research article modeling and simulation of control...

Research ArticleModeling and Simulation of Control ActuationSystem with Fuzzy-PID Logic Controlled BrushlessMotor Drives for Missiles Glider Applications

Murali Muniraj and Ramaswamy Arulmozhiyal

Department of Electrical and Electronics Engineering Sona College of Technology Salem 636005 India

Correspondence should be addressed to Murali Muniraj muralimunrajgmailcom

Received 20 April 2015 Revised 5 September 2015 Accepted 14 September 2015

Academic Editor Patricia Melin

Copyright copy 2015 M Muniraj and R Arulmozhiyal This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

A control actuation system has been used extensively in automotive aerospace and defense applications The major challengesin modeling control actuation system are rise time maximum peak to peak overshoot and response to nonlinear system withpercentage error This paper addresses the challenges in modeling and real time implementation of control actuation system formissiles glider applications As an alternative fuzzy-PID controller is proposed inBLDCmotor drive followed by linkagemechanismto actuate fins in missiles and gliders The proposed system will realize better rise time and less overshoot while operating inextreme nonlinear dynamic system conditions Amathematical model of BLDCmotor is derived in state space formThe completecontrol actuation system is modeled in MATLABSimulink environment and verified by performing simulation studies A realtime prototype of the control actuation is developed with dSPACE-1104 hardware controller and a detailed analysis is carried outto confirm the viability of the proposed system

1 Introduction

Brushless DC motor drive is used extensively in processindustries robotics aerospace and home appliance Indefense gliders andmissiles are used to assail rivals Amotioncontroller is realized to control fins of missiles and gliders toreach their target for which a BLDC motor drive is used tocontrol fins BLDCmotor has features of protracted perform-ing viability high dynamic response and efficiency BLDCmotor response is the challenge task to control position finsin desired direction with reference to the steering commandBLDC motor offers efficient speed torque characteristics andclosed loop control techniques which is a cause to use motorin motion control applications [1] Nasri et al presented themathematical model construction of a brushless DC motorvia MATLABSimulink [2] to view real time performance ofmotor in nonlinear conditions A power electronics switchinginverter is used to drive BLDC motor for control actuationsystem The PWM-generation logic is to switch inverterto drive BLDC motor depending on error generator from

controller To acquire feedback signals a quadrature encodermodel is used to acquire rotor position information of BLDCmotor to controller [3 4] Modeling of controller is primarytask of actuation system to maintain optimum responsevarious command inputs The conventional PID controlleris used in many industries even though delivery of positionresponse is poor for nonlinear type of system [5 6] Theconventional PID control had been implemented in BLDCmotor drive But these controllers suffer fromdrawbacks lackof performance in nonlinear system and more rise time withoscillatory response [7ndash9]

Recently as alternative to PID controller a fuzzy basedcontrol technique is considered for BLDC motor drive tooptimize gain values in systematic approach [10ndash12] Theproposed fuzzy technique includes self-tuning response tooptimize gain values of controller for different commandinputs

Fuzzy logic inference system has human intelligence innature and is associated with rule based system successfullyapplied in control applications [13] The following are virtues

Hindawi Publishing Corporatione Scientific World JournalVolume 2015 Article ID 723298 11 pageshttpdxdoiorg1011552015723298

2 The Scientific World Journal

AC RectifierL

CPWM

inverter

PWMmodulator

Fuzzylogiccontroller

e120596ref

120596m

iref

d

dt

Referencecurrent

generator

120579

iaref

ibref

icref

ia

ib

ic

BLDCmotor

Shaftencoder

supply

Figure 1 Block diagram of proposed setup

of fuzzy control (i) improved stability (ii) less sensitivity toload dynamics (iii) simple control configuration and (iv) lowcost and more time

Ko explained application of fuzzy logic PI controller incontrolling shaft position of a motor [12] Todic et al [8]implemented PID control techniques in BLDC motor forelectromechanical actuation applications The servo-basedactuators are designed to control fins surfaces through plan-etary gear system and linkage mechanism such as wingsand fins for aerodynamic control and its steering The FCAScontrols four actuators and associated control drive systemwith integrated electronics into a ring that matches themold outer line of the missile The main objective of thispaper is to model fin control actuation system using fuzzy-PID controller in missiles glider applications The completesystem is modeled with MATLABSimulink environmentThe proposed system is validated through a real time testbench dSPACE controller cp1104

2 Modeling of BLDC Motor Drive

Theproposed systemBLDCmotor drive for control actuationsystem with fuzzy-PID control is modeled using MAT-LABSimulink and overview of blocks is shown in Figure 1

21 BLDC Motor Modeling BLDC motor terminal voltageequation can be represented in (1) and derived as state spacemodel equations and simulated in MATLAB toolbox [14]

119881119886= 119877119886119868119886+ 119871119886

119889119894119886

119889119905+ 119872119886119888

119889119894119887

119889119905+ 119872119887119888

119889119894119888

119889119905+ 119890119886

119881119887= 119877119887119868119887+ 119871119887

119889119894119887

119889119905+ 119872119886119888

119889119894119886

119889119905+ 119872119887119888

119889119894119888

119889119905+ 119890119887

119881119888= 119877119888119868119888+ 119871119888

119889119894119888

119889119905+ 119872119886119888

119889119894119887

119889119905+ 119872119887119888

119889119894119886

119889119905+ 119890119888

(1)

where 119877119886-119887 is resistance per phase equal to all phases 119871

119886-119887is inductance per phase equal to all phases 119872

119886119888and 119872

119887119888are

mutual inductance For BLDC motor net effect value will beZero 119894

119886 119894119887 and 119894

119888are stator currentphase 119881

119886 119881119887 and 119881

119888are

the phase voltage of the winding

Table 1 Hall and back EMF signals

ha hb Hb EMF119886

EMF119887

EMF119888

0 0 0 0 0 00 0 1 0 minus1 +10 1 0 minus1 +1 00 1 1 minus1 0 +10 0 0 +1 0 minus10 0 1 +1 minus1 00 1 0 0 +1 minus10 1 1 0 0 0

Motor parameters torque and Electromagnetic Force(EMF) of BLDC motor in trapezoidal nature are calculatedin (2) in which 119862

119900and 119862V are friction torque in static and

dynamic conditions and 119879119897is load torque of the motor [15ndash

17]

119890119886= 119891119886(120579)119870119890120596

119890119887= 119891119887(120579)119870119890120596

119890119888= 119891119888(120579)119870119890120596

119879119890 = 119879119897minus 119862119900minus 119862V

(2)

The Final Output power is developed by motor

119875 = 119879119890 lowast 120596 (3)

where 120596 is Angular Velocity of the motor in radians persecond and 119875 is total power output

The motor parameter such as stator resistance induc-tance and back EMF constant parameter implicates controlresponse of motor The motor parameters are responsiblefor maximum overshoot unsteady state with more transientresponse which reduces time response of control actuationsystem To overcome the above drawbacksmotor gain param-eters need to be tuned using a conventional PID controllerwhich is not self-tuned and compactable for time varyingsystem For better dynamic response a fuzzy-PID controller isproposed to optimize gain parameters as a self-tuned systemwhich is diverse with input command signal The BLDCmotor parameters are modeled with reference to FaulhaberMotor K 3564 series parameters from their data sheet andpresented as in the Appendix [18] The required parametersof BLDC motor are taken as configurable parameters andmodeled using state space representation of MATLABmodelas shown in Figure 2

22 Modeling of Inverter Circuit BLDC Motor Driver isIGBT based inverter circuitry and operates with switchingPWM signal as input and generates three-phase voltage todrive BLDC motor The three hall sensors are placed at 120electrical degrees in rotor and acquire the rotor positioninformation as a feedback to the controllerThree hall sensorswith eight combinations generate hall signals with 120-electrical-degree sensor phasing for six input combinationsTable 1 representsHall Signals representation of our proposedmotor model with corresponding EMF signals [19]

The Scientific World Journal 3

Tload

1

4

1

2

3

4

TL

dT

A

B

C

x998400 = Ax + Bu

y = Cx + Du

State space

P

P

P 120579e

120579e

120579e

wm

we

we

eabc

eabc

iabc

iabc

iabc

120579e we120601998400rabc

BEMF flux Product

x

Te

Te

The HallHall

Hall effect sensor

sum

Ua

Ub

Uc

Eabc

3

5

2

dVab

dVbc

Figure 2 Mathematical model of BLDC motor in state space equation

The inverter for BLDC motor drive is modeled usingpower electronics IGBT mathematical switches in MATLABas shown in Figure 3 The PWM switching current controltechnique is implemented as shown in Figure 3 comparinginput with relational operator to generate six PWM signalsto drive inverter of BLDC motor

23 Modeling of Encoder In modeling the control actuationsystem a quadrature encoder is implemented to acquire rotorposition information from BLDC motor as a feedback to thecontroller The shaft encoder model subsystem as shown inFigure 4 is attached to BLDCmotor shaftThis encoder blockwill give the informative output of quadrature encoder pulses119876119886and 119876

119887 which has velocity direction pulse frequency

and phase shifting position of rotor The shaft encoder pulsesare taken for computing the speed position and direction ofmotorThe entire computation is a triggered subsystemwhichis used to compute information of square wave coming fromencoder using MATLAB Simscape model [20]

3 Modeling of Conventional PID Controller

The conventional Proportional-Integral-Derivative (PID)controllers are used in immense control actuation applica-tions The PID controller has the ability to eliminate steady-state error through integral action as the output changes

corresponding to controller derivative action with respect toinput command signal The PID tuning method namely theZiegler-Nichols method confirms gain parameters needs toobtain the step response of the system [21]

The continuous control signal 119906(119905) of the PID controller[22ndash24] is given by

119906 (119905) = 119870119901119890 (119905) + (

1

119879119894

)int 119890 (119905) 119889119905 + 119879 (119889119905) (4)

where 119870119901is the proportional gain 119879

119894is the integral time

constant 119879119889is the derivative time constant and 119890(119905) is the

error signal The proportional integral and derivative termsenumerate to obtain desired output of the PID controller 119906(119905)as the output of PID-controller equation to be the final formof the PID algorithm is

119906 (119905) = 119870119901119890 (119905) 119889119905 + 119870

119894119890 (119905) 119889119905 + 119870

119889

119889

119889119905sdot 119890 (119905) (5)

where 119870119901is proportional gain a tuning parameter 119870

119894is

integral gain a tuning parameter 119870119889is gain a tuning

parameterAccording to (5) control signals calculated for conven-

tional PID gain parameters 119870119901 119870119894 and 119870

119889


Switch1

T

F

T

F

T

F

T

F

T

F

T

F

Switch Switch2

Switch3

[c1]

Goto5

[c]

Goto4

[b1]Goto3

[b]

Goto2

[a1]Goto1

[a]

Goto

12

Gain

Gain1

Gain2

From1

[a] [b] [c]

[c1][b1][a1]

From From2Switch4

From4

Switch5From5From3

0Constant3 Constant4 Constant5

Gate

11

02

03

2

++

+

++

+ + +

+minusminus

++

+minus

minus12

-K-

Vs

Vb VcVa

Figure 3 Inverter model for BLDC motor drive

1

2

1

u

Z

Solverconfiguration

S PS

Simulink-PSconverter

1

P

REF

Z

B

A

C

R

Incremental shaftencoder

RCS

Ideal angularVelocity

1

source

we

wm

f(x) = 0 Qa

Qb

Figure 4 Encoder model for BLDC motor drive


NB NM NS Z PS PM PB

minus1 minus066 minus033 0 033 066 +1

e(k) uFP(k minus 1)

e(k) uFP(k minus 1)

Figure 5 Membership functions for input and output variables

4 Modeling of Fuzzy-PID Controller

In fuzzy-PID controller modeling a variable of drive moduleis selected as input and output Here a speed error 119890(119896) andthe delayed feedback control signal 119906

119865119875(119896minus1) are considered

as the inputs [24ndash26]The output of the fuzzy-PID controllersis the gain 119865119870

119875 The fuzzy linguistic variable ldquo119890(119896)rdquo has

ranges positive large (PL) zero (ZE) and negative large (NL)with corresponding proportional membership function asshown in Figure 5 The fuzzy sets can be represented byuniversal limits minus1 +1 119865

119894 119894 = 1 2 and 119895 = 1 2 3 Their

corresponding membership functions can be symbolized by120583119865119895

(119890 119906119865119875

(119896 minus 1)) 119895 = 1 2The fuzzy controller is modeled using IF-THEN interfer-

ence rules

119877(119896) if 119890(119896) is 119865

1 and 119906

119865(119896 minus 1) is 119865119897

then 119865 is 119862119897119896for 119895 = 1 3 119897 = 1 3 119896 = 1 9

The output from fuzzy-PID controller is derived from (3) andits output parameters are negative very large (NVL) negativelarge (NL) negative medium (NM) and negative small (NS)and zero positive small (PS) positive medium (PM) positivelarge (PL) and positive very large (PVL) The same singletonmembership functions of Figure 5 are used similar to thefuzzy sets and corresponding rule is formed in Table 2

The final controller output is obtained from

119865119870119875= 120572119875(119890 (119896) 119906

119865119875(119896 minus 1)) (6)

For better control performance and simplicity structurea triangular shaped function is implemented as membershipfunction with limits (minus1 +1) a seven level is used for all inputand output variables

The fuzzy-PID controller is modeled inMATLABSimulinkenvironment with gains 119870

119901 119870119894 and 119870

119889which is shown in

Figure 6 and its corresponding rule viewer in Figure 7 toanalyze stability of the system

5 Gearhead Modeling

The fins of missiles will be actuated from BLDC motor shaftdrive through a planetary gearhead with gear ratio of 14 1 Aplanetary gear type has three wheels named Sun Carrier andRing in which the Ring and Carrier run anticlockwise withSun gear [27]

Table 2 7 times 7 rule base table for fuzzy-PID controller

119890 119906119865119875(119896 minus 1) NB NM NS ZO PS PS PB

NB NB NB NB NB NM NS ZONM NB NB NB NM NS ZO PSNS NB NB NM NS ZO PS PMZO NB NM NS ZO PS PM PBPS NM NS ZO PS PM PB PBPM NS ZO PS PM PB PB PBPB ZO PS PM PB PB PB PB

The planetary gear and its ratio are calculated usingequations below

120596119904= 2 (1 + 119904) 120596

119888

120596119903= (1 +

2119904

119904)120596119888

(7)

where 120596119904is Angular Velocity of Sun gear 120596

119888is Angular

Velocity of Carrier gear 120596119903is Angular Velocity of Ring gear

or Internal gear 119904 is gear ratioThe simulation of drive train model is modeled using

Simscape in which motor shaft is coupled with gearheadThis tool extends the fast capability in MATLABSimulinkenvironment in the future The gearhead is modeled usingSIM-DRIVELINE a tool ofMATLABwith reduction ratio forRing and Sun that is 14 1 as shown in Figure 8

6 Results of Simulation

The complete actuation system is modeled in MATLAB toverify simulation studies of the proposed system The MAT-LAB Simscape tools are used tomodel gear of motor and cor-responding physical parameters The results are confirmedby Faulhaber BLDC Motor K 3564 series specificationswith 38(1s) planetary gearheads that are referred to fromsupplementary materials I and II (in SupplementaryMaterialavailable online at httpdxdoiorg1011552015723298) AnIncremental Decoder is modeled using Simscape LibraryBlock to detect hall position sensor The rotor positionsignals to generate gate signals as per Table 1 Hall Signalsrepresentation to corresponding gate signals switches ofIGBT driver circuit The trapezoidal back EMF is modeledas a function of rotor position from encoder using back EMFconstant (119870119890)

61 PID Controller The control actuation system usingBLDC motor is modeled using PID controller The systemresponses are obtained from various command signals ThePID controller based actuation system is tested for 2100commands signals as shown in Figure 9 The PID controllerfor 2100 command signals has delay rise time (725ms) whichis critical for an actuation system For different operatingconditions of PID based control actuation system is unableto deliver better performance in nonlinear conditions forchanging load conditions and different commanded signalsTo compensate the demand of nonlinear controllers a fuzzy-PID is proposed


u

1

60

0611

Fuzzy

1Set

Saturation

2

Act

Discrete-timeintegrator2

Discrete-timeintegrator

U

CUe

e

E

CEminus1

minus

+

minus

minus

+ inferencesystem

-K- -K-

-K-

KTs

z minus 1

KTs

z minus 1

+ +++

+

+

1

kd1

kp1

Figure 6 Fuzzy-PID controller for BLDC motor drive

005

10

051

ece

minus1

minus1 minus1

minus05

minus05 minus05

0

05

1

u

Figure 7 Surface viewer of fuzzy-PID controller for BLDC drive

62 Fuzzy-PID Controller The control actuation systemusing BLDC motor is modeled using fuzzy-PID controllerSimulated BLDC motor parameters like speed back EMFgenerated and current of control actuation system are shownin Figure 10 for fuzzy-PID controller Fuzzy PID controllerreaches system load torque of 180mN-m with operationaltime of 48 milliseconds Fin control actuation angle analysis

is carried out for the performance of conventional PID con-troller and fuzzy-PID controller Figure 10 shows that fuzzy-PID controller has better performance than the conventionalone for BLDC motor drive response The drive fin controlactuation system response for fuzzy-PID controller and PIDcontroller is shown in Figure 11

7 Hardware Results and Verification

The Hardware results are verified for a proposed fuzzy-PID controller with DSPACE 1104 controller and a realtime controller The complete simulation model is simulatedin MATLAB environment Through control desk softwareMATLAB and dSPACE environment is interfaced to validateproposed systems stability for various load disturbances Thecontrol actuation system using BLDC motor with encoderand gearhead is modeled an interface with dSPACE con-troller test bench as shown in Figure 12

Figures 13(a) and 13(b) show the PWMs generated by thedSPACE controller which is given as input to drive the IGBTswitches with the switching frequency of 10 KHz Separateencoder has been modeled for 100 ppr From the QEP signals119876119886and 119876

119887 speed and position of motor shaft are calculated

using pulse count decoder block System builds with innerloop as current control and outer loop as speedpositioncontrol as shown in Figure 15 Current 119868dc is controlledthrough fixed PWMof 10KHz and it is limited from 6A peak


3

th2tl

1

V

1

Env

Mechanical

T

B

F

Torque

C

R

S

Planetary

p

V

Motion

Inertia2

Inertia1

Inertia

Drivelineenvironment

shaftgear

sensor sensor1

120591

120596Env

Figure 8 Gearhead modeling for control actuation system

Act-pulse countsSet-pulse counts

0

1000

2000

Num

ber o

f pul

se co

unts

002 004 006 008 01 012 014 016 018 020

minus1

minus05

0

05

1

Spee

d (r

pm)

002 004 006 008 01 012 014 016 018 020

times104

Ea

minus10

minus5

0

5

10

002 004 006 008 01 012 014 016 018 020

minus10

minus5

0

5

10

I a

002 004 006 008 01 012 014 016 018 020Time (sec)

Time (sec)

Time (sec)

Time (sec)

Figure 9 Position response of PID controller based control actua-tion system for 2100 counts

0500

1000150020002500

Num

ber o

f pul

se co

unts

times104

minus1

minus05

0

05

1

Spee

d (r

pm)

002 004 006 008 01 012 014 016 018 020Time (sec)

Ea

minus20

minus10

0

10

20

016004 006 008 01 012 014 018 020020Time (sec)

002 004 006 008 01 012 014 016 018 020Time (sec)

minus10

minus5

0

5

10

I a

002 004 006 008 01 012 014 016 018 020Time (sec)

Figure 10 Position response of fuzzy-PID controller based controlactuation system for 2100 counts


minus01

minus005

0

005

01

015

Ang

le (d

eg)

12 14 16 31 22 24 26 2818 2

Time (sec)

Desired angleAngle response

Angle response(fuzzy-PID controller)

(PID controller)

Figure 11 Angle response of PID and fuzzy-PID controller

Figure 12 Hardware setup of control actuation system

to minus6A peak Necessary hall signal decoding logic is builtin with the proposed system Feedback controller for bothcurrent and speedposition was developed with conventionalPID as well as fuzzy-PID controller A motion controller isdesigned using fuzzy-PID control as input is set as step inputfor 2100 counts

71 Speed Control Performance The result shows the speedcontrol of motor with inner loop current control for bothconventional PID and fuzzy-PID (see Figure 14) The closedloop speed with 10000 rpm of set speeds both conventionalPID starting response and fuzzy-PID starting response asshown in Figure 14 Fuzzy-PID controller performance hasbetter rise time with minimum peak to peak overshoot forthe desired speed

For step change of speed analysis is as shown in Figure 15the speed step rose from 5000 rpm into 10000 rpm at 005 secthen step down from 10000 rpm into 5000 rpm at 01 secAnalysis suggests that fuzzy performance is better than con-ventional controller in considering the settling errors From

(a)

(b)

Figure 13 PWM duty cycle generation for fuzzy-PID controllersignals

Fuzzy-PIDSet speed

Conventional PID

01501250075 0100500250Time (sec)

0

2000

4000

6000

8000

10000

12000

Spee

d (r

pm)

Figure 14 Step speed change (5000ndash10000ndash5000) rpm

the step change analysis fuzzy-PID improves the performanceof the actuation system compared with conventional PID

72 Position Control Performance The position control stepanalysis is carried out for control actuation system Figure 16shows the position control equivalence pulse counts of BLDC


Fuzzy-PID

0025 005 0075 01 0125 0150Time (sec)

minus15

minus1

minus05

0

05

1

15

Spee

d (r

pm)

times104

Set speedConventional PID

Figure 15 Speed reversal performances

Fuzzy-PIDSet-count

0150135009 0105 0120060045 007500300150Time (sec)

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

Conventional PID

Figure 16 Position control at 2100 pulse counts

motor with inner loop current control for both conventionalPID and fuzzy-PID Unit step change of fins movement for 1degree required is 2100 pulse counts from motor shaft withstep analysis as reference for desired 2100 pulse counts Thestep responses of conventional PID and fuzzy-PID are shownin Figure 16 From the experimental results it is observed thatconventional PID requires 75ms to settle with 115 of errorFuzzy-PID requires 525ms to reach the set target with 001of error

Further analyses of step change position control areshown in Figure 17 step change from pulse counts of 2100into 0 pulse counts The BLDC motor operates in reverse toreach the initial pulse count (0) and from the experimental

Table 3 Results of PID controller based control actuation system

Parameters Fuzzy PID Conventional PIDRise timemdash119879

119903(ms) 525 725

Settling timemdash119879119904(ms) 565 778

Deceleration timemdash119879119889(ms) 5024 53

Transient behavior Smooth OscillatoryPeak overshoot 27 13 error 001 115

Fuzzy-PIDSet-count

minus300

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

003 006 009 012 0150 021 024 027 03018Time (sec)

Conventional PID

Figure 17 Step change from 2100 to 0 pulse counts

results fin moves forward and reverse (to reach 0 pulsecounts) and required the same time to reach unit set-pulsecounts 50 for both conventional and fuzzy-PID controllersFigure 18 shows the step increment analysis of unit stepchange of fin from 1-degree to 2-degree equivalent pulsecounts of 2100 to 4200 pulse counts From the variousstep analyses fuzzy performance is better than conventionalcontroller with detailed step performance parameter of risetime peak overshoot and percentage error as presented inTable 3

8 Conclusion

A fuzzy-PID based control actuation system has been pro-posed with planetary gearhead modeling A self-tuningwith optimum gain parameter of fuzzy controller has beenemployed to control BLDC motor drive The position offins is controlled by controlling BLDC motor input voltageusing gains values An electronic commutation of BLDCmotor is used from the error between input and referencecommanded values Moreover a quadrature type encoderis used to sense accurate rotor position information andas a feedback controller An improved dynamic response


Table 4 Specifications of BLDC motor

S number Parameters Values1 Nominal voltage 24 volts2 Terminal resistance (phase to phase) 116Ohm3 Output power 101W4 Back EMF constant 2107mVrpm5 Torque constant 2012mNmA6 Rotor inertia 34 gcm2

7 Gearhead type 301 s

Fuzzy-PIDSet-count

0

525

1050

1575

2100

2625

3150

3675

4200

4725

Pulse

coun

ts

005 01 015 020 03025Time (sec)

Conventional PID


of BLDC motor drive has been achieved for a wide rangeof step response commanded values Experimental resultshave shown excellent performance of proposed fuzzy-PIDcontroller and are well demonstrated for uncertain nonlinearconditionsThe rise time of BLDCmotor drive for fuzzy-PIDcontroller is well within 525 (ms) In this way performanceof fuzzy technique attracts engineers and practitioners todevelop fuzzy based control actuation system in fins andglider application

Appendix

See Table 4

Conflict of Interests

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

Acknowledgment

The authors wish to thank the Defense Research Develop-mentOrganization (DRDO) for providing necessary funds tocarry out this work This project is supported through GrantAid-In Scheme

References

[1] T J E Miller Brushless Permanent Magnet amp Reluctance MotorDrives vol 2 Clarendon Press Oxford UK 2003

[2] M Nasri H Nezamabadi-Pour and M Maghfoori ldquoA PSO-based optimum design of PID controller for a linear brushlessDCmotorrdquoWorld Academy of Science Engineering and Technol-ogy vol 26 pp 211ndash215 2007

[3] M A Rahman ldquoSpecial section on permanent magnet motordrivesrdquo IEEE Transactions on Industrial Electronics vol 43 no2 p 245 1996

[4] D D Dhawale J G Chaudhari and M V Aware ldquoPositioncontrol of four switch three phase BLDC motor using PWMcontrolrdquo in Proceedings of the 3rd International Conference onEmerging Trends in Engineering and Technology (ICETET rsquo10)pp 374ndash378 Goa India November 2010

[5] L V Hongli D Peiyong C Wenjian and J Lei ldquoDirectconversion of PID controller to fuzzy controller method forrobustnessrdquo in Proceedings of the 3rd IEEE Conference onIndustrial Electronics andApplications (ICIEA rsquo08) pp 790ndash794IEEE Singapore June 2008

[6] S Enocksson Modeling in MathWorks Simscape by Building aModel of an Automatic Gearbox Uppsala University UppsalaSweden 2011

[7] A Rubaai M J Castro-Sitiriche and A Ofoli ldquoDSP-basedimplementation of fuzzy-PID controller using genetic opti-mization for high performance motor drivesrdquo in Proceedingsof the IEEE Industry Applications Conference 42nd AnnualMeeting (IAS rsquo07) vol 22 pp 1649ndash1656 NewOrleans La USASeptember 2007

[8] I Todic M Milos and M Pavisic ldquoPosition and speed con-trol of electromechanical actuator for aerospace applicationsrdquoTehnicki Vjesnik vol 20 no 5 pp 853ndash860 2013

[9] M Naidu T W Nehl S Gopalakrishnan and L WurthldquoKeeping cool while saving space andmoney a semi-integratedsensorless PM brushless drive for a 42-V automotive HVACcompressorrdquo IEEE Industry Applications Magazine vol 11 no4 pp 20ndash28 2005

[10] E Cerruto A Consoli A Raciti and A Testa ldquoFuzzy adaptivevector control of induction motor drivesrdquo IEEE Transactions onPower Electronics vol 12 no 6 pp 1028ndash1040 1997

[11] J L Silva Neto and H L Huy ldquoFuzzy controller with afuzzy adaptive mechanism for the speed control of a PMSMrdquoin Proceedings of the 23rd IEEE International Conference onIndustrial Electronics pp 995ndash1000 November 1997

[12] J S Ko ldquoRobust position control of BLDC motors usingintegral-proportional-plus fuzzy logic controllerrdquo IEEE Trans-actions on Industrial Electronics vol 41 pp 308ndash315 1994

[13] dSPACE dSPACE Userrsquos Guide Digital Signal Processing andControl Engineering dSPACE Paderborn Germany 2003

[14] J Goetz W Hu and J Milliken ldquoSensorless digital motorcontroller for high reliability applicationsrdquo in Proceedings ofthe 21st Annual IEEE Applied Power Electronics Conference andExposition (APEC rsquo06) pp 1645ndash1650 IEEE Dallas Tex USAMarch 2006


[15] L V Hongli L H D Peiyong C Wenjian and J Lei ldquoDirectconversion of PID controller to fuzzy controller method forrobustnessrdquo in Proceedings of the 3rd IEEE Conference onIndustrial Electronics andApplications (ICIEA rsquo08) pp 790ndash794IEEE Singapore June 2008

[16] S G Anavatti S A Salman and J Y Choi ldquoFuzzy + PID con-troller for robotmanipulatorrdquo in Proceedings of the InternationalConference on Computational Intelligence for Modelling Controland Automation and International Conference on IntelligentAgents Web Technologies and Internet Commerce p 75 IEEESydney Australia November-December 2006

[17] M T Soylemez M Gokasan and O S Bogosyan ldquoPositioncontrol of a single-link robot-arm using a multi-loop PIcontrollerrdquo in Proceedings of the IEEE Conference on ControlApplications vol 2 pp 1001ndash1006 IEEE Istanbul Turkey June2003

[18] Technical DataManual FaulhaberMotor Schonaich Germany2013

[19] M A Akcayol A Cetin and C Elmas ldquoAn educationaltool for fuzzy logic-controlled BDCMrdquo IEEE Transactions onEducation vol 45 no 1 pp 33ndash42 2002

[20] S K Awaze ldquoFour quadrant operation of BLDC motor inMATLABSIMULINKrdquo in Proceedings of the 5th InternationalConference on Computational Intelligence and CommunicationNetworks (CICN rsquo13) pp 569ndash573 Mathura India September2013

[21] B Subudhi A Kumar and D Jena ldquodSPACE implementationof fuzzy logic based vector control of induction motorrdquo inProceedings of the IEEE Region 10 Conference (TENCON rsquo08)Hyderabad USA November 2008

[22] T Kenjo and S Nagamori Permanent Magnet Brushless DCMotors Clarendon Press Oxford UK 1985

[23] C M Ong Dynamic Simulations of Electric Machinery UsingMATLABSIMULINK Prentice Hall PTR Englewood CliffsNJ USA 1st edition 1998

[24] F Rodriguez and A Emadi ldquoA novel digital control techniquefor brushless DCmotor drivesrdquo IEEE Transactions on IndustrialElectronics vol 54 no 5 pp 2365ndash2373 2007

[25] A Visioli ldquoTuning of PID controllers with fuzzy logicrdquo IEEProceedings Control Theory and Applications vol 148 no 1 pp1ndash8 2001

[26] B Subudhi A K Kumar andD Jena ldquodSPACE implementationof fuzzy logic based vector control of induction motorrdquo inProceedings of the IEEE Region 10 Conference (TENCON rsquo08)pp 1ndash6 Hyderabad India November 2008

[27] httpwwwmathworkscom

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



AC RectifierL

CPWM

inverter

PWMmodulator

Fuzzylogiccontroller

e120596ref

120596m

iref

d

dt

Referencecurrent

generator

120579

iaref

ibref

icref

ia

ib

ic

BLDCmotor

Shaftencoder

supply

Figure 1 Block diagram of proposed setup

of fuzzy control (i) improved stability (ii) less sensitivity toload dynamics (iii) simple control configuration and (iv) lowcost and more time

Ko explained application of fuzzy logic PI controller incontrolling shaft position of a motor [12] Todic et al [8]implemented PID control techniques in BLDC motor forelectromechanical actuation applications The servo-basedactuators are designed to control fins surfaces through plan-etary gear system and linkage mechanism such as wingsand fins for aerodynamic control and its steering The FCAScontrols four actuators and associated control drive systemwith integrated electronics into a ring that matches themold outer line of the missile The main objective of thispaper is to model fin control actuation system using fuzzy-PID controller in missiles glider applications The completesystem is modeled with MATLABSimulink environmentThe proposed system is validated through a real time testbench dSPACE controller cp1104

2 Modeling of BLDC Motor Drive

Theproposed systemBLDCmotor drive for control actuationsystem with fuzzy-PID control is modeled using MAT-LABSimulink and overview of blocks is shown in Figure 1

21 BLDC Motor Modeling BLDC motor terminal voltageequation can be represented in (1) and derived as state spacemodel equations and simulated in MATLAB toolbox [14]

119881119886= 119877119886119868119886+ 119871119886

119889119894119886

119889119905+ 119872119886119888

119889119894119887

119889119905+ 119872119887119888

119889119894119888

119889119905+ 119890119886

119881119887= 119877119887119868119887+ 119871119887

119889119894119887

119889119905+ 119872119886119888

119889119894119886

119889119905+ 119872119887119888

119889119894119888

119889119905+ 119890119887

119881119888= 119877119888119868119888+ 119871119888

119889119894119888

119889119905+ 119872119886119888

119889119894119887

119889119905+ 119872119887119888

119889119894119886

119889119905+ 119890119888

(1)

where 119877119886-119887 is resistance per phase equal to all phases 119871

119886-119887is inductance per phase equal to all phases 119872

119886119888and 119872

119887119888are

mutual inductance For BLDC motor net effect value will beZero 119894

119886 119894119887 and 119894

119888are stator currentphase 119881

119886 119881119887 and 119881

119888are

the phase voltage of the winding

Table 1 Hall and back EMF signals

ha hb Hb EMF119886

EMF119887

EMF119888

0 0 0 0 0 00 0 1 0 minus1 +10 1 0 minus1 +1 00 1 1 minus1 0 +10 0 0 +1 0 minus10 0 1 +1 minus1 00 1 0 0 +1 minus10 1 1 0 0 0

Motor parameters torque and Electromagnetic Force(EMF) of BLDC motor in trapezoidal nature are calculatedin (2) in which 119862

119900and 119862V are friction torque in static and

dynamic conditions and 119879119897is load torque of the motor [15ndash

17]

119890119886= 119891119886(120579)119870119890120596

119890119887= 119891119887(120579)119870119890120596

119890119888= 119891119888(120579)119870119890120596

119879119890 = 119879119897minus 119862119900minus 119862V

(2)

The Final Output power is developed by motor

119875 = 119879119890 lowast 120596 (3)

where 120596 is Angular Velocity of the motor in radians persecond and 119875 is total power output

The motor parameter such as stator resistance induc-tance and back EMF constant parameter implicates controlresponse of motor The motor parameters are responsiblefor maximum overshoot unsteady state with more transientresponse which reduces time response of control actuationsystem To overcome the above drawbacksmotor gain param-eters need to be tuned using a conventional PID controllerwhich is not self-tuned and compactable for time varyingsystem For better dynamic response a fuzzy-PID controller isproposed to optimize gain parameters as a self-tuned systemwhich is diverse with input command signal The BLDCmotor parameters are modeled with reference to FaulhaberMotor K 3564 series parameters from their data sheet andpresented as in the Appendix [18] The required parametersof BLDC motor are taken as configurable parameters andmodeled using state space representation of MATLABmodelas shown in Figure 2

22 Modeling of Inverter Circuit BLDC Motor Driver isIGBT based inverter circuitry and operates with switchingPWM signal as input and generates three-phase voltage todrive BLDC motor The three hall sensors are placed at 120electrical degrees in rotor and acquire the rotor positioninformation as a feedback to the controllerThree hall sensorswith eight combinations generate hall signals with 120-electrical-degree sensor phasing for six input combinationsTable 1 representsHall Signals representation of our proposedmotor model with corresponding EMF signals [19]


Tload

1

4

1

2

3

4

TL

dT

A

B

C

x998400 = Ax + Bu

y = Cx + Du

State space

P

P

P 120579e

120579e

120579e

wm

we

we

eabc

eabc

iabc

iabc

iabc

120579e we120601998400rabc

BEMF flux Product

x

Te

Te

The HallHall

Hall effect sensor

sum

Ua

Ub

Uc

Eabc

3

5

2

dVab

dVbc










119906 (119905) = 119870119901119890 (119905) + (

1

119879119894

)int 119890 (119905) 119889119905 + 119879 (119889119905) (4)





119906 (119905) = 119870119901119890 (119905) 119889119905 + 119870

119894119890 (119905) 119889119905 + 119870

119889

119889

119889119905sdot 119890 (119905) (5)


119894is




119889


Switch1

T

F

T

F

T

F

T

F

T

F

T

F

Switch Switch2

Switch3

[c1]

Goto5

[c]

Goto4

[b1]Goto3

[b]

Goto2

[a1]Goto1

[a]

Goto

12

Gain

Gain1

Gain2

From1

[a] [b] [c]

[c1][b1][a1]

From From2Switch4

From4

Switch5From5From3


Gate

11

02

03

2

++

+

++

+ + +

+minusminus

++

+minus

minus12

-K-

Vs

Vb VcVa


1

2

1

u

Z

Solverconfiguration

S PS


1

P

REF

Z

B

A

C

R


RCS


1

source

we

wm

f(x) = 0 Qa

Qb



NB NM NS Z PS PM PB


e(k) uFP(k minus 1)

e(k) uFP(k minus 1)








119894 119894 = 1 2 and 119895 = 1 2 3 Their


(119890 119906119865119875


ence rules

119877(119896) if 119890(119896) is 119865

1 and 119906

119865(119896 minus 1) is 119865119897

then 119865 is 119862119897119896for 119895 = 1 3 119897 = 1 3 119896 = 1 9



119865119870119875= 120572119875(119890 (119896) 119906

119865119875(119896 minus 1)) (6)



119901 119870119894 and 119870



5 Gearhead Modeling






120596119904= 2 (1 + 119904) 120596

119888

120596119903= (1 +

2119904

119904)120596119888

(7)


119888is Angular








u

1

60

0611

Fuzzy

1Set

Saturation

2

Act



U

CUe

e

E

CEminus1

minus

+

minus

minus

+ inferencesystem

-K- -K-

-K-

KTs

z minus 1

KTs

z minus 1

+ +++

+

+

1

kd1

kp1


005

10

051

ece

minus1

minus1 minus1

minus05

minus05 minus05

0

05

1

u










3

th2tl

1

V

1

Env

Mechanical

T

B

F

Torque

C

R

S

Planetary

p

V

Motion

Inertia2

Inertia1

Inertia


shaftgear

sensor sensor1

120591

120596Env



0

1000

2000

Num

ber o

f pul

se co

unts

002 004 006 008 01 012 014 016 018 020

minus1

minus05

0

05

1

Spee

d (r

pm)

002 004 006 008 01 012 014 016 018 020

times104

Ea

minus10

minus5

0

5

10

002 004 006 008 01 012 014 016 018 020

minus10

minus5

0

5

10

I a

002 004 006 008 01 012 014 016 018 020Time (sec)

Time (sec)

Time (sec)

Time (sec)


0500

1000150020002500

Num

ber o

f pul

se co

unts

times104

minus1

minus05

0

05

1

Spee

d (r

pm)

002 004 006 008 01 012 014 016 018 020Time (sec)

Ea

minus20

minus10

0

10

20

016004 006 008 01 012 014 018 020020Time (sec)

002 004 006 008 01 012 014 016 018 020Time (sec)

minus10

minus5

0

5

10

I a

002 004 006 008 01 012 014 016 018 020Time (sec)



minus01

minus005

0

005

01

015

Ang

le (d

eg)

12 14 16 31 22 24 26 2818 2

Time (sec)



(PID controller)






(a)

(b)


Fuzzy-PIDSet speed

Conventional PID

01501250075 0100500250Time (sec)

0

2000

4000

6000

8000

10000

12000

Spee

d (r

pm)





Fuzzy-PID

0025 005 0075 01 0125 0150Time (sec)

minus15

minus1

minus05

0

05

1

15

Spee

d (r

pm)

times104



Fuzzy-PIDSet-count

0150135009 0105 0120060045 007500300150Time (sec)

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

Conventional PID






119903(ms) 525 725




Fuzzy-PIDSet-count

minus300

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

003 006 009 012 0150 021 024 027 03018Time (sec)

Conventional PID



8 Conclusion






Fuzzy-PIDSet-count

0

525

1050

1575

2100

2625

3150

3675

4200

4725

Pulse

coun

ts

005 01 015 020 03025Time (sec)

Conventional PID



Appendix

See Table 4



Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Tload

1

4

1

2

3

4

TL

dT

A

B

C

x998400 = Ax + Bu

y = Cx + Du

State space

P

P

P 120579e

120579e

120579e

wm

we

we

eabc

eabc

iabc

iabc

iabc

120579e we120601998400rabc

BEMF flux Product

x

Te

Te

The HallHall

Hall effect sensor

sum

Ua

Ub

Uc

Eabc

3

5

2

dVab

dVbc










119906 (119905) = 119870119901119890 (119905) + (

1

119879119894

)int 119890 (119905) 119889119905 + 119879 (119889119905) (4)





119906 (119905) = 119870119901119890 (119905) 119889119905 + 119870

119894119890 (119905) 119889119905 + 119870

119889

119889

119889119905sdot 119890 (119905) (5)


119894is




119889


Switch1

T

F

T

F

T

F

T

F

T

F

T

F

Switch Switch2

Switch3

[c1]

Goto5

[c]

Goto4

[b1]Goto3

[b]

Goto2

[a1]Goto1

[a]

Goto

12

Gain

Gain1

Gain2

From1

[a] [b] [c]

[c1][b1][a1]

From From2Switch4

From4

Switch5From5From3


Gate

11

02

03

2

++

+

++

+ + +

+minusminus

++

+minus

minus12

-K-

Vs

Vb VcVa


1

2

1

u

Z

Solverconfiguration

S PS


1

P

REF

Z

B

A

C

R


RCS


1

source

we

wm

f(x) = 0 Qa

Qb



NB NM NS Z PS PM PB


e(k) uFP(k minus 1)

e(k) uFP(k minus 1)








119894 119894 = 1 2 and 119895 = 1 2 3 Their


(119890 119906119865119875


ence rules

119877(119896) if 119890(119896) is 119865

1 and 119906

119865(119896 minus 1) is 119865119897

then 119865 is 119862119897119896for 119895 = 1 3 119897 = 1 3 119896 = 1 9



119865119870119875= 120572119875(119890 (119896) 119906

119865119875(119896 minus 1)) (6)



119901 119870119894 and 119870



5 Gearhead Modeling






120596119904= 2 (1 + 119904) 120596

119888

120596119903= (1 +

2119904

119904)120596119888

(7)


119888is Angular








u

1

60

0611

Fuzzy

1Set

Saturation

2

Act



U

CUe

e

E

CEminus1

minus

+

minus

minus

+ inferencesystem

-K- -K-

-K-

KTs

z minus 1

KTs

z minus 1

+ +++

+

+

1

kd1

kp1


005

10

051

ece

minus1

minus1 minus1

minus05

minus05 minus05

0

05

1

u










3

th2tl

1

V

1

Env

Mechanical

T

B

F

Torque

C

R

S

Planetary

p

V

Motion

Inertia2

Inertia1

Inertia


shaftgear

sensor sensor1

120591

120596Env



0

1000

2000

Num

ber o

f pul

se co

unts

002 004 006 008 01 012 014 016 018 020

minus1

minus05

0

05

1

Spee

d (r

pm)

002 004 006 008 01 012 014 016 018 020

times104

Ea

minus10

minus5

0

5

10

002 004 006 008 01 012 014 016 018 020

minus10

minus5

0

5

10

I a

002 004 006 008 01 012 014 016 018 020Time (sec)

Time (sec)

Time (sec)

Time (sec)


0500

1000150020002500

Num

ber o

f pul

se co

unts

times104

minus1

minus05

0

05

1

Spee

d (r

pm)

002 004 006 008 01 012 014 016 018 020Time (sec)

Ea

minus20

minus10

0

10

20

016004 006 008 01 012 014 018 020020Time (sec)

002 004 006 008 01 012 014 016 018 020Time (sec)

minus10

minus5

0

5

10

I a

002 004 006 008 01 012 014 016 018 020Time (sec)



minus01

minus005

0

005

01

015

Ang

le (d

eg)

12 14 16 31 22 24 26 2818 2

Time (sec)



(PID controller)






(a)

(b)


Fuzzy-PIDSet speed

Conventional PID

01501250075 0100500250Time (sec)

0

2000

4000

6000

8000

10000

12000

Spee

d (r

pm)





Fuzzy-PID

0025 005 0075 01 0125 0150Time (sec)

minus15

minus1

minus05

0

05

1

15

Spee

d (r

pm)

times104



Fuzzy-PIDSet-count

0150135009 0105 0120060045 007500300150Time (sec)

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

Conventional PID






119903(ms) 525 725




Fuzzy-PIDSet-count

minus300

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

003 006 009 012 0150 021 024 027 03018Time (sec)

Conventional PID



8 Conclusion






Fuzzy-PIDSet-count

0

525

1050

1575

2100

2625

3150

3675

4200

4725

Pulse

coun

ts

005 01 015 020 03025Time (sec)

Conventional PID



Appendix

See Table 4



Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Switch1

T

F

T

F

T

F

T

F

T

F

T

F

Switch Switch2

Switch3

[c1]

Goto5

[c]

Goto4

[b1]Goto3

[b]

Goto2

[a1]Goto1

[a]

Goto

12

Gain

Gain1

Gain2

From1

[a] [b] [c]

[c1][b1][a1]

From From2Switch4

From4

Switch5From5From3


Gate

11

02

03

2

++

+

++

+ + +

+minusminus

++

+minus

minus12

-K-

Vs

Vb VcVa


1

2

1

u

Z

Solverconfiguration

S PS


1

P

REF

Z

B

A

C

R


RCS


1

source

we

wm

f(x) = 0 Qa

Qb



NB NM NS Z PS PM PB


e(k) uFP(k minus 1)

e(k) uFP(k minus 1)








119894 119894 = 1 2 and 119895 = 1 2 3 Their


(119890 119906119865119875


ence rules

119877(119896) if 119890(119896) is 119865

1 and 119906

119865(119896 minus 1) is 119865119897

then 119865 is 119862119897119896for 119895 = 1 3 119897 = 1 3 119896 = 1 9



119865119870119875= 120572119875(119890 (119896) 119906

119865119875(119896 minus 1)) (6)



119901 119870119894 and 119870



5 Gearhead Modeling






120596119904= 2 (1 + 119904) 120596

119888

120596119903= (1 +

2119904

119904)120596119888

(7)


119888is Angular








u

1

60

0611

Fuzzy

1Set

Saturation

2

Act



U

CUe

e

E

CEminus1

minus

+

minus

minus

+ inferencesystem

-K- -K-

-K-

KTs

z minus 1

KTs

z minus 1

+ +++

+

+

1

kd1

kp1


005

10

051

ece

minus1

minus1 minus1

minus05

minus05 minus05

0

05

1

u










3

th2tl

1

V

1

Env

Mechanical

T

B

F

Torque

C

R

S

Planetary

p

V

Motion

Inertia2

Inertia1

Inertia


shaftgear

sensor sensor1

120591

120596Env



0

1000

2000

Num

ber o

f pul

se co

unts

002 004 006 008 01 012 014 016 018 020

minus1

minus05

0

05

1

Spee

d (r

pm)

002 004 006 008 01 012 014 016 018 020

times104

Ea

minus10

minus5

0

5

10

002 004 006 008 01 012 014 016 018 020

minus10

minus5

0

5

10

I a

002 004 006 008 01 012 014 016 018 020Time (sec)

Time (sec)

Time (sec)

Time (sec)


0500

1000150020002500

Num

ber o

f pul

se co

unts

times104

minus1

minus05

0

05

1

Spee

d (r

pm)

002 004 006 008 01 012 014 016 018 020Time (sec)

Ea

minus20

minus10

0

10

20

016004 006 008 01 012 014 018 020020Time (sec)

002 004 006 008 01 012 014 016 018 020Time (sec)

minus10

minus5

0

5

10

I a

002 004 006 008 01 012 014 016 018 020Time (sec)



minus01

minus005

0

005

01

015

Ang

le (d

eg)

12 14 16 31 22 24 26 2818 2

Time (sec)



(PID controller)






(a)

(b)


Fuzzy-PIDSet speed

Conventional PID

01501250075 0100500250Time (sec)

0

2000

4000

6000

8000

10000

12000

Spee

d (r

pm)





Fuzzy-PID

0025 005 0075 01 0125 0150Time (sec)

minus15

minus1

minus05

0

05

1

15

Spee

d (r

pm)

times104



Fuzzy-PIDSet-count

0150135009 0105 0120060045 007500300150Time (sec)

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

Conventional PID






119903(ms) 525 725




Fuzzy-PIDSet-count

minus300

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

003 006 009 012 0150 021 024 027 03018Time (sec)

Conventional PID



8 Conclusion






Fuzzy-PIDSet-count

0

525

1050

1575

2100

2625

3150

3675

4200

4725

Pulse

coun

ts

005 01 015 020 03025Time (sec)

Conventional PID



Appendix

See Table 4



Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










NB NM NS Z PS PM PB


e(k) uFP(k minus 1)

e(k) uFP(k minus 1)








119894 119894 = 1 2 and 119895 = 1 2 3 Their


(119890 119906119865119875


ence rules

119877(119896) if 119890(119896) is 119865

1 and 119906

119865(119896 minus 1) is 119865119897

then 119865 is 119862119897119896for 119895 = 1 3 119897 = 1 3 119896 = 1 9



119865119870119875= 120572119875(119890 (119896) 119906

119865119875(119896 minus 1)) (6)



119901 119870119894 and 119870



5 Gearhead Modeling






120596119904= 2 (1 + 119904) 120596

119888

120596119903= (1 +

2119904

119904)120596119888

(7)


119888is Angular








u

1

60

0611

Fuzzy

1Set

Saturation

2

Act



U

CUe

e

E

CEminus1

minus

+

minus

minus

+ inferencesystem

-K- -K-

-K-

KTs

z minus 1

KTs

z minus 1

+ +++

+

+

1

kd1

kp1


005

10

051

ece

minus1

minus1 minus1

minus05

minus05 minus05

0

05

1

u










3

th2tl

1

V

1

Env

Mechanical

T

B

F

Torque

C

R

S

Planetary

p

V

Motion

Inertia2

Inertia1

Inertia


shaftgear

sensor sensor1

120591

120596Env



0

1000

2000

Num

ber o

f pul

se co

unts

002 004 006 008 01 012 014 016 018 020

minus1

minus05

0

05

1

Spee

d (r

pm)

002 004 006 008 01 012 014 016 018 020

times104

Ea

minus10

minus5

0

5

10

002 004 006 008 01 012 014 016 018 020

minus10

minus5

0

5

10

I a

002 004 006 008 01 012 014 016 018 020Time (sec)

Time (sec)

Time (sec)

Time (sec)


0500

1000150020002500

Num

ber o

f pul

se co

unts

times104

minus1

minus05

0

05

1

Spee

d (r

pm)

002 004 006 008 01 012 014 016 018 020Time (sec)

Ea

minus20

minus10

0

10

20

016004 006 008 01 012 014 018 020020Time (sec)

002 004 006 008 01 012 014 016 018 020Time (sec)

minus10

minus5

0

5

10

I a

002 004 006 008 01 012 014 016 018 020Time (sec)



minus01

minus005

0

005

01

015

Ang

le (d

eg)

12 14 16 31 22 24 26 2818 2

Time (sec)



(PID controller)






(a)

(b)


Fuzzy-PIDSet speed

Conventional PID

01501250075 0100500250Time (sec)

0

2000

4000

6000

8000

10000

12000

Spee

d (r

pm)





Fuzzy-PID

0025 005 0075 01 0125 0150Time (sec)

minus15

minus1

minus05

0

05

1

15

Spee

d (r

pm)

times104



Fuzzy-PIDSet-count

0150135009 0105 0120060045 007500300150Time (sec)

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

Conventional PID






119903(ms) 525 725




Fuzzy-PIDSet-count

minus300

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

003 006 009 012 0150 021 024 027 03018Time (sec)

Conventional PID



8 Conclusion






Fuzzy-PIDSet-count

0

525

1050

1575

2100

2625

3150

3675

4200

4725

Pulse

coun

ts

005 01 015 020 03025Time (sec)

Conventional PID



Appendix

See Table 4



Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










u

1

60

0611

Fuzzy

1Set

Saturation

2

Act



U

CUe

e

E

CEminus1

minus

+

minus

minus

+ inferencesystem

-K- -K-

-K-

KTs

z minus 1

KTs

z minus 1

+ +++

+

+

1

kd1

kp1


005

10

051

ece

minus1

minus1 minus1

minus05

minus05 minus05

0

05

1

u










3

th2tl

1

V

1

Env

Mechanical

T

B

F

Torque

C

R

S

Planetary

p

V

Motion

Inertia2

Inertia1

Inertia


shaftgear

sensor sensor1

120591

120596Env



0

1000

2000

Num

ber o

f pul

se co

unts

002 004 006 008 01 012 014 016 018 020

minus1

minus05

0

05

1

Spee

d (r

pm)

002 004 006 008 01 012 014 016 018 020

times104

Ea

minus10

minus5

0

5

10

002 004 006 008 01 012 014 016 018 020

minus10

minus5

0

5

10

I a

002 004 006 008 01 012 014 016 018 020Time (sec)

Time (sec)

Time (sec)

Time (sec)


0500

1000150020002500

Num

ber o

f pul

se co

unts

times104

minus1

minus05

0

05

1

Spee

d (r

pm)

002 004 006 008 01 012 014 016 018 020Time (sec)

Ea

minus20

minus10

0

10

20

016004 006 008 01 012 014 018 020020Time (sec)

002 004 006 008 01 012 014 016 018 020Time (sec)

minus10

minus5

0

5

10

I a

002 004 006 008 01 012 014 016 018 020Time (sec)



minus01

minus005

0

005

01

015

Ang

le (d

eg)

12 14 16 31 22 24 26 2818 2

Time (sec)



(PID controller)






(a)

(b)


Fuzzy-PIDSet speed

Conventional PID

01501250075 0100500250Time (sec)

0

2000

4000

6000

8000

10000

12000

Spee

d (r

pm)





Fuzzy-PID

0025 005 0075 01 0125 0150Time (sec)

minus15

minus1

minus05

0

05

1

15

Spee

d (r

pm)

times104



Fuzzy-PIDSet-count

0150135009 0105 0120060045 007500300150Time (sec)

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

Conventional PID






119903(ms) 525 725




Fuzzy-PIDSet-count

minus300

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

003 006 009 012 0150 021 024 027 03018Time (sec)

Conventional PID



8 Conclusion






Fuzzy-PIDSet-count

0

525

1050

1575

2100

2625

3150

3675

4200

4725

Pulse

coun

ts

005 01 015 020 03025Time (sec)

Conventional PID



Appendix

See Table 4



Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










3

th2tl

1

V

1

Env

Mechanical

T

B

F

Torque

C

R

S

Planetary

p

V

Motion

Inertia2

Inertia1

Inertia


shaftgear

sensor sensor1

120591

120596Env



0

1000

2000

Num

ber o

f pul

se co

unts

002 004 006 008 01 012 014 016 018 020

minus1

minus05

0

05

1

Spee

d (r

pm)

002 004 006 008 01 012 014 016 018 020

times104

Ea

minus10

minus5

0

5

10

002 004 006 008 01 012 014 016 018 020

minus10

minus5

0

5

10

I a

002 004 006 008 01 012 014 016 018 020Time (sec)

Time (sec)

Time (sec)

Time (sec)


0500

1000150020002500

Num

ber o

f pul

se co

unts

times104

minus1

minus05

0

05

1

Spee

d (r

pm)

002 004 006 008 01 012 014 016 018 020Time (sec)

Ea

minus20

minus10

0

10

20

016004 006 008 01 012 014 018 020020Time (sec)

002 004 006 008 01 012 014 016 018 020Time (sec)

minus10

minus5

0

5

10

I a

002 004 006 008 01 012 014 016 018 020Time (sec)



minus01

minus005

0

005

01

015

Ang

le (d

eg)

12 14 16 31 22 24 26 2818 2

Time (sec)



(PID controller)






(a)

(b)


Fuzzy-PIDSet speed

Conventional PID

01501250075 0100500250Time (sec)

0

2000

4000

6000

8000

10000

12000

Spee

d (r

pm)





Fuzzy-PID

0025 005 0075 01 0125 0150Time (sec)

minus15

minus1

minus05

0

05

1

15

Spee

d (r

pm)

times104



Fuzzy-PIDSet-count

0150135009 0105 0120060045 007500300150Time (sec)

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

Conventional PID






119903(ms) 525 725




Fuzzy-PIDSet-count

minus300

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

003 006 009 012 0150 021 024 027 03018Time (sec)

Conventional PID



8 Conclusion






Fuzzy-PIDSet-count

0

525

1050

1575

2100

2625

3150

3675

4200

4725

Pulse

coun

ts

005 01 015 020 03025Time (sec)

Conventional PID



Appendix

See Table 4



Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus01

minus005

0

005

01

015

Ang

le (d

eg)

12 14 16 31 22 24 26 2818 2

Time (sec)



(PID controller)






(a)

(b)


Fuzzy-PIDSet speed

Conventional PID

01501250075 0100500250Time (sec)

0

2000

4000

6000

8000

10000

12000

Spee

d (r

pm)





Fuzzy-PID

0025 005 0075 01 0125 0150Time (sec)

minus15

minus1

minus05

0

05

1

15

Spee

d (r

pm)

times104



Fuzzy-PIDSet-count

0150135009 0105 0120060045 007500300150Time (sec)

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

Conventional PID






119903(ms) 525 725




Fuzzy-PIDSet-count

minus300

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

003 006 009 012 0150 021 024 027 03018Time (sec)

Conventional PID



8 Conclusion






Fuzzy-PIDSet-count

0

525

1050

1575

2100

2625

3150

3675

4200

4725

Pulse

coun

ts

005 01 015 020 03025Time (sec)

Conventional PID



Appendix

See Table 4



Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Fuzzy-PID

0025 005 0075 01 0125 0150Time (sec)

minus15

minus1

minus05

0

05

1

15

Spee

d (r

pm)

times104



Fuzzy-PIDSet-count

0150135009 0105 0120060045 007500300150Time (sec)

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

Conventional PID






119903(ms) 525 725




Fuzzy-PIDSet-count

minus300

0

300

600

900

1200

1500

1800

2100

2400

Pulse

coun

ts

003 006 009 012 0150 021 024 027 03018Time (sec)

Conventional PID



8 Conclusion






Fuzzy-PIDSet-count

0

525

1050

1575

2100

2625

3150

3675

4200

4725

Pulse

coun

ts

005 01 015 020 03025Time (sec)

Conventional PID



Appendix

See Table 4



Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













Fuzzy-PIDSet-count

0

525

1050

1575

2100

2625

3150

3675

4200

4725

Pulse

coun

ts

005 01 015 020 03025Time (sec)

Conventional PID



Appendix

See Table 4



Acknowledgment


References































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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