N. K. Quang, N. T. Hieu, and Q. P. Ha, “FPGA-Based Sensorless PMSM Speed Control Using Reduced-Order Extended Kalman Filters,” IEEE Transactions on Industrial Electronics, vol. 61, no. 12, pp. 6574-6582, December 2014.

[29] Z. Xu and M. F. Rahman, “Comparison of a Sliding Observer and a Kalman Filter for Direct-Torque-Controlled IPM Synchronous Motor Drives,” IEEE Transactions on Industrial Electronics, vol. 59, no. 11, pp. 4179-4188, November 2012.

[30] D. Xu, S. Zhang, and J. Liu, “Very-Low Speed Control of PMSM Based on EKF Estimation with Closed Loop Optimized Parameters,” ISA Trans-actions, vol. 52, no. 6, pp. 835-843, November 2013.

[31] A. Najjar-Khodabakhsh and J. Soltani, “MTPA Control of Mechanical Sensorless IPMSM Based on Adaptive Nonlinear Control,” ISA Transactions, vol. 61, pp. 348-356, March 2016.

[32] M. R. Khan and A. Iqbal, “MRAS Based Sensorless Control of a Series-Connected Five-Phase Two-Motor Drive System,” Journal of Electrical Engineering & Technology, vol. 3, no. 2, pp. 224-234, 2008.

[33] M. R. Khan and A. Iqbal, “Extended Kalman Filter Based Speeds Estimation of Series-Connected Five-Phase Two-Motor Drive System,” Simulation Modelling Practice And Theory, vol. 17, no. 7, pp. 1346-1360, August 2009.

[34] A. Hosseyni, R. Trabelsi, M. F. Mimouni, A. Iqbal, and R. Alammari, “Sensorless Sliding Mode

Observer for a Five-Phase Permanent Magnet Synchronous Motor Drive,” ISA Transactions, vol. 58, pp. 462-473, September 2015.

[35] A. Hosseyni, R. Trabelsi, S. Kumar, M. F. Mimouni, and A. Iqbal, “New Sensorless Sliding Mode Control of a Five-Phase Permanent Magnet Synchronous Motor Drive Based on Sliding Mode Observer,” International Journal of Power Electronics and Drive System (IJPEDS), vol. 8, no. 1, pp. 184-203, March 2017.

[36] W. K. Wibowo1and S.-K. Jeong, “Improved Estimation of Rotor Position for Sensorless Control of a PMSM Based on a Sliding Mode Observer,” Journal of Central South University, vol. 23, no. 07, pp. 1643-1656, July 2016.

[37] Z. Qiao, T. Shi, Y. Wang, Y. Yan, C. Xia, and X. He, “New Sliding-Mode Observer for Position Sensorless Control of Permanent-Magnet Synchronous Motor,” IEEE Transactions on Industrial Electronics, vol. 60, no. 2, February 2013.

[38] J. J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, New Jersey, 1991.

[39] M. Jones, O. Dordevic, N. Bodo, and E. Levi, “PWM Algorithms for Multilevel Inverter Supplied Multiphase Variable-Speed Drives,” Electronics, vol. 16, no. 1, pp.22-31, June 2012.

[40] D. Dujic, M. Jones, and E. Levi, “Generalized Space Vector PWM for Sinusoidal Output Voltage Generation with Multiphase Voltage Source Inverters,” Int. J. Industrial Electronics and Drives, vol. 1, no. 1, pp. 1-13, 2009.

Tounsi Kamel was born in Bousaada, Algeria in 1990. He received the Licence degree in Electrical Engin-eering from M’sila University, Algeria in 2012, his Master degree from M’sila University in 2014. He is currently working towards his PhD degree in Electrical Engineering from Chlef

University, Algeria. His areas of interest are multi machine and Process Control, wind energy conversion.

Abdelkader Djahbar was born in Chlef, Algeria, in February 1970. He received the Eng. And M.Sc. degrees in electrical engineering from the National Polytechnic school of Algiers, Algeria, in 1995 and 1998, respectively, and the Ph.D. degree in electrical engineering from the Mohamed

Boudiaf University of Science and Technology of Oran (USTO), Algeria, in 2008 and the Habilitation to lead

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Researches in 2012 at the USTO University, Algeria. In December 2002, he joined the electrical engineering department of Hassiba Ben Bouali Univesity of Chlef, Algeria. Since August 2012, he is Associate Professor in the same department. He is associate researcher in the LMOPS laboratory of the Université de Lorraine and Centrale Supélec since April 2014 and researcher at the GEER laboratory of UHBC since 2013. His scientific work is related to electrical machines and drives and Power Electronics. His present research interests include multi machine drives, matrix converter and power quality.

Said Barkat received the Engineer, Magister, and Ph.D. degrees, all in electrical engineering, from the National Polytechnic School of Algiers, Algeria, in 1994, 1997, and 2008, respectively. In 2000, he joined the Department of Electrical Engineering, Faculty of Technology at University of

M'sila, Algeria. His research interests include renewable energy conversion, power electronics, and advanced control theory and applications.

Atif Iqbal Senior Member IEEE, PhD (UK), Fellow IE (India)- Associate Editor IEEE Tran. On Industry Appli-cation, Associate Professor at Electrical Engineering, Qatar University and Former Full Professor at Electrical Engineering, Aligarh Muslim University (AMU), Aligarh, India. Recipient of

Outstanding Faculty Merit Award AY 2014-2015 and Research excellence award at Qatar University, Doha, Qatar. He received his B.Sc. (Gold Medal) and M.Sc. Engineering (Power System & Drives) degrees in 1991 and 1996, respectively, from the Aligarh Muslim University (AMU), Aligarh, India and PhD in 2006 from Liverpool John Moores University, Liverpool, UK. He has been employed as a Lecturer in the Department of Electrical Engineering, AMU, Aligarh since 1991 where he served as Full Professor until Aug. 2016. He is recipient of Maulana Tufail Ahmad Gold Medal for standing first at B.Sc. Engg. Exams in 1991 from AMU. He has received best research papers awards at IEEE ICIT-2013 and IET-SESICON-2013. He has published widely in International Journals and Conferences his research findings related to Power Electronics and Renewable Energy Sources. Dr. Iqbal has authored/coauthored more than 280 research papers and one book and two chapters in two other books. He has supervised several large R&D projects. His principal area of research interest is modeling and simulation of power electronic converters, control of multi-phase motor drives and renewable energy sources.

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