Numerical Modelling of Sinusoidal Brushless Motor for … · 2017-05-12 · modelling of the PMSM for electromagnetic aerospace actuator systems for future diagnostic and prognostic

Abstract:

next generation aircraft, based on the More Electric design. Electromechanical act

increased acceptance as they are becoming more and more safety

health management purposes of EMA, reliable and representative simulation models are needed in order to

identify failure

of the Permanent Magnet Synchronous Motor (PMSM), also kwon as Sinusoidal Brushless Motor. The choice

of the multi domain simulation is necessary to improve the si

in numerical models and that are mostly used for prognostic analyses of electromechanical actuators.

Key

1In the last few years, the interest in brushless motors

has increased because of their advantages compared

with traditional brushed motors. The need of

improvement in the design of electric motors was

first reported during

in World War II: in fact, at about 30000 ft, a rapid

brush wear occurred [1

exploration, the brush problem became crucial due

to the outgassing phenomena. Brushless motors

have been designed to ov

disadvantages: the electronic commutation, which is

made possible by using electronic switches, replaces

the mechanical commutation based on carbon made

brushes.

research activity focused on

modelling of the PMSM for electromagnetic

aerospace actuator systems for future diagnostic and

prognostic applications. For this purpose, short

circuit and static eccentricity failure conditions will

be implemented in the developed PMSM mode

Furthermore, the developed model takes into

account dry friction and it overcomes the typical

limitations (e.g. simplifying assumptions such as the

superposition of the effects) which are unable to

assess nonlinear effects arising from failure

condition

multi

development of simulation algorithms properly

sensitive to faults.

Abstract:




identify failure




Key

1 IntroductionIn the last few years, the interest in brushless motors













brushes.












condition

multi



Abstract:




identify failure




Key-Words:

IntroductionIn the last few years, the interest in brushless motors













brushes.












condition

multi-domain numerical method which allows the



Abstract:




identify failure




Words:














brushes. This study shows the firs results of our












conditions. This purpose is achieved by means of a

domain numerical method which allows the



Abstract: - The interest in electromechanical actuators (EMA) has been growing because of the development of




identify failure




Words: -














This study shows the firs results of our












s. This purpose is achieved by means of a




The interest in electromechanical actuators (EMA) has been growing because of the development of




identify failures. This paper presents a multi domain model of EMA and it focuses on the numerical modelling




- PMSM, Electromechanical Actuator (EMA), Prognostics, PHM, Numerical Model






























M. D. L. DALLA VEDOVA P. MAGGIORE M. SCANAVINO





s. This paper presents a multi domain model of EMA and it focuses on the numerical modelling




PMSM, Electromechanical Actuator (EMA), Prognostics, PHM, Numerical Model






























Numerical Modelling of Sinusoidal Brushless











Introduction In the last few years, the interest in brushless motors




first reported during high altitude strategic bombing


























[email protected], [email protected]










In the last few years, the interest in brushless motors




high altitude strategic bombing


brush wear occurred [1-























Motor for Aerospace Actuator Systems


Department of Mechanical and Aerospace Engineering

















-3]. Later on, during space



have been designed to overcome the brushed motor







































]. Later on, during space



ercome the brushed motor























Corso Duca degli Abruzzi 24




































































research activity focused on the numerical











































the numerical











































the numerical


















Politecnico di Torino


























the numerical












































the numerical




















ITALY

























the numerical



prognostic applications. For this purpose, short-


be implemented in the developed PMSM model.















ITALY

























the numerical



-


l.















ITALY

















ITALY








of the multi domain simulation is necessary to improve the simplifying hypotheses that are typically considered



2 Flight control systems allow to con

dynamic: this is made possible by means of the

proper actuation of the flight control surfaces.

The aerodynamic forces, exerted on the flight

control surfaces, will result in the aircraft rotation

around one of the three body axes

decades, fl

hydromechanical or electrohydraulic

in recent years, the electromechanical systems are

gradually asserting (e.g. UAVs, secondary or stand

by systems)

systems, EMAs off

weight is reduced, maintenance is simplified and

hydraulic fluids, which are often contaminant,

flammable or polluting, can be eliminated.

reasons, as reported in [4], the use of actuation

systems based on EMAs is quic

several fields of aerospace technology.






Corso Duca degli Abruzzi 24 –








mplifying hypotheses that are typically considered



EM Flight Control ActuatorsFlight control systems allow to con






decades, fl




by systems)

systems, EMAs off







Fig. 1:






– 10129, Turin




increased acceptance as they are becoming more and more safety-critical actuation devices: for prognostics and













decades, fl




by systems)

systems, EMAs off







Fig. 1:





10129, Turin




critical actuation devices: for prognostics and













decades, fl




by systems)

systems, EMAs off







Fig. 1: Schematic of the considered EMA system





10129, Turin

















decades, flight control actuators were generally




by systems).

systems, EMAs off







Schematic of the considered EMA system





10129, Turin

















ight control actuators were generally




Indeed, w

systems, EMAs off












10129, Turin





















Indeed, w

systems, EMAs off












10129, Turin





















Indeed, w

systems, EMAs offer many advantages: overall














next generation aircraft, based on the More Electric design. Electromechanical actuators have been gaining


















Indeed, with respect to hydraulic

er many advantages: overall














uators have been gaining


















ith respect to hydraulic


































































systems based on EMAs is quickly increasing in












EM Flight Control ActuatorsFlight control systems allow to control the aircraft







hydromechanical or electrohydraulic but, especially









kly increasing in











EM Flight Control Actuatorstrol the aircraft





around one of the three body axes; in the last


but, especially









kly increasing in









EM Flight Control Actuators trol the aircraft





in the last


but, especially







flammable or polluting, can be eliminated. For these


kly increasing in









trol the aircraft





in the last


but, especially







For these


kly increasing in









trol the aircraft





in the last


but, especially







For these


kly increasing in









trol the aircraft





in the last


but, especially


gradually asserting (e.g. UAVs, secondary or stand-





For these


kly increasing in

WSEAS TRANSACTIONS on POWER SYSTEMS M. D. L. Dalla Vedova, P. Maggiore, M. Scanavino

E-ISSN: 2224-350X 102 Volume 12, 2017

for primary flight control, is presented. The EMA

system is composed by:

1.

2.

3.

4.

5.

6.

3The authors’ models implement the motor features

only (rotor speed control loop and related reference

current controller, pulse

inverter, electromagnetic model of the stator circuit

and related electromechanical model, internal

sensors and considered faults).

composed by five subsystems:

1.

2.

3.

In Fig. 1, an electromechanical actuator scheme,



1. an actuator control elect

the feedback loop, by comparing the commanded

position (FBW) with the actual one; it elaborates

the corrective actions and generates the reference

current (

2. a Power Drive Electronics (PDE) that regulates

the electrical power

system to the electric motor;

3. an electric motor, often a

type

4. a gear reducer that decreases the motor angular

speed and increases its mechanical torque;

5. a system that transforms rotary motion into linear

motion: ball screws or roller screws are usually

preferred because a conversion with higher

efficiency can be performed;

6. a network of sensors that are used to close the

feedback loops (current, motor spee

position) controlling the whole actuation system

(reported in Fig.1 as RVDT).

3 Proposed PMSM Numerical MThe authors’ models implement the motor features






Fig. 2: Block diagram of the EMA numerical model

The proposed model is shown in Fig. 2 and it is


1. W_ref

motor speed;

2. PMSM Motor Controller Model

actuator control electronics closing

loops and generat

3. PMSM Motor ElectroM

the power drive electronics and the sinusoidal

PMSM electromagnetic behaviour. Furthermore,

it evaluates the mechanical torque developed by

the electrical motor as a function of the voltages

generated by the three




an actuator control elect




current (

a Power Drive Electronics (PDE) that regulates



an electric motor, often a

type

a gear reducer that decreases the motor angular


a system that transforms rotary motion into linear




a network of sensors that are used to close the




Proposed PMSM Numerical MThe authors’ models implement the motor features









W_ref

motor speed;

PMSM Motor Controller Model


loops and generat

PMSM Motor ElectroM













current (





type;




















W_ref: input block that generates the reference

motor speed;



loops and generat

PMSM Motor ElectroM













current (I_ref
























W_ref: input block that generates the reference

motor speed;



loops and generat

PMSM Motor ElectroM













I_ref
























: input block that generates the reference

motor speed;



loops and generat

PMSM Motor ElectroM













I_ref);

























motor speed;



loops and generat

PMSM Motor ElectroM







































loops and generating

PMSM Motor ElectroM





























current controller, pulse-










ing the reference current

PMSM Motor ElectroM








an actuator control electronics (ACE) that closes





from the aircraft electrical















-wi










the reference current

PMSM Motor ElectroMecc. Model





generated by the three-phase electrical



ronics (ACE) that closes







an electric motor, often a three













width modulation (PWM)











PMSM Motor ElectroMecc. Model





phase electrical










three













dth modulation (PWM)









ecc. Model





phase electrical









three-phase

















PMSM Motor Controller Model: it simulates th



ecc. Model





phase electrical









phase







feedback loops (current, motor speed and angular










: it simulates th

actuator control electronics closing the feedback


ecc. Model: it simulates





phase electrical









phase







d and angular










: it simulates th

the feedback


: it simulates





phase electrical regulator;









phase brushless







d and angular


Proposed PMSM Numerical ModelThe authors’ models implement the motor features








: it simulates th

the feedback

the reference current I_ref

: it simulates





regulator;









brushless






d and angular


odelThe authors’ models implement the motor features








: it simulates th

the feedback

I_ref

: it simulates





regulator;









brushless






d and angular


odel The authors’ models implement the motor features








: it simulates the

the feedback

I_ref;

: it simulates





regulator;









brushless






d and angular


The authors’ models implement the motor features







e

the feedback

: it simulates





4.

5.

It must be noted that these numerical models ca

also consider the electrical noise acting on the signal

lines [4], the rotor bearings dry friction and the limit

switches [5].

of the previous work carried out for the trapezoidal

brushless motor BLDC [6]. A Circuital Mo

Detailed Inverter (CMDI) has been implemented:

the physical data used to implement these numerical

algorithms and to run the corresponding simulations

are referred to the TC 40 0.32 01 Tetra Compact

sinusoidal brushless motor (as reported in Table

resistance

the back electromagnetic force

introduced: they are related to the magnetic flux

time derivative.

is

this case, sinusoidal functions are used to describe

the back electromagnetic forces and currents.

Three different reference systems are introduced to

study the PMSM (

1.

PMSM Motor Dynamic Model

motor mechanical behaviour by means of a two

degree

TR

acting on the rotor shaft.




switches [5].








Phase

Phase

Back

Each phase line is characterised by the same

resistance



time derivative.

similar to the BLDC model shown in [6] but, in




study the PMSM (

where the

and it is defined by starting from the symmetrical

axis of the phase 1.



degree

TR: input block that simulates the external load





switches [5].








Nominal voltage

Phase

Phase-

Torque constant

Back

Stall Torque

Rotor Inertia


resistance



time derivative.





study the PMSM (

where the





degree-of

: input block that simulates the external load





switches [5].








Nominal voltage

Phase-phase resistance

-phase inductance

Torque constant

Back-EMF constant

Stall Torque

Rotor Inertia


resistance R



time derivative.




Fig. 4:


study the PMSM (

axes

where the





of-freedom dynamic system;






switches [5]. The PMSM model is the development








Table 1: Main PMSM data

Nominal voltage

phase resistance

phase inductance

Torque constant

EMF constant

Stall Torque

Rotor Inertia


R and the same inductance



time derivative.




Fig. 4:


study the PMSM (

axes

where the





freedom dynamic system;






The PMSM model is the development









Nominal voltage

phase resistance

phase inductance

Torque constant

EMF constant

Stall Torque

Rotor Inertia


and the same inductance



time derivative. The layout of the numerical model




Fig. 4: Brushless Reference systems


study the PMSM (

axes: it is a stationary reference system

axis is fixed on the PMSM stator




















Nominal voltage

phase resistance

phase inductance

Torque constant

EMF constant

Stall Torque

Rotor Inertia





The layout of the numerical model




Brushless Reference systems


study the PMSM (as shown in

: it is a stationary reference system





















Nominal voltage

phase resistance

phase inductance

Torque constant

EMF constant











as shown in






















phase resistance

phase inductance











as shown in































as shown in




















48

1.10

0.72

0.094

0.0544

0.34

0.047











as shown in Fig. 4)




PMSM Motor Dynamic Model: it simulates the
















48

1.10

0.72

0.094

0.0544

0.34

0.047











Fig. 4)




: it simulates the
















0.0544


and the same inductance L

,








Fig. 4):




: it simulates the















[Nm/A

[V

[kg cm


Leq; moreover,











: it simulates the








brushless motor BLDC [6]. A Circuital Model with






[V]

[Ω

[mH]

[Nm/A

[Vpp

[Nm]

[kg cm


; moreover,

and











: it simulates the








del with






[V]

[Ω]

[mH]

[Nm/App

pp/App

[Nm]

[kg cm2


; moreover,

and










: it simulates the








del with





1).

pp]

pp]

2]


; moreover,

are









: it simulates the



It must be noted that these numerical models can





del with





1).


; moreover,

are









E-ISSN: 2224-350X 103 Volume 12, 2017

2.

3.

The relative angle between the stator and the rotor

axes is

results

balance and, referred to

where

magnetic flux respectively.

The

right handed Cartesian system is obtained. The

angle

angles along the stator starting from the

2. the rotor. The

while the

The angle

angles along the rotor, starting from the

3. Three

reference system where the axes (1, 2 and

into line with the thr

motor:

1


axes is

results

Moreover, for a balanced three

The motor torque is obtained from the power


where


The


angle


the rotor. The

while the

The angle


Three



motor:

1-axis corresponds to the


axes is

results




where


The


angle Φ


the rotor. The

while the

The angle


Three-phase reference system



motor:

axis corresponds to the


axes is .

results that:




where P and


axis is perpendicular to


angle Φ is used as a polar coordinate to describe


axes

the rotor. The

while the

The angle


-phase reference system



motor: the axes are out of phase by 120° and the



. Applying Kirchhoff’s law on each line it

that:




and




Φ is used as a polar coordinate to describe


axes: it is a rotating reference system with

the rotor. The

while the

The angle ξ is a polar coordinate


phase reference system



the axes are out of phase by 120° and the



Applying Kirchhoff’s law on each line it


0



and λmagnetic flux respectively.



is used as a polar coordinate to describe


: it is a rotating reference system with

the rotor. The

axis is perpendicular to the

The angle ξ is a polar coordinate










0



are the pole pair number and the







axis points to the nor


ξ is a polar coordinate









!

"

#













is a polar coordinate

























into line with the three




















ee-phase windings of the


axis corresponds to the axis.





axes, it results [7]:











phase reference system: it is a stationary


phase windings of the


axis.



Moreover, for a balanced three-




Fig. 5: PMSM Electromechanical Model subsystem










: it is a stationary




axis.



-phase circuit:





axis so that a







is a polar coordinate describing








phase circuit:





axis so that a





axis points to the north pole line,


describing








phase circuit:





axis so that a



angles along the stator starting from the axis;


th pole line,


describing

angles along the rotor, starting from the axis;







phase circuit:





axis so that a



axis;


th pole line,

axis.

describing

axis;


reference system where the axes (1, 2 and 3) fall





phase circuit:





axis so that a



axis;


th pole line,

axis.

the

axis;


3) fall





(1)

(2)

(3)

(4)


(5)



axis so that a




th pole line,

axis.

the


3) fall





(1)

(2)

(3)

(4)


(5)




phase reference currents from the reference

current, Park and Clarke transformations are needed

(as

obtained from the

motor torque is turned into the reference current by

using the motor torque

3.1The subsystem in Fig. 5 models a three

circuit: it receives, as input, the reference current

I_ref

speed and position. The reference current subsystem

generates the reference si

three

are set equal to the reference current

respectively. The inverse Park and Clarke

transformation

the

Torque subsystems are the same as in [6],

implemented in the Circuital

Inverter model. On the left bottom of Fig. 5 we can

notice the normalized back electromagnetic forc

which are sinusoidal functions of the electric angle.

multiplying the normalized BEMFs and the motor

angular speed. The

implements the short circuit and static eccentricity

failu


It must be noted that, in order to obtain the three



(as described

obtained from the



3.1 The subsystem in Fig. 5 models a three


I_ref, the electrical angle and the rotor mechanical



three-



transformation

the corresponding

The PWM, Inverter, Phase Currents and Motor






The back electromagnetic forces are obtained


angular speed. The


failure as shown in [





described

obtained from the



PMSMThe subsystem in Fig. 5 models a three


, the electrical angle and the rotor mechanical



-phase circuit: the



transformation

corresponding









angular speed. The


re as shown in [





described

obtained from the








phase circuit: the



transformation

corresponding









angular speed. The


re as shown in [





described in

obtained from the








phase circuit: the



transformation

corresponding









angular speed. The


re as shown in [





in [8]

obtained from the



PMSM Electromechanical Model The subsystem in Fig. 5 models a three





phase circuit: the



transformation matrixes are implemented to obtain

corresponding









angular speed. The


re as shown in [





[8]).

obtained from the



Electromechanical Model The subsystem in Fig. 5 models a three





phase circuit: the



matrixes are implemented to obtain

corresponding three









angular speed. The


re as shown in [9





). The reference current (

obtained from the motor controller: a reference








phase circuit: the




hree-









angular speed. The Failure Functions


9].




The reference current (

otor controller: a reference







phase circuit: the




-phas









Failure Functions












generates the reference sinusoidal currents for a

and




phase reference currents.









Failure Functions












nusoidal currents for a

and are set equal to the reference current



e reference currents.



implemented in the Circuital Model with Detailed






Failure Functions













reference currents







Model with Detailed






Failure Functions













reference currents

are set equal to the reference current I_ref






Model with Detailed






Failure Functions













reference currents

I_ref






Model with Detailed






Failure Functions





The reference current (I_ref








reference currents

I_ref and zero






Model with Detailed






subsystem





I_ref



Electromechanical Model The subsystem in Fig. 5 models a three-phase





reference currents

and zero






Model with Detailed






subsystem





I_ref) is



phase





reference currents

and zero






Model with Detailed


notice the normalized back electromagnetic forces,




subsystem


It must be noted that, in order to obtain the three-


) is



phase





reference currents

and zero





Model with Detailed


es,




subsystem



E-ISSN: 2224-350X 104 Volume 12, 2017

3.2

speed controller

to define the reference torque, which is turned into


on the signal error, properly filtered, in order to

ensure the stability of the entire system: a low

filter is a

The integral contribution is achieved with the anti

windup filter, which allows the desaturation of the

integral term when the reference torque reaches the

maximum value allowed. The three gains of the

PI

4In this section, in order to explain the performance

of the proposed numerical model, the motor

response to a reference speed is presented, in load

conditions.

nominal motor speed (3000 rpm). An external load

(50% of

%

history, while in Fig. 8 the BEMFs and the actual

three

that the phase currents increase when the external

load is applied; at t

BEMFs is visible, due to the proportional

relationship between the motor speed and BEMFs.

In Fig. 9 the sinusoidal waveform of the actual three

phase currents and the reference ones are shown.

The motor torque time history

3.2 The motor control is achieved by means of a PID

speed controller





filter is a





PID PMSM speed controller are shown in Table 2.

&

4 ResultsIn this section, in order to explain the performance



conditions.


(50% of

%


three








PMSM Speed ControllerThe motor control is achieved by means of a PID

speed controller





filter is a





D PMSM speed controller are shown in Table 2.

Table 2: PMSM speed controller PID gains

&' [Nm/rad/s]

0

ResultsIn this section, in order to explain the performance



conditions.


(50% of

0.15


three-phase currents are shown. It can be noticed









speed controller





filter is added to the derivative line for this purpose.







[Nm/rad/s]

0.025




conditions.


(50% of

15+


phase currents are shown. It can be noticed








Fig. 7: PMSM motor speed time history


speed controller





dded to the derivative line for this purpose.







[Nm/rad/s]

025




conditions. The reference speed is set equal to the


the stall torque) is applied at time

+.












speed controller












[Nm/rad/s]

Results In this section, in order to explain the performance



The reference speed is set equal to the



Fig. 7 shows the motor speed time












speed controller [10]












In this section, in order to explain the performance


















[10]: the input speed error is used


the reference current I_ref










&











load is applied; at the same time, a reduction in the








: the input speed error is used


I_ref










[Nm/rad]

0.235











he same time, a reduction in the










I_ref. The derivative term acts










[Nm/rad]

235





















. The derivative term acts










[Nm/rad]

235
















The motor torque time history is shown in Fig. 10.


PMSM Speed Controller The motor control is achieved by means of a PID




























is shown in Fig. 10.


The motor control is achieved by means of a PID













&































& [Nm/rad/s

1































[Nm/rad/s

1































[Nm/rad/s

6























ensure the stability of the entire system: a low-pass





maximum value allowed. The three gains of the said


[Nm/rad/s2]






















pass-


The integral contribution is achieved with the anti-



said


]






















-


-



said
















Fig. 9: PMSM reference and actual phase currents

Fig. 10: PMSM motor torque T



Fig. 8: BEMFs and phase currents






friction torque f




friction torque f




friction torque f




friction torque f




friction torque f




friction torque fatt time history



Fig. 10: PMSM motor torque TM

time history



M, external load T

time history



, external load T

time history



, external load T

time history


, external load T


, external load TR


R and

and


E-ISSN: 2224-350X 105 Volume 12, 2017

5 Conclusions The numerical modelling of the electromechanical

actuator using permanent magnet synchronous

motor has been developed. The model was created

in Matlab/Simulink environment. The Park and the

Clarke transformations were introduced to describe

the three-phase reference currents. The sinusoidal

waveform of the normalized back electromagnetic

force was introduced in order to describe the correct

motor behaviour and evaluate the total motor torque.

The PMSM motor control was developed imposing

the reference quadrature current and setting the

direct current equal to zero, as it normally does

not contribute to the motor torque generation.

In order to improve the developed model, some

suggestions are given:

1. the Hysteresis Control should be replaced with

the d-q axes direct control, in order to avoid the

phase voltage and current distortions at high

rotor speed;

2. the failure conditions could be studied in details.

Demagnetisation failure could be considered in

order to improve the failure conditions;

3. a simplified model of the actuator should be

developed in order to monitor the motor actual

behaviour. This solution would be interesting for

future diagnostic and prognostic applications.

References:

[1] Midwest Research Institute – NASA, Brushless

DC Motors, January 1975.

[2] NASA Practice No. PD-ED-1229, Selection of

electric motors for aerospace applications.

[3] P. Pillay, R. Krishnan, Application Charac-

teristics of Permanent Magnet Synchronous and

Brushless dc Motors for Servo Drives, IEEE

Transactions on industry applications, Vol.21,

No.5, September/October 1991.

[4] D. Belmonte, M. D. L. Dalla Vedova, P.

Maggiore, New prognostic method based on

spectral analysis techniques dealing with motor

static eccentricity for aerospace electro-

mechanical actuators, WSEAS Transactions On

Systems, Vol.14, 2015, ISSN: 1109-2777.

[5] L. Borello, M. D. L. Dalla Vedova, G. Jacazio,

M. Sorli, A Prognostic Model for Electro-

hydraulic Servovalves, Annual Conference of

the Prognostics and Health Management

Society, San Diego, CA, USA, 2009.

[6] L. Pace, M. D. L. Dalla Vedova, P. Maggiore,

S. Facciotto, Numerical methods for the

electromagnetic modelling of actuators for

primary and secondary flight controls,

Computational Science and Systems

Engineering, Vol.58, pp. 126-133, 2016. ISSN:

1790-5117

[7] P. Moreton, Industrial Brushless Servomotors,

Newnes, January 2000.

[8] S. Chattopadhyay, M. Mitra, S.Sengupta,

Electric Power Quality, Springer, Cap. 12.

[9] M. D. L. Dalla Vedova, P. Maggiore, L. Pace,

A. Desando, Evaluation of the correlation

coefficient as a prognostic indicator for

electromechanical servomechanism failures,

International Journal of Prognostics and

Health Management, Vol.6, No.1, 2015. ISSN:

2153-2648.

[10] M. H. Rashid, Power electronics handbook, 3rd

Edition, Butterworth-Heinemann, 2011.


E-ISSN: 2224-350X 106 Volume 12, 2017

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Numerical Modelling of Sinusoidal Brushless Motor for … · 2017-05-12 · modelling of the PMSM for electromagnetic aerospace actuator systems for future diagnostic and prognostic