Control system. Electrical engineering
Abstract— This paper describes the design of feedback
linearization and fuzzy PI controllers for the maglev guiding
system of linear elevator. The controllers so designed based on
the nonlinear control techniques are applied to control the gap
of permanent magnet synchronous linear motor (PMLSM)
with the aim of improving the vertical thrust and control the
horizontal vibration and noise in the process of elevator
operation. Matlab modeling of this system is used in this paper.
The simulation result of the entire system are presented in this
paper.
Key words: Maglev Guiding System, Fuzzy PI Control,
Nonlinear control, Linear Elevator, Feedback Linearization
I. INTRODUCTION
ONIENTIONAL elevators consist of an elevator car in
a shaft operated by a rope, which is mounted on a
traction sheave. The mechanical guiding of such
elevators is well-known. Usually, slideways or roller guides
are used. However, compared with non-contact solutions,
the conventional lead frame has many disadvantages. Since
more and more high- rise buildings occur in world, the
efficiency of passenger transport become more important.
The higher the speed is, the more deteriorated the effect is.
Conventional rail require lubrication and regular
maintenance. The improved non-contact rail can get higher
comfort through subtractive the audible noise and
controlling the oriented stiffness[1][2].
The conventional elevator guide shoes prone to car
vibration when the elevator is running at high-speed. The
elevator vibration is one of the concerns in engineering
circles, it should be said that mechanical and electrical
reasons can be individually or jointly caused the vibration of
elevator system. Suspension technologies has brought the
technological innovations, the planform and stereogram of
placement for the maglev guiding device can been seen as in
Fig.1and Fig.2.
The elevator external disturbances and non-linear friction
for elevator guide shoes has a larger impact, such as, when
the elevator is running at low speed, such as leveling or
maintenance parking, a slow-fast phenomena will be occur
This work is supported by Liaoning Province Education Department Fund #L2010404.
Qing Hu is with the School of Electrical Engineering, Shenyang University of Technology, China (e-mail: aqinghu@163.com).
Mingliang Hao is with the School of Electrical Engineering, Shenyang
University of Technology, China (e-mail: haomingliang100@163.com). Hao Liu is with the School of Electrical Engineering, Shenyang
University of Technology, China (e-mail: liuhaosunyi@126.com).
sometimes, in severe cases, even a high-frequency vibration
and vibration noise will appear, this time it has led to
elevator car panels resonance in fact, which the comfort of
the elevator riding is seriously affected. Therefore, magnetic
levitation technology is applied to elevator guide shoes to
restrain the car disturbance and vibration problems. In the
elevator is running, the stability of air gap for liner motor is
particularly important, it can be affects the magnitude of the
propulsion force, using magnetic levitation guide shoes, by
controlling its current, the air gap of the magnetic levitation
(also called the air gap of linear motor) is controlled[3-6].
II. SYSTEM DESCRIPTION AND MODELING
According to Newton's second law, suppose the gravity
and the linear motor thrust balance with each other and
obtain the equations of motion:
( ) ( ) ( ) ( )tFiFtFtm DK , +−= δδ (1)
Fuzzy PI Control of Maglev Guiding System based on Feedback
Linearization
Qing Hu , Mingliang Hao , Hao Liu,
C
Fig. 1: Linear elevator with maglev guiding system
Fig. 2: Stereogram of linear elevator with maglev guiding system
1213978-1-4244-8738-7/11/$26.00 c©2011 IEEE
where , )(tδ , F(i, ), and FK(t)and FD(t) is the air gap
length, differential of air gap, electromagnetic force, another electromagnetic force, and external disturbance force,
respectively.
Due to the resistance in the electromagnet and the rail has
been ignored, the reluctance of magnetic circuit composed
of electromagnets and maglev rail focused on the air gap
between the two, the effective air-gap reluctance as follows:
A R
0μ
δ = (2)
where 0 and A is permeability of the vacuum and
cross-section of the air gap respectively.
The pulling force of the electromagnetic force is given by
( ) ( )
( )t tiAN
iF 2
22 0
4 ,
δ
μ δ −= (3)
which N and ( )ti is the number of winding turns and the current of single maglev device.
( ) ( ) ( )
( ) ( )
( ) ( )t
t
tiAN ti
t
AN tRitu δ
δ
μ
δ
μ 2
2 0
2 0
22 −+= (4)
Math model of a single electromagnetic device is obtained
as follow:
( ) ( ) ( ) ( )
( ) ( )
( )
( ) ( ) ( )
( ) ( )
( ) ( )−+=
−=
+−=
t t
tiAN ti
t
AN tRitu
t
tiAN iF
tFiFtFtm
δ δ
μ
δ
μ
δ
μ δ
δδ
2
2 0
2 0
2
22 0
DK
42
4 ,
,
(5)
where 4
2 0 AN
k μ
= and [ ]T321 xxx=x , the state
variable δ=1x , δ=2x ix =3 , and output of system
1xy == δ are chosen, then nonlinear state function is
obtained
( ) ( )
=
+++−=
1
KD
1
2
2
3
2
3
2
1
0
0
2
0
0
xy
m
tF
m
tF u
k
xx
x
m
k
x
x
x
x
(6)
where ( )
m
tFK can be seen as the disturbance as
( ) m
tFD .
III. CONTROLLER DESIGN
A. Feedback Linearization
State variable vector is chosen as follow,
[ ] T
1
3 21
T 321 −==
x
x
m
k xxzzzz (7)
then the state function of system can be derived[7]
[ ] ==
+=+=
Cz
BAzzz
001
1
0
0
000
100
010
y
vv (8)
Nonlinear voltage feedback control principle is given by
( ) ( ) v x
mx Rxvxxu
3
1 3 −=+= βα (9)
B. PI State feedback Controller Design
The definition of deviation e(t) is given by
( ) expyyte −= (10)
where y is the actual output of the system. From the state
space function (8), yexp is defined as expected output of the
system. By integration of the system deviation p can be
derived
( )= t
ttep 0
d . (11)
then derivative of p is obtained
( ) ( ) expytetp −== Cz (12)
By equation (8) and (12) together form the augmented
system, its open-loop state equation is derived
[ ]=
− ++=
p y
y v
p
z C
Bz
C
Az
0
0
000
0
exp (13)
1214 2011 Chinese Control and Decision Conference (CCDC)
where augmented system is controllable.
In order to achieve arbitrary pole placement, the following
state feedback control law is chosen as follow:
[ ]= p
Kv z
K I (14)
where the state feedback gain vector K is defined
[ ]210 KKK=K (15)
and KI is the integral coefficient is set as follow:
( )+++= t
tteKzKzKzKv 0
I322110 d (16)
C. Fuzzy PI Controller Design
After linearization in order to eliminate the ignored
factors, which impact on the system, this paper adopts the
fuzzy PI control method to design controller.
Fuzzy control principle and membership function is seen
as Tab.1 and Fig.3, respectively.
IV. SIMULATION
Reference maglev model and fuzzy PI control are
proposed, the entire system is comprised of the above two
parts. Matlab Simulink of system is seen as Fig.4 to Fig.6,
respectively.
The parameters of the magnetic levitation system for
single maglev device are: A = 0.50×0.50m2, N = 400 turns,
= 0.003m, FK = 5000N, M = 500kg. The simulation results
are shown in Fig.7, 8, 9, 10 and 11. Fig.7 is given and sensed
air gap of single maglev device without external
disturbance; the air gap error of maglev system can be
reduced rapidly.
TAB. 1: FUZZY CONTROL LAW
EC
E
NB NM NS ZO PS PM PB
NB
NM
NS
ZO
PS
PM
PB
PB
PB
PM
PM
PS
PS
ZO
PB
PB
PM
PM
PS
ZO
ZO
PM
PM
PM
PS
ZO
NS
NM
PM
PS
PS
ZO
NS
NM
NM
PS
PS
ZO
NS
NS
NM
NM
ZO
ZO
NS
NM
NM
NM
NB
ZO
NS
NS
NM
NM
NB
NB
Fig. 3: Membership function
Fig. 4: Maglev device model
Fig. 5: Fuzzy PI control model
Fig. 6: Single maglev system model
Fig. 7: The air gap of single maglev device (without external
disturbance)
2011 Chinese Control and Decision Conference (CCDC) 1215
Fig.8 and Fig.9 are external disturbance force and
response of the maglev force, respectively. The disturbance
force at 350N is added to the single maglev device started at
t = 0.45s, and ended at t = 0.5s, respectively. Fig.10 is the
acceleration of maglev device.Fig.11 is the air gap of single
maglev device added the external disturbance.
V. CONCLUSION
This paper deals with control design of the maglev
guiding system in linear elevator. Based on the control
requirements that is robustness and following behaviors of
maglev device.
Feedback linearization is used in maglev device.
Meanwhile, the fuzzy PI controller is designed. Simulation
results have shown that the built controller achieves good
performance with robustness.
REFERENCES
[1] Morishita M, Akashi M.Electromagnetic Non-contact Guide System
for Elevator Cars [C]. The Third International Symposium on Linear Drives for Industry Applications, Nagano, Japan, October 2001, pp.
416-419. [2] Inaba H, Shigeta M.,Ando T, ect. Attitude control system of a
super-high speed elevator car based on magnetic guides [J]. Industrial
Electronics, Control and Instrumentation, 1994, 2, pp. 1028 – 1033. [3] M. Miyatake, T. Koseki, S. Sone. Evaluation of Operational
Performance in Ropeless Elevator Systems[J].Journal of The Japan Society of Applied Electromagnetic and Mechanics, 1997,Vol. 5, No.
3, pp. 49-55.
[4] Benedikt Schmülling, Oliver Effing, Kay Hameyer. State Control of an Electromagnetic Guiding System for Ropeless Elevators [C].
Power Electronics and Applications, 2007 European Conference , 2007, pp. 1-10.
[5] Benedikt Schmulling, Rudiger Appunn, and Kay Hameyer.
Electromagnetic guiding of vertical transportation vehicles: state control of an over-determined system [C]. Proceeding of the 2008
International Conference on Electrical Machines, 2008, pp.1-6. [6] K. Yoshida, S. Moriyama, X. Zhang. Contactless Elevator Motion
Control in Ropeless Linear Elevator [J].2003 National Convention
Record, IEE Japan, 5-084, pp.130. [7] R. Appunn, B. Schmulling and K. Hameyer. Electromagnetic Guiding
of Vertical Transportation Vehicles: Experimental Evaluation [J]. IEEE Transactions on Industrial Electronics, 2009, pp.1109-1117.
Fig. 8: External disturbance force
Fig. 9: Response of maglev force
Fig. 10: Acceleration of maglev device
Fig. 11: The air gap of single maglev device (added the external disturbance)
1216 2011 Chinese Control and Decision Conference (CCDC)
<< /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Gray Gamma 2.2) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Error /CompatibilityLevel 1.6 /CompressObjects /Off /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJDFFile false /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.0000 /ColorConversionStrategy /LeaveColorUnchanged /DoThumbnails true /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams true /MaxSubsetPct 100 /Optimize false /OPM 0 /ParseDSCComments false /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo false /PreserveFlatness true /PreserveHalftoneInfo true /PreserveOPIComments false /PreserveOverprintSettings true /StartPage 1 /SubsetFonts false /TransferFunctionInfo /Remove /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true /Algerian /Arial-Black /Arial-BlackItalic /Arial-BoldItalicMT /Arial-BoldMT /Arial-ItalicMT /ArialMT /ArialNarrow /ArialNarrow-Bold /ArialNarrow-BoldItalic /ArialNarrow-Italic /ArialUnicodeMS /BaskOldFace /Batang /Bauhaus93 /BellMT /BellMTBold /BellMTItalic /BerlinSansFB-Bold /BerlinSansFBDemi-Bold /BerlinSansFB-Reg /BernardMT-Condensed /BodoniMTPosterCompressed /BookAntiqua /BookAntiqua-Bold /BookAntiqua-BoldItalic /BookAntiqua-Italic /BookmanOldStyle /BookmanOldStyle-Bold /BookmanOldStyle-BoldItalic /BookmanOldStyle-Italic /BookshelfSymbolSeven /BritannicBold /Broadway /BrushScriptMT /CalifornianFB-Bold /CalifornianFB-Italic /CalifornianFB-Reg /Centaur /Century /CenturyGothic /CenturyGothic-Bold /CenturyGothic-BoldItalic /CenturyGothic-Italic /CenturySchoolbook /CenturySchoolbook-Bold /CenturySchoolbook-BoldItalic /CenturySchoolbook-Italic /Chiller-Regular /ColonnaMT /ComicSansMS /ComicSansMS-Bold /CooperBlack /CourierNewPS-BoldItalicMT /CourierNewPS-BoldMT /CourierNewPS-ItalicMT /CourierNewPSMT /EstrangeloEdessa /FootlightMTLight /FreestyleScript-Regular /Garamond /Garamond-Bold /Garamond-Italic /Georgia /Georgia-Bold /Georgia-BoldItalic /Georgia-Italic /Haettenschweiler /HarlowSolid /Harrington /HighTowerText-Italic /HighTowerText-Reg /Impact /InformalRoman-Regular /Jokerman-Regular /JuiceITC-Regular /KristenITC-Regular /KuenstlerScript-Black /KuenstlerScript-Medium /KuenstlerScript-TwoBold /KunstlerScript /LatinWide /LetterGothicMT /LetterGothicMT-Bold /LetterGothicMT-BoldOblique /LetterGothicMT-Oblique /LucidaBright /LucidaBright-Demi /LucidaBright-DemiItalic /LucidaBright-Italic /LucidaCalligraphy-Italic /LucidaConsole /LucidaFax /LucidaFax-Demi /LucidaFax-DemiItalic /LucidaFax-Italic /LucidaHandwriting-Italic /LucidaSansUnicode /Magneto-Bold /MaturaMTScriptCapitals /MediciScriptLTStd /MicrosoftSansSerif /Mistral /Modern-Regular /MonotypeCorsiva /MS-Mincho /MSReferenceSansSerif /MSReferenceSpecialty /NiagaraEngraved-Reg /NiagaraSolid-Reg /NuptialScript /OldEnglishTextMT /Onyx /PalatinoLinotype-Bold /PalatinoLinotype-BoldItalic /PalatinoLinotype-Italic /PalatinoLinotype-Roman /Parchment-Regular /Playbill /PMingLiU /PoorRichard-Regular /Ravie /ShowcardGothic-Reg /SimSun /SnapITC-Regular /Stencil /SymbolMT /Tahoma /Tahoma-Bold /TempusSansITC /TimesNewRomanMT-ExtraBold /TimesNewRomanMTStd /TimesNewRomanMTStd-Bold /TimesNewRomanMTStd-BoldCond /TimesNewRomanMTStd-BoldIt /TimesNewRomanMTStd-Cond /TimesNewRomanMTStd-CondIt /TimesNewRomanMTStd-Italic /TimesNewRomanPS-BoldItalicMT /TimesNewRomanPS-BoldMT /TimesNewRomanPS-ItalicMT /TimesNewRomanPSMT /Times-Roman /Trebuchet-BoldItalic /TrebuchetMS /TrebuchetMS-Bold /TrebuchetMS-Italic /Verdana /Verdana-Bold /Verdana-BoldItalic /Verdana-Italic /VinerHandITC /Vivaldii /VladimirScript /Webdings /Wingdings2 /Wingdings3 /Wingdings-Regular /ZapfChanceryStd-Demi /ZWAdobeF ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 150 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages false /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /ColorImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 15 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 15 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 150 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages false /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /GrayImageDict << /QFactor 0.76 /HSamples [2 1 1 2] /VSamples [2 1 1 2] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 15 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 15 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 600 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /Description << /CHS <FEFF4f7f75288fd94e9b8bbe5b9a521b5efa7684002000410064006f006200650020005000440046002065876863900275284e8e55464e1a65876863768467e5770b548c62535370300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c676562535f00521b5efa768400200050004400460020658768633002> /CHT <FEFF4f7f752890194e9b8a2d7f6e5efa7acb7684002000410064006f006200650020005000440046002065874ef69069752865bc666e901a554652d965874ef6768467e5770b548c52175370300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c4f86958b555f5df25efa7acb76840020005000440046002065874ef63002> /DAN <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> /DEU <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> /ESP <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> /FRA <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> /ITA (Utilizzare queste impostazioni per creare documenti Adobe PDF adatti per visualizzare e stampare documenti aziendali in modo affidabile. I documenti PDF creati possono essere aperti con Acrobat e Adobe Reader 5.0 e versioni successive.) /JPN <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> /KOR <FEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020be44c988b2c8c2a40020bb38c11cb97c0020c548c815c801c73cb85c0020bcf4ace00020c778c1c4d558b2940020b3700020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002e> /NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken waarmee zakelijke documenten betrouwbaar kunnen worden weergegeven en afgedrukt. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.) /NOR <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> /PTB <FEFF005500740069006c0069007a006500200065007300730061007300200063006f006e00660069006700750072006100e700f50065007300200064006500200066006f0072006d00610020006100200063007200690061007200200064006f00630075006d0065006e0074006f0073002000410064006f00620065002000500044004600200061006400650071007500610064006f00730020007000610072006100200061002000760069007300750061006c0069007a006100e700e3006f002000650020006100200069006d0070007200650073007300e3006f00200063006f006e0066006900e1007600650069007300200064006500200064006f00630075006d0065006e0074006f007300200063006f006d0065007200630069006100690073002e0020004f007300200064006f00630075006d0065006e0074006f00730020005000440046002000630072006900610064006f007300200070006f00640065006d0020007300650072002000610062006500720074006f007300200063006f006d0020006f0020004100630072006f006200610074002000650020006f002000410064006f00620065002000520065006100640065007200200035002e0030002000650020007600650072007300f50065007300200070006f00730074006500720069006f007200650073002e> /SUO <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> /SVE <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> /ENU (Use these settings to create PDFs that match the "Recommended" settings for PDF Specification 4.0) >> >> setdistillerparams << /HWResolution [600 600] /PageSize [612.000 792.000] >> setpagedevice