TWO LINK ROBOT CONTROLLERS BASED ON FUZZY TYPE-2 AND HIGHER ORDER SLIDING MODE

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1 Iteratioal Joural Of Egieerig Ad Computer Sciece ISS:39-74 Volume Issue 5 May, 03 Page o TWO LIK OBOT COTOLLES BASED O FUZZ TPE- AD HIGHE ODE SLIDIG MODE Abstract Ali Pajeshahi, Assef Zare, Saeed Balochia * Departmet of Electrical Egieerig, Goabad Brach, Islamic Azad Uiversity, Goabad, Ira (pajeshahiali@yahoo.com)(saeed.balochia@gmail.com) I th paper, the multi-variable cotrol of a two-lik robot cosidered. Idustrial robots, such as robot of two degrees, are the high acceptace i idustry ad academic eviromets. They are also a classic problem i robotics for testig ad evaluatig the ew cotrollers. I th research, two cotrollers based o fuzzy type ad higher order sildig mode are employed for th case. The implemetatio of these cotrollers o robot models shows a proper trackig for each lik. Key words: -Lik obot- Higher Order Slidig Mode-Type- Fuzzy m m l l C C C S S OMECLATUE Mass of first lik Mass of secod lik Legth of first lik Legth of secod lik Agle of first lik Agle of secod lik Agular velocity of first lik Agular velocity of secod lik Agular acceleratio of first lik Agular acceleratio of secod lik cos( ) cos( ) cos( ) si( ) si( ) First lik torque Secod lik torque Ali Pajeshahi, IJECS Volume Issue 5 May, 03 Page o Page 57

2 ITODUCTIO The dyamics of the robot cost of two parts, the direct ad iverse dyamics []. Purpose of direct dyamics, to gai the mometum, velocity ad acceleratio of the robot tool holdig forces ad torques applied to the joits or irritatig, but the iverse dyamic modelig with kowledge of routes, velocities ad acceleratios of the robot tool, or mometa forces drivig the joits are calculated. Amog classical methods for the calculatio of dyamic robot models, methods, Lagrage, D'Alember method, ewto, Euler equatios, virtual work ad Hamilto []. owadays, may robots eed to work quickly ad efficietly, are used. Such as the use of robots o assembly lies, medical, machiig ad may other applicatios metioed. The use of idustrial robots i the productio process ad automatio idustry has grow cosiderably i recet decades. Most machie tool spidle apparatus used for the series chai kiematics. Due to the widespread use of dyamic structures, cotrol vital to the commet [3]. Cervates, i 00, the movemet of the robot arm doe by a PID cotroller [4-7]. Lopez et al., cosidered i 008, a proportioal cotroller, derivative ad itegral o a si degree of freedom parallel robot [8]. Cotroller of proportioal, derivative ad itegral are always used i differet idustrial lies. Aother brach of the robot ca be cotrolled o the refereces [9-] ca be see. Oe of the importat sues i desigig a robot cotroller desig restat to the ucertaity of the mass of such chage. obust cotrol theory, the slidig mode cotrol law to form a simple procedure could brig ito etece [0]. Because of the importace of usig a o-liear slidig mode cotroller that it has log bee oted. May systems have used th type of approach. efereces, a eample of th method widely used i egieerig scieces as a cotroller, a estimatio ad optimizatio are preseted. Oe of the mai difficulties that slidig mode cotroller o the way. There are chatterig, through the use of strategies that have bee proposed so far []. To reduce ad elimiate the classical slidig mode cotrol ca be used up. The super twt algorithm comes, data etry eed ot chage the slidig surface, ad hece, the algorithm suitable for may dyamic systems. I the year 993, Levat, itroduced secod order slidig mode i h paper [3]. The theory of fuzzy sets i 965 by Lotfi Ali Asker Zadeh, was itroduced [4]. I comple systems, they are faced with the challeges ad sues that are associated with reasoig ad decio makig, Fuzzy logic as a tool ca be employed. Select a system highly depedet o the compleity of its iteral systems. Fuzzy type sets i recet years could be a possible substitute for traditioal sets. They cosider the ucertaities of system dyamics [5-]. Medel, Wu, reviewed ad gives some beefit poits i their papers. Wu, also publhed a tutorial for traiig fuzzy type i MATLAB [, 3]. Th paper orgaized as follows: I Part, the dyamic equatios of the robot ad the direct dyamic solutio process. I Part 3, the slidig mode cotroller desiged i secod order, ad type- fuzzy logic described. I sectio 4, the simulatio doe i MATLAB-SIMULIK by ode45 solver ad fially i sectio 5, the paper cocluded. Dyamic Equatios ad Simulated obots Iverse dyamics equatios of the robot are described i detail i referece to the robot. Oly the fial equatios are give below. Fig. Schematic of two-lik series robot[] ml mll C m m l m l l S m l l S m l gc m m( l gc ) mll C mll S mlgc ml For a robot motio cotrol, it s eeded to kow the amout of torque required to achieve the desired movemet of the joit. Th approach, the so-called robot, called direct dyamics. A direct dyamic solutio of the robot, because of differetial operators, has bee associated with differet challeges. I th paper, the oliear equatios of robots, writte i MATLAB eviromet ad programmig techiques have bee used i SIMULIK. Figures ad 3 show the mai body of the robot model i SIMULIK. Ali Pajeshah,i IJECS Volume Issue 5 May, 03 Page o Page 573

3 Fig. Schematic model of the series robot by SIMMECHAICS i SIMULIK mai problem i the implemetatio of high order slidig mode icreasig demad for iformatio. Fig4. The secod-order slidig mode system[] Fig3. Joit modelig of multiple robots by meas of SIMMECHAICS Secod Order Slidig Mode Cotroller Desigig Cosider the followig Dyamic system, Sigle iput - sigle output: f ( ) u (), the desired output adu, the Cotrol iput. oliear fuctio f ( ) composed of two parts: determitic ad o-determitic. The aim of cotrol to maitai the state at zero ad for th purpose the slidig mode cotrol theory employ the surface Slip as the trackig error: S (3) The the Cotrol problem to remai o the surface s which equivalet to be S 0. Geerally, slidig mode cotrol composed of two mai parts. The first part called the equivalet cotrol has the phase slip whe the system ucertai. Th sectio of the slidig mode cotrol, said Holder. Although usig th cotroller ca alig the system i ucertaities. But the chatterig achieved by icreasig the cotrol effort ot admsible. Usig higher order slidig mode oe method of reducig uwated chatterig i slidig mode cotrol. Th method reta the advatage of the origial stadard methods (robustess), it also elimiates the Chatterig. The I th study, it s better to eglect the usig derivative products durig the solutio. For th reaso, the best algorithm for the desig of secod-order slidig mode cotrol of maipulator cotroller Super Twtig Which does ot use derivative of the slidig surface. The architecture of th method guaratees the robustess of cotrollig i the face of ucertaity: U Ueq k S sig( S) k sig( S) d,0 (4 Accordig to the relatios (), (3) ad (4), the supplier of the algorithm Super Twtig followed by: S k S sig S) k sig( S) d Give ( ) (5) S, Equatio (5) ca be epressed as the followig state equatios: k sig( ) ksig( ) (6) The mai advatage of th algorithm that it does ot require ay derivative iformatio from the slidig surface but oly asymptotic stability cosidered. For covergece i a fiite time, the followig criteria must be satfied. W 0 m 4 ( W ) ( W ) m 3 m (7) Ali Pajeshah,i IJECS Volume Issue 5 May, 03 Page o Page 574

4 The cotrol law for th cotroller derived from previous sectios as: u t u t u t u u u Wsig( s ) u u s sig( s ) s s s sig( s ) s s (8) : If : If 3 : If 4 : If ad ad ad ad (0 Table, shows the rules tabular. I the et relatios, the magitude ad umber itervals are cosidered. Table. Table of ules, THE y, THE y, THE y, THE y 3 4 ) Cotroller Desigig Based O FUZZ Type- 3 I traditioal fuzzy sets, the membership fuctios put o figures idividually by crp poits. But i fuzzy type-, a dtace for the fuctios cosidered. As figure 5 shows, P to P9 ca build the as sigle membership fuctio [ 500 0] [ 0 500] [ 500 0] [0 500] 4 () () To compute the output value, it s eeded to calculate the mai fuzzy type- values as: Fig5. The positio of a simple fuzzy typ sets The rules of these systems could be mad as relatio9. : IF THE y ad ad (9) For cotroller desigig, four modes are cosidered. If the directio of motio of each lik CCW, cosider the positive ad egative cotrast, four of the table ca be cosidered a robot. The programmig eviromet for Wu Toolbo ca be used by cosiderig 9 poits i figure metioed above. Each lik usually moves more tha 90 or less tha -90 ad ot the.5 ad 0.5 radias ad egative umbers i calculatios. k f y y mi k l k, k f f k L f y L L f f L k f y y ma k r k, k f f k f f y y y l r (3) (4) (5) To calculate the mai parameters eeded, we cosider the Karik-Medel Algorithm. From Karik-Medel Algorithm, we have: 3, L [0]. Ali Pajeshah,i IJECS Volume Issue 5 May, 03 Page o Page 575

5 A A Implemetatio ad esult I th sectio, both of the cotrollers, slidig mode ad fuzzy are merged ad implemeted i the robot. SIMULIK eviromet used for simulatig. The solver ode45 employed for solvig differet states. Slidig mode cotrols the first lik ad fuzzy cosiders the secod oe. Figures 6 ad 7 show the SIMULIK parts for buildig them. Table. omial values for robot parts m m l l 5 Kg Kg Figures 8 ad 9 show the result of the cotroller performace. As they demostrate, the fuzzy cotroller ca cotrol the radom trajectory ijected ito robot joit. m m Plot Plot A Fig8. First lik cotrolled by SMC, secod order A Fig9. Lik cotrolled by Fuzzy type- Fig6. SIMULIK eviromet for implemetatio of robot ad its cotrollers There are some poits which are obtaied from simulatio. Both of two cotrollers ca track the agle i elapsed time. It importat to maitai a robot lik i a certai agle ad also aother lik i a desired agle. Although the slidig mode ca decrease the chatterig, but a vible chatterig ca be foud. While i figure 9, fuzzy type, the cotroller ca behave as a robust cotroller durig the ucertaity. Th result ca be achieved by usig fuzzy type. Coclusio Fig7. Iside of cotroller block, fuzzy ad slidig mode The omial values used i the simulatio are show i table. I th paper, the two approaches of traditioal ad ew theories about a robot with two degrees of restace i series were studied. Both cases were used to cotrol the robot. First Lik ad Lik by secodorder slidig mode fuzzy cotroller type, was used. Usig higher-order slidig mode algorithm for super twtig, chatterig become less tha other cotrollers, which provides better cotrol of the robot i positio. Th while the type- fuzzy cotroller ca also show stregth i the face of ucertaity to a large etet. The robots are modeled i the cotet of both traditioal ad wireless Mechaics modelig approach used. Ali Pajeshah,i IJECS Volume Issue 5 May, 03 Page o Page 576

6 efereces. Craig, J.J., Itroductio to robotics: mechaics ad cotrol Ageles, J. ad O. Ma, Dyamic simulatio of -a serial robotic maipulators usig a atural orthogoal complemet. The Iteratioal Joural of obotics esearch, (5): p Codourey, A., Dyamic modelig of parallel robots for computed-torque cotrol implemetatio. The Iteratioal Joural of obotics esearch, (): p Alvarez-amirez, J.,. Kelly, ad I. Cervates, Semiglobal stability of saturated liear PID cotrol for robot maipulators. Automatica, (6): p Cervates, I. ad J. Alvarez-amirez, O the PID trackig cotrol of robot maipulators. Systems & cotrol letters, 00. 4(): p Villarreal-Cervates, M.G., C.A. Cruz-Villar, ad J. Alvarez-Gallegos. Structure-cotrol mechatroic desig of the plaar 5r dof parallel robot. i Mechatroics, 009. ICM 009. IEEE Iteratioal Coferece o IEEE. 7. Villarreal-Cervates, M.G., et al., Differetial evolutio techiques for the structure-cotrol desig of a five-bar parallel robot. Egieerig Optimizatio, 00. 4(6): p Todu, B. ad P. Lopez, Modelig ad cotrol of McKibbe artificial muscle robot actuators. Cotrol Systems, IEEE, (): p Ariua, D. ad W. Shigeyoshi. Itelliget cotrol i dyamic system. i 004 IEEE Coferece o obotics, Automatio ad Mechatroics, December, December 3, Sigapore, Sigapore: Istitute of Electrical ad Electroics Egieers Ic. 0. Bego, P., F. Pierrot, ad P. Dauchez. Fuzzy slidig mode cotrol of a fast parallel robot. i obotics ad Automatio, 995. Proceedigs., 995 IEEE Iteratioal Coferece o IEEE.. Helferty, J.J., J.B. Coll, ad M. Kam. eural etwork learig strategy for the cotrol of a oe-legged hoppig machie. i IEEE Iteratioal Coferece o obotics ad Automatio - 989, May 4, May 9, Scottsdale, AZ, USA: Publ by IEEE.. Perruquetti, W. ad J.P. Barbot, Slidig mode cotrol i egieerig. Vol.. 00: CC. 3. Levat, A., Slidig order ad slidig accuracy i slidig mode cotrol. Iteratioal Joural of Cotrol, (6): p Zadeh, L.A., Toward a theory of fuzzy iformatio graulatio ad its cetrality i huma reasoig ad fuzzy logic. Fuzzy Sets ad Systems, (): p Medel, J.M., Type- fuzzy sets: some questios ad aswers. IEEE Coectios, ewsletter of the IEEE eural etworks Society, 003. : p Medel, J.M. O the importace of iterval sets i type- fuzzy logic systems. i IFSA World Cogress ad 0th AFIPS Iteratioal Coferece, 00. Joit 9th. 00. IEEE. 7. Medel, J.M., Advaces i type- fuzzy sets ad systems. Iformatio Scieces, (): p Medel, J.M. Fuzzy sets for words: a ew begiig. i Fuzzy Systems, 003. FUZZ'03. The th IEEE Iteratioal Coferece o IEEE. 9. Medel, J.M., Computig derivatives i iterval type- fuzzy logic systems. Fuzzy Systems, IEEE Trasactios o, 004. (): p Medel, J.M.,.I. Joh, ad F. Liu, Iterval type- fuzzy logic systems made simple. Fuzzy Systems, IEEE Trasactios o, (6): p Medel, J.M. ad.i.b. Joh, Type- fuzzy sets made simple. Fuzzy Systems, IEEE Trasactios o, 00. 0(): p Wu, D. ad J.M. Medel, Ucertaity measures for iterval type- fuzzy sets. Iformatio Scieces, (3): p Wu, H. ad J.M. Medel, Ucertaity bouds ad their use i the desig of iterval type- fuzzy logic systems. Fuzzy Systems, IEEE Trasactios o, 00. 0(5): p Ali Pajeshah,i IJECS Volume Issue 5 May, 03 Page o Page 577