NGHIEN CUTU - TRAO Ddl
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^ BO DIEU KHIEN MCT CHONG LAC CO BU MA SAT CHO CAU TRUC KHI THAY DOI CHIEU DAI CAP NANG TAI
AN ANTI-SWING FUZZY CONTROLLER WITH FRICTION COMPENSATION FOR BRIDGE CRANES: CHANGING ROPE LENGTH
IVinh Luang Mien Trudng Dai hgc Giao thdng Van tai
T6M TAT
Trong linh vuc cong nghiip, xdy dung vd giao thdng van tdi, cdu true dugc sir dung rdt rpng rdi vd la doi tugng phi tuyen manh, chiu tdc dpng lan bai nhiiu ma sdt. Mpt bp dieu khiin chong ldc tdi, CO bu thdnh phdn ma sdt, dam bdo cho cdu true luon bdm theo quy dao dat ciia vi trixe con khi thay doi chiiu ddi ddy cdp, trin ca so logic ma dugc trinh bdy cu the trong bdi bdo ndy. Kit qud mo phong tren Matlab cho thdy ro nhirng iru diim vuot trpi ciia bp dieu khien ma co bu thdnh phdn ma sdt khi so sdnh vai bp diiu khiin khdc - bp dieu khiin ma khong bit ma sdt, bp diiu khien PID.
Tir khoa: Cdu true, chong ldc, diiu khiin ma, bii ma sdt, thay doi chiiu ddi cdp ndng tdi.
]i: ABSTRACT
In the field of an industry, contraction and transportation, bridge crane is widely used and is a strong nonlinear object, is strongly influenced by friction noise. An anti-swing controller with the firction compensation, guarantees that the bridge crane is always tracking the reference trajectories
of the trolley position as varying rope length, based on fuzzy logic is clearly proposed in this paper.
Simulation results in the Matlab show clearly the superior advantages of the fuzzy controller with friction compensation for nonlinear bridge crane model, as compared with these other controllers
-fuzzy controller without friction compensation, PID controller.
Keywords: Bridge crane, anti-swing, fuzzy controller, friction compensator, changing rope
length. ^
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1. BAT \ .\> DE
Ngay nay, cau true dngc six dung rat phd biln de nang ha va van chuyen vat heu. Chiing dugc sir dung rdng rai trong cac nha may, cac cdng trinh xay dung va cdng trinh giao thdng.
Trong tit ca cac lmh vuc ung dung, hoat dgng phd bien nhat cua cau true la van chuyen tai tir vi tri nay ddn vi tri khac. Hinh 1 md ta chuyen dgng cua can true trong he tga do 2D - Oxy, gdm di chuyen ciia xe con va chuyen ddng nang ha tai.
Cd ba yeu td het sue quan trgng ddi vdi cac hoat ddng ciia cau true, dd la: Tdc do di chuyen, do chinh xac va an toan. Tiiy theo tung ung dung ma mdt he cau true can phai dap iing dugc eae cae tieu chi boat ddng nay nhung an toan la mdt ddi hdi bat budc. Ngoai ra, khi hoat ddng, tai ciia cau true thudng bi dao ddng, dieu nay ciing anh hudng den do an toan va gay khd khan cho viec dieu khien chuyen ddng chinh xae cfiu true.
1G(«., y j
Hinh L Md hinh chuyen ddng cdu true trong hi tpa dp 2D
Cau true la mot ddi tugng phiic tap cd tinh phi tuyen manh. Hien da cd nhidu nghien Cliu nham tim ra phucmg an dieu khien va van hanh cau true mdt each hieu qua [1-14]. Cac bd didu khien phan hoi trang thai hay theo luat PID [10-14], PID kdt hgp vdi logic md [1,4], pro ehinh dinh thdng sd [5] da thu dugc mdt sd thanh cdng nhit dinh. Phuong an didu khidn phan hdi trang thai he ciu true [10,13], hay ap dung bd dieu khien tdi uu LQL (Lmear Quadratic Regulation) [3,8] ciing td ra kha hieu qua. Tit
ca cac bd didu khidn nay ddu dugc thidt ke dna tren md hinh tuydn tinh ciia cau true va van tffli tai dao dgng cua tai khi xe con di chuyen hay khi thay ddi chieu dai day cap. Ciing da cd mdt so nghien ciiu de c ^ den tinh dgng hgc phi tuyra cua cau true theo hudng ap dung ham dieu khiea Lyapunov [16], hay nguyen ly dieu khien tdi im phi tuyen [9], nguyen ly dieu khien trugt [2], k^
hgp dieu khien trucrt vdi logic md [15], hay sir dung mang na-ron [6], tuy nhien. eac thuat toan nay ddi hdi khdi lugmg edng viec tinh toan Imi va eiing mdi chi de cap den tae dgng cua nhiai ma sat ddi vdi di chuyen cua xe con [7,10], ma ehua xet tdi su thay ddi chieu dai cap nang tai.
Bai bao nay trinh bay ve mgt cau tiuc dieu khien can true don gian nhimg rat hieu qua tren ea sd logic md, cd tinh toan bii nhieu ma sat xuat hien trong he thdng. Bd dieu khien nay giup xe con chuyen ddng chinh xac den vi tri dat khi phep thay ddi chieu dai cap nang tai va tri^
tieu dugc dao dgng ciia tai trong thdi gian ngan, ddng thdi han ehe dugc tac dgng eua ma sat dai ehat lugng dieu khien he thdng bang khau tinh toan bu ma sat d ^ tren logic md.
2. MO HL\B DONG LlTC HOC CUA HE CAU TRUC
2.1. Xay dung md hinh dong lire hoc cua he can true
De dieu khien cau true chuydn dpng ehinh xac den vi tri mong mudn trong khdng gian lam viec \ a triet tieu dugc dao ddng tai, thi viec xay dimg chinh xac md hinh ddng luc hoc cua can true la dieu hdt sue quan trgng. Khao sat chuyen dgng cua ciu true Irong he tga do 2D-Oxy, nhu hinh 1, trong do: x{t) la \i tri cua xe con di chuyen theo phmmg Ox, l(t) la chi^u dai cap nang tai theo phirong Oy, coi sgi cap la thanh ciing va cd khdi lugng khong dang ke, a(t) la gdc lac ciia tai xung quanh phucmg thing diing, m^ va m^. tuong iing la khdi lugng xe cfflt
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NGHIEN ctfu-TRAO DOI
va khdi lugng tai, mH la khdi lugng co cau treo tai, F^
va F| lan lugt la luc di chuyen xe con va luc nang tai, F^.
la luc ma sat anh hudng den di chuyen cua xe con tren thanh ram, bd qua anh hudng ciia luc ma sat tai ca cau tdi nang ha tai.
Md hinh ddng luc hge eiia he can true dugc xac dinh theo nguyen ly Lagrange [11,3,7]:
[!iij+!nQ)x+mQ{ma)l+mJ{zosa)ii+2mQ{<:osa)ld-mJ{ma)d^ =F^ -Fj m(.(sino;)x+{ffl(,+%)i-?ng/ff^-mcgcosa=/' ^Ij m(,/{cosa)i+(fflg/^ +/)a+2m5iid:+fflgg/an a=0
Trong dd: I la md men quan tinh eua tai; g la gia tdc trgng trudng; i,/,i2r tuong iing la tdc do di chuyen Clia xe con, tdc do nang tai va tdc do gdc lac cua tai.
Tien hanh dat cac bien trang thai:
Xj = x{i) X2 = l(.t) x^ = a(t) x^ = x,X5 = /,X(, = d:, va dat tin hi$u dieu khienM, = F^,U2 = F , , khi dd, phuang trinh ddng lue hgc ciia he cau true cd the dugc bieu dien trong khdng gian trang thai va cho phep ta dl dang xay dimg dugc md hinh ddng luc hgc ciia he cau true tren Matlab.
2.2. Xay dung mo hinh ma sat cho h§ cau true Ma sat xuit hien nhu mdt luc tiep tuyen giiia I hai be mat tiep xiie trong cac he chuyen ddng. Hau het thanh phin ma sat la phi tuyen va chiing phu thudc vao miic do cudng biie chuyen ddng nhu vi tri tiep xiic, j dae tinh bd mat tiep xiic, van tde di chuyen, dau bdi
\ tron... Ma sat tdn tai dudi hai dang chinh: Ma sat tinh ,va ma sat ddng. Trong md hinh ma sat tiiih [17,10,7], lire ma sat la ham ciia tdc do di chuyen ma dien hinh la , bdn d ^ g CO ban: Ma sat Coulumb, ma sat Stiction, ma
^ sat nhdt, hieu iing Stribeck. Cae md hinh ma sat tiiih J chua xet tdi hudng di chuyen va chua bao ham cae anh J hudng ddng nhu hien tugng tre, eae di chuyen nhd...
.Chinh vi v^y, trong thuc te, ddi vdi cac chuyen ddng , cua he cau true ngudi ta thudng ap dung md hinh ma
\ sat dgng LuGre nhu la mgt chgn lira phu hgp de danh ,gia cac tac ddng ciia luc ma sat len he thdng [17,7,10]:
Ff =<T(,z+ffi — - ^ o . v \ dt
gfy)=lF, HK-F,)e dz _ _\v\ . _
-(V/V5XV/V5)
^ ( v )
V^o
(2)
Trong dd: a^ la he sd ciing; o, la he sd tat dan; a^ la he sd ket dinh; F^
la lgc ma sat Coulumb; F^ la lire ma sat Stiction; v la tdc do Stribeck.
Hinh 2. Ddc tinh md hinh ma sdt ddng trong hi cdu triAc
Trong thue te khdng phai liic nao ciing xac dinh dugc bd thdng sd eua md hinh ma sat, bd thdng sd nay duge tinh toan bang thirc nghiem, do dae nen gay ra sai sd ldn,... Vi vay, mgt phuang phap nhan dang true tuy§n luc raa sat he can true dua tren md hinh md Takagi-Sug- eno-Kang (TSK) dd bii lai cac tac ddng Clia nd len he thdng dugc de xuat ap dung trong bai bao nay.
3.THIET KE BO DIEU K H I E N CAU TRUC CHONG L A C CO BU MA SAT KHI THAY DOI CHIEU DAI CAP 3.1. Cau triic he thong dieu khien cau true chong lie co bu ma sat khi thay doi chieu dai cap
Khi xem xet eau true chiu anh hudng ciia ma sat va yeu can dieu khien "^
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cau true vira di chuyen chuyen xe con theo phucmg ngang, dong thcri co the thay doi chieu dai cap nang tai theo phuang diing, ta de xuat cau true bg dieu khien cau true chong lac co bu ma sat khi thay doi chieu dai cap nhu hinh 3.
Hinh 3. Sado khoi he thong dieu khiin cdu true co bit ma sdt
Trong do: x^(t) va I/t) la vi tri xe con va chiSu dai cap yen cau; x(t), l(t) va a(t) la vi tri xe con, chiSu dai cap va goc ldc tai do dupc khi van hanh cau true.
Bg dieu khien cau true dugc thi^t k^ dira tren h? logic ma, co dae diSm chinh sau:
Thii nhat, do la sir dung ba ca cbi suy diln ma FIE - Fuzzy Inference Engine (FIE bam vi tri, FIE nang tai va FIE giam ISc), eimg vai cac kh6i kk hgp (khdi kit hgp vi tri, khdi k6t hgp nang tai) ii tag ra tin hieu dilu khiln la lire di chuyin xe con (kit hgp FIE bam vi tri vai FIE giam 1 Jc) va lyc nang tai (kit hgp FIE nang tai vai FIE giam ISc) nhSm dam bao dua tai den vj tri mong muln (vi tri xe con va do cao nang hang yeu chn) dam bao dao dgng tai la triet tieu frong thoi gian ngin.
Thu hai, la sir dung khau uoc Iugng ma sat TSK de tinh toan bii thanh phin ma sat xuit hien trong he cau true dua tren mo hinh ma TSK, nham han chl anh hucmg ciia thanh phin ma sat den chit lugng he thing dilu khiln.
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3.2. Xay dung cac cff che suy dien mff FIE va khau uffc luong ma sat TSK
Ca ba ca che suy dien FIE bam vi tri, FIE nang tai, FIE giam lac deu co hai dau vao la sai lech VI tri/goc lac (Ex, EI. Ea), toe do sai lech vi tri/goc lac (DEx, DEI, DEa), va mgt diu ra la liic tac dong ien xe con FX, luc nang tai FL, luc hieu chinli FC de giam dao dpng cho tai khi xe con di chuyen ciing nhu khi nang lai.
Thuc hien ma hoa bien dau vao va biln dau ra vai 7 lap md NL, NM, NS, Z, PS, PM, PL, sii dung ham lien thuoc lam giac. Miln gia tri vat Ii ciia cac bien dau vao/ra dugc chgn nhu sau: Exe[-I,I]. D£.xe[-250.250], FXe[-75,751:
Ele[-I,I], DEle[-55,5]. FLe[-I00,100]; Eae [-1 5,1,5], DEae[-I0.I0],FCe[-10,10].
Dira trcn nguyen lac dieu khiln xe con bam Iheo quy dao dat nhinig dam bao chlng ldc tai ngay ca khi chilu dai cap thay dli. la tiln banh xay dung 49 Iuat dieu khien md tuang ung cho timg ca che suy dien nliu trong bang I Iheo dang sau:
If (Ee IS A) and (DEe is B) then fPF is C). trong do: A, B, C = (PL, PM, PS, Z, NS.
NM, NL); Ee=|Ex. El. Ea|: DEe={DEx. DEI.
Dea!;FF={FX, FL. FC}
Thuc hien giai md theo phuang phap diem trung binh trpng lam. la thu dupc cac gia trj rd dau ra tuang ung vdi 3 co chl suy diln mcr Fx-track, Fl-track, Fx-correct= Fl-correcl.
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Ket hgp cac tin hieu dau ra ciia 3 ca che suy dien md lai vdi nhau, ta thu dugc cac tin hieu tac ddng len he cau true theo bidu thiic (3):
F^^KFT'^'^^KF"'""''
cho nhu sau: m,^ ^ 2[kg], m^, = 0.25[kg], m ^ j - 0.15[kg], I = 0.001[kgm^], 1 = 0.25-l[m], x - 0 - l [ m ] , a = ±10°~±0.2[rad]
De kiem chung va danh gia chat lugng cua he thdng dieu khien cau true da dugc de xuat trong hinh 5, ta tien hanh md phdng he thdng tren Matlab (hinh 4) vdi 3 bd dieu khien, do la:
(1) - Bd dieu khien md vdi khau udc lugng ma sat TSK (ky hieu la FLC-TSK), (2) - Bd didu khien md khdng cd khau udc lugng ma sat TSK (ky hieu la FLC) va (3) - Bd dilu khidn PHTT dua tren luat PID [10,13].
F, = K,F;"'"' +K;^Fr (3) Vdi K^ K^^ Kj K^^ la cac hSng so cd gia tri: K^-1, K^„=8-13, K , - l , K,„=l-2
Tiep theo ta di xay dung khau uoc lugng ma sat TSK. Khau udc lugng ma sat can true cd hai dau vao la vi tri xe con x va tdc do di chuyen cua nd, mdt dau ra la luc ma sat udc lugng dugc / . Thuc hien md hda 2 dau vao X, DX va 1 dau r a / b 5 n g 7 tap md NB, NM, NS, Z, PS, PM, PB, su dung ham lien thudc hinh tam giac cho cac tap md dau vao, ham singleton cho bd md hda dau ra, xay dung 49 luat rad cho khau udc lugng nay nhu trong bang 2 theo dang sau:
If (X IS M) and (DX is N) then (FF is V), trong dd: M, N, V = {NB, NM, NS, Z, PS, PM, PB}
Lua chgn giai md trung binh trong tam, khi do ta thu dugc dau ra ciia khau udc lugng la lire ma s a t / . Dua vao luc ma sat udc Iugng nay, ta tien hanh bu thanh phan ma sat xuat hien trong cau tryc.
3.3. Mo phdng v^ danh gia ket qua Khao sat can true co thdng sd dugc
Hinh 4. Sa dd md phdng he thong diiu khiin cdu true kht cd thdnh phdn ma sdt
Tien hanh md phdng vdi 3 trudng hgp van hanh cau true, do la: Trudng hgp (1) - thay ddi vi tri xe con va chieu dai cap khdng ddi, tnrdng hgp (2) - giii nguyen vi tri xe con va thay ddi chieu dai cap nang tai, trudng hgp (3) - Thay ddi ddng thdi vi tri xe con va chieu dai cap nang tai.
Ket qua md phdng d hinh 5 cho thay dao ddng cua tai chiu anh hudng ldn cua di chuyen xe con va thanh phan ma sat. Bd dieu khien FLC- TSK cho dap ung vi tri xe con va chieu dai cap nang tai bam dugc theo gia tri dat, thdi gian qua do ngan (<3[s]), khdng cd do qua dieu chinh (hoac rat nhd), khdng cd sai lech tihh (hoac rat nho) va dao ddng cua tai vdi bidn do vki be (<0.02[rad]) va tit hoan toan sau thdi gian rat ng4n (<5[s]), cho du xe con hay ca cau nang tai lam viec d d c ' ^
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lap, ddng thdi. Bd dieu khidn FLC, mac dii cd dap ung chidu dai nang tai tdt nhung dap ung vi tri cua xe con lau han so voi FLC-TSK va xuit hien sai lech bam vi tri ciia xe con do thanh phan ma sat gay ra, hon niia tai dao ddng vdi bien dp ldn hon va khdng tk hoan toan khi xe con dugc yeu cau thay ddi vi tri bdc dd hang nhidu lkn trong thdi gian ngin. Trong khi bo didu khi^n PI/PID cd thdi gian qua do ldn, tdn tai sai lech tfeh ddi vdi ca dap iing vi tri xe con va chieu dai cap, ludn tdn tai dao ddng khdng tit cua tai vdi bien do kha ldn(>0.1[rad]).
Nhu vay, trong ca 3 truang hgp ta thSy bd digu khidn FLC-TSK cho chat lugng dik khidn tdt nhit, thd hien d cac chi tieu: Thdi gian qua dp nhd, khdng cd dp qua dieu chinh (ho^
rit nhd), khdng cd sai lech tinh (neu cd ciing rSt nhd) va dao dong cua tai vdi bien do rat nhd, tat hoan toan sau thdi gian rat ngan cho du xe con hay ca ciu nang tai lam viec ddc lap/ddng thai.
Ket qua md phdng dugc danh gia va tdng hgp trong bang 3.
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Hinh 5. Kit qud mo phong he thdng (1- Gid tri ddt, 2- FLC-TSK, 3- FLC, 4- PI/PlD)
Chi tieu danh gia Thdi gian tang
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Thdi gian qua do/
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Ket qua md phdng cho thay: Bd diSu khidn FLC-TSK vdi su kdt hgp linh hoat cua ba ca che suy dien md cung vdi bd udc lugng thanh phan ma sat cho chat lugng tdt han bd dieu khien FLC (khdng cd bii ma sat), hay bg dieu khien PI/PID. Bd didu khidn FLC-TSK cho phep vfn hanh can true mdt each linh boat; Vua di chuyen xe den vi tri mong mudn, vua nang ha tai den dg cao yeu cau ma van dam bao triet tieu dupc dao ddog ciia tai sau thdi gian ngan. Han niia, cau tnic bg didu khidn FLC-TSK cd bd sung kh^u udc lupng ma sat nen loai bd dugc ca ban su anh hudng ciia thanh phan ma sat xuat hien trong cau true, qua dd nang cao chat lugng dieu khien cau true, dam bao an toan van hanh, tang hieu qua khai thac sii dung cau true, gdp phan mang lai lgi ich kinh td to ldn cho ngudi dung.<*
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Ngay nhan bai: 16/4/2015 Ngay phan bien: 11/5/2015
Tai lieu tham khao:
[ 1 ]. Amanpreet Kaur, Priyahansha, Shashiprabha Kumari, Tanvi Singh, Position Control of Overhead Cranes Usingjuzzy Controller, International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, 2014.
[2].Shibly Ahmed AL-Samarraie, Bashar Fateh Midhat, Sliding Mode Controller Design for a Crane Container System,UCCCE,2(ilA.
[3].J. Jafari, M. Ghazal, M. Nazemizadeh, A LQR Optimal Method to Control the Position of an Overhead Crane, Intemational Joumal of Robotics and Automation, 2014.
[4].A. K. Pal and R, K. Mudi, An Adaptive PD-Type FLC and Its Real Time Implementation to Overhead Crane Control, Intemational Association of Scientific Innovation and Research, 2013.
[5].M.Naze;miza.de;h, A PID Tuning Method for Tracking Control of an Underactuated GantryCrane,\JmveTsal Joumal of Engineering Mechanics, 2013.
[6].CHEN Zhi-mei, MENG Wen-jim, ZHANG Jing-gang, Intelligent NN anti-swing control for bridge crane, J. Cent. South Univ., 2012.
[7] Quang hieu ngoa, Tnmg tinh tranb, Keum-shik hongc, Anti-sway control of container cranes in the presence of friction. International Joumal of Innovative Management, Information and Production, 2012.
[8].Shebel Asad, Maazouz Salahat, Design of Fuzzy PD-Controlled Overhead Crane System with Anti-Swing Compensation, S. ASAD ET AL Engineering, 2011.
[9].Mahan Mahrueyan and Hamid Khaloozadeh, Designing a Nonlinear Optimal Anti-Sway Controller for Container Crane Systems, International Conference on Circuits, System and Simulation, 2011.
[lOj.Jadranko Matu, Fetah Koloni, Friction compensation of gantry crane model based on the B-spUne neural compensator, 14th Intemational Power Electronics and Motion Control Conference, 2010.
[UJ.Hahn Park, Dongkyoung Chwa, andKeum-Shik Hong,/4Fee(/6flcil./«eanzarion Control of Container Cranes • varying rope length, Intemalional Joumal of Control Automation and Systems, 2007.
[12]. Khalid L. Sorensen, William Singhose, Stephen Dickerson, A controller enabling precise positioning and sway reduction in bridge and gantry cranes. Control Engineering Practice 15, 2007.
[13]. Z.N. Masoud, A.H. Nayfeh, and N.A. Nayfeh, Sway reduction on quayside container cranes using delayed feedback controller: simulations and experiments, Joumal of Vibration and Control 11,2005.
[14].Yong-Seok Kim, Keum-Shik Hong, and Seung-Ki Sul, Anti-Sway Control of Container Cranes:
Inclinometer, Observer, and State Feedback, International Journal of Control Automation and Systems, 2004.
[15]. Diantong Liu, Jianqiang Yi, Dongbin Zhao, Wei Wang, Adaptive sliding mode fuzzy control for a two-dimensional overhead crane, Mechatronics 15,2005.
[16], Y. Fang, E. Zergeroglu, Nonlinear coupling control laws for overhead crane system, lEEE/ASME Transaction on Mechatronics, 2003.
[17].H. Olsson, K.J. Astrom, C. Canudas de Wit, M. Gafvert, P.Lischinsky, Friction Models And Friction Compensation, European Journal of Control, 1998.
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