Modeling and Motion Control Selection and Design of Electric Motor for Mechatronics Robotics Applications

Transcription

1 NTERNATONAL JOURNAL OF CONTROL, AUTOMATON AND SYSTEMS VOL.1 NO. ARL 13 SSN 1-77 (rin) SSN 1- (Online) hp:// Modeling and Moion Conrol Selecion and Design of Elecric Moor for Mecharonics Roboics Applicaions Ahmed M. Aloaibi Absrac To simplify mecharonics moion conrol sysems design, his paper proposes mahemaical modeling, simulaion and conrol of a given elecric moor in erms of inpu vol, V in and oupu moions. The proposed model can be used o selec,design, es and validae boh plan's and moion conrol design o mee desired oupu performance.the proposed model was esed in he design of wo sysems; a single join robo arm and mobile roboic sysem. eywords DC moor, simulink model, robo arm, mobile robo, conrol sysem.. NTRODUCTON n mecharonics applicaions, conrol of moionsin desired fashion is of concern. The ulimae goal of his paper is o propose a mahemaical and Simulink models ha can be used o simplify mecharonics moion conrol sysems dynamics analysis and conrol sysem selecion and design o mee desired performance, including, opimal plan's parameers. To es he proposed model, i will be applied o selec, design, es and validae sysem and moion conrol in wo differen sysems; mobile robo, and single join robo arm, shown in Fig.1. Mos used acuaor in mecharonics moion conrol applicaions is DC moors. Despie a lo of resources ha propose differen selecions and design of conrol sraegies o conrol moions in desired fashion, for insan[1-],mos conrol sysem used are based on convenion D conroller [7]. Fig. Mobile robo. MODELNG OF DC MOTOR Mos used acuaor in mecharonics moion applicaions is DC moor, herefore, moion conrol can be simplified o DC moor moion conrol. MDC moor is an example of elecromechanical sysem, having boh mechanical of elecric componens, a simplified equivalen represenaion he armaure conrolled MDC moor's wocomponens is shown in Fig.3, []. Fig.3 simplified equivalen represenaion of MDC moor elecromechanical componen [3]. The moor orque is given by Eq.(1). The generaed EMF volage, e a, is given by Eq.() (1) () Applying irchoff s law around he elecrical loop, subsiuing, resul in Eq(3).Taking Laplace ransform and rearranging, resul in Eq(): Fig.1 Single join robo arm. Ahmed Mohammed Hazzaa Aloaibi wih Taif universiy,, Taif, Saudi Arabia. He is now wih deparmen of mechanical engineering, Faculy of Engineering, Mecharonics program ( [email protected]) 1 erforming he energy balance; he sum of he orques mus equal zero, yields Eq.(), Taking Laplace ransform and rearranging, resul in Eq(): (3) ()

2 NTERNATONAL JOURNAL OF CONTROL, AUTOMATON AND SYSTEMS VOL.1 NO. ARL 13 SSN 1-77 (rin) SSN 1- (Online) hp:// d d Load m m * i T J b d d (s)= (J m s + b m ) s θ(s) () moor's wo componens are coupled by orque consan given by Eq.(1), subsiuing Eq.() in Eq.( ) and rearranging, o have he ransfer funcion given by Eq.(7)in erms of he inpu volage, V(s) and oupu moor shaf angle, and he ransfer funcionin erms of he inpu volage, V(s), and oupu moor shaf angular speed given by Eq.(). he oal equivalen ineria, J oal and oal equivalen damping, b oal a he armaure of he moor are given by: b J b b, J J n n Load Load equiv m equiv m () (7) () The geomery of he par deermines he momen of ineria, for robo arm: considering robo arm as hin rod of mass m, lengh l, (so ha m = ρ*l*s), he momen of ineria of he robo arm can be found by Eq.(9). For mobile robo, he mobile robo can be considered o be of such shape, wih he ineria calculaed by Eq.(1): J 1 (9) 1 3 bh J (1) 1 arm _ load Jarm ml J mobil _ load mobile The oal equivalen ransfer funcion, relaing inpu volage V in and Arm-load oupu angular posiionθ Load, is given by Eq.(11).The oal equivalen ransfer funcion, relaing inpu volage V in and mobile robo oupu angular speed ω Load, is given by Eq.(1). These equaions used o buil he simulink model of open loop sysem, shown in Fig., his model can be used o analyze he moions in erms of oupu posiion and speed, he model is suppored wih manual swiches o swich beween oupu speed or angle (robo arm or mobile robo model). Running his model for given sysems parameers will resul in response curves shown in Fig. G G posiion speed Load ( s ) * n ( s) V ( ) 3 in s LaJ arm s ( RaJ arm barm La s ( Rabarm b ) s robo ( s ) / n ( s) Vin ( s) ( LaJ mobile ) s ( RaJ mobile bmobile La ) s ( Rabmobile b ) (11) (1) Fig. General Simulink model for open loop robo moion: arm angle and mobile speed.

3 Curren, Amp linear speed, M/s NTERNATONAL JOURNAL OF CONTROL, AUTOMATON AND SYSTEMS VOL.1 NO. ARL 13 SSN 1-77 (rin) SSN 1- (Online) hp:// Rad 1 1 Angular pos/time 1 3 Torque/Time Linear Accel., M/s Fig (a) Open loop robo sysem angular posiion/ime, linear speed/ime, orque/ime and angular acceleraion/ ime response curves for 1V inpu. linear Accel., M/s linear Acceleraion/Time 1 3 Fig (b) Open loop robo sysem linear angle/ime, curren /ime curves for 1V inpu. CONTROLLER DEDGN 1 3 Angular Acceleraion/Time. Differen resources inroduce differen mehodologies and approaches for moion conroller design, for insan, [] inroducesmodeling and conrol of mobile robo using deadbea response. n [] roposes Mecharonics design of a mobile robo sysem. [9] roposes modeling of moion conrol sysem for moorized robo arm using MATLAB. [1] roposes analysis and speed conrol design mehods of a DC Moor. [11] roposes conrol of DC moor using differen conrol sraegies To simplify he selecion and verificaion of conrol sysem, he proposed simulink model will include mos applied conrol sraegiesfor moion conrol, including, D, D, lead, lag compensaors D conrollers are mos used conrol sysems o achieve he desired behavior of differen ypes of dynamic plans. The D gains (,, D ) are o be uned experimenally o obain he desired overall desired response. The D conroller ransfer funcion is given by: Linear speed/time, Curren/ Time 1 3 conroller is widely used in variable speed applicaions and curren regulaion of elecric moors, because of is simpliciy and ease of design. conroller ransfer funcion is given by: s Gcurren ( s ) G ( s ) s s (1) s s Z o s s Where, Zo: zero of he -conroller :he proporional gain. Lead compensaor:lead compensaor is a sof approximaion of D-conroller, The D conroller, given by G D (s) = + D s, is no physically implemenable, since i is no proper, and i would differeniae high frequency noise, hereby producing large swings in oupu. o avoid his, D-conroller is approximaed o lead conroller of he following form[]: G ( s s D ) G Lead ( s ) D s The larger he value of, he beer he lead conroller approximaes D conrol, rearranging gives: s s Ds GLead ( s ) D s s s D s D GLead ( s ) D s s Now, le C D and Z, D we obain he following approximaed conroller ransfer funcion of D conroller, and called lead compensaor: s Z G ( s ) C s f Z < his conroller is called a lead conroller (or lead compensaor). f Z > : his conroller is called a lag conroller (or lag compensaor).the ransfer funcion of lead compensaoris given by: s Zo Glead ( s ) c ( s ) Where : Z o < o O (1) Lag compensaor; The Lag compensaor is a sof approximaion of conroller, i is used o improve he seady sae response, paricularly, o reduce seady sae error of he sysem, he reducion in he seady sae error accomplished by adding equal numbers of poles and zeroes o a sysems. (13) 3

4 NTERNATONAL JOURNAL OF CONTROL, AUTOMATON AND SYSTEMS VOL.1 NO. ARL 13 SSN 1-77 (rin) SSN 1- (Online) hp:// s s G ( s ) Glag ( s ) s s s Since conroller by iself is unsable, we approximae he conroller by inroducing value of o ha is no zero bu near zero; he smaller we make o, he beer his conroller approximaes he conroller, and he approximaion of conroller will have he form: s Zo Glag ( s ) (1) c ( s O ) Where: Z o > o, and Z o small numbers near zero and Z o = /, he lag compensaor zero. o : small number,the smaller we make o, he beer his conroller approximaes he conroller. Sensors modeling: speed and posiionsensors To conrol he oupu moion in erms of angle or speed, a sensing device is o be used, wo main sensors are used. For oupu angular displacemen measuring and conrol (robo arm), oeniomeer is used o measure he acual oupu posiion, θ L, conver ino corresponding vol, V p and hen feeding back his value, he oeniomeer oupu is proporional o he acual shaf (robo arm) posiion, θ L. The oupu volage of poeniomeer is given by: V p = θ L * po Where:θ L :he acual robo arm posiion. po he poeniomeer consan; is equal o he raio of he volage change o he corresponding angle change, we are o conrol he robo arm moion o move from zero o 9 degree, po is given by: (Volage change) 1 po.1333 V / degree (Degree change) 9 For oupu angular speed measuring and conrol (mobile robo), Tachomeer is used o measure he acual oupu angular speed,ω.. Dynamics of achomeer can be represened by following equaion: V ou () = ac *d θ()/d = V ou () = ac * ω The ransfer funcion of he achomeer is given by: Vou s ac s We are o drive our roboic plaform sysem, wih linear velociy of. m/s, he angular speed is obained as: ω=v/r =./.7 =.7 rad/s. Subsiuing values, we have Tachomeerconsan, given by: 1 ac V. Closed loop robo sysem conrol and analysis Simulink model shown in Fig., can be modified, o have he general form shown in Fig (a), hemodel is buil wihmos applied conrol sraegies including,, D,, D, Lead, andcorresponding feedback sensing unis for reading boh speed and angle. This suggesed simulink model, wih supporing m.file for defining required variables and parameers, simplifies he selecion and design process by allowing designer o es, analyze and evaluae he moion conrol and performance of a given sysemin erms of inpu volage and oupu angular posiion, angular speed, linear speed(e.g. mobile robo or robo arm), curren, orque and acceleraion, when a specific conrol sraegy is applied, where designer can swich from evaluaion oupu posiion o oupu speed, and beween conrollers ypes by swiching corresponding manual swiches, also using D simulink block feaures, designer can swich o any of D subsysems;,, D and D conrollers,also he suggesed model gives visual reading of oupu angular posiion and speed, finally, he proposed model can be modified o include oher conrol sraegies. The resuled response curves are used o es overall sysem performance, when a seleced conrol sysem is applied and finally selec he mos suiable acuaor, plans parameers, and conrol sysem for achieving desired oupu moion. For oupu speed conrol applicaions, in our case mobile robo sysem and conroller selecion and design, he model is o be swiched o oupu speed conrol by acivaing achomeer sensor, henapplying D conrollerwih gains ( = , =3.3913, D = ), for desired oupu robo linear speed of. m/s, will resul in response curves shown in Fig (b),hese response curves are o be used o evaluae and verify design. To analyze and evaluae he performance of mobile robo, when conroller is applied, model is firs swich o conroller, Running his model, wih zero z1=.3 and p=.; for desired speed of. m/s, will resul in response curves shown in Fig (c), running his model, when applying lead compensaor, will resul in response curves shown in Fig (d), gains, poles and zeros can be adjused, or specially designed, o mee desired performance specificaions. For oupu posiion conrol applicaions, in our case robo arm and conroller selecion and design, he model is o be swiched o oupu angle conrol by acivaing poeniomeer sensor.applying D conroller for desired oupu robo arm maximum posiion of 9 degree, running and uning, he model, will resul in response curves shown in Fig 7.

5 Curren, Amp linear speed,, M/s, Rad/sec linear speed, M/s Curren, Amp M/s Amp linear speed,, M/s, Rad/sec Rad/sec Nm NTERNATONAL JOURNAL OF CONTROL, AUTOMATON AND SYSTEMS VOL.1 NO. ARL 13 SSN 1-77 (rin) SSN 1- (Online) hp:// Fig (a), Simulink model for robo moion (posiion and speed). Linear speed/ Time, Angular speed/ Time Angular speed/ime 1 Torque/ime... Torque/ Time Curren/ Time Fig (b), Angular speed/ime, linear speed/ime, orque/ime, and curren/ime response curves of close loop mobile robo sysem using D conroller... Linear speed/ Time, Angular speed/ Time. 1 Linear speed/ime Fig (d), Angular speed/ime, linear speed/ime, orque/ime, and curren/ime response curves of close loop mobile robo sysem using lead compensaor. 1 angular pos/time. 1 Curren/ime 1 Linear speed/time,.., Rad Torque/ Time Curren/ Time Torque/Time 1 linear Acceleraion/Time linear Accel., M/s 1-1 Fig (c), angular speed/ime, linear speed/ime, orque/ime, and curren/ime response curves of close loop mobile robo sysem using conroller. - - Fig 7(a) Angular speed/ime, linear speed/ime orque/ime, and curren/ime response curves of close loop robo arm sysem using D conroller.

6 linear speed, M/s Rad/sec NTERNATONAL JOURNAL OF CONTROL, AUTOMATON AND SYSTEMS VOL.1 NO. ARL 13 SSN 1-77 (rin) SSN 1- (Online) hp:// Fig 7(b) Robo arm sysem angular posiion response applying D conroller, Rad Time (seconds) 1 angular pos/time 1 Robo arm angular posiion/ime Fig 7(b) Robo Torque/Time arm sysem angular posiion linear response Acceleraion/Time applying lead conroller 3 1 V. CONCLUSON 1 Linear speed/time, buil-in funcion and simulink model, Acceped,.J. Engineering and Manufacuring, 13. [] Ahmad Aallah Salem, Farhan A. Salem, Musafa amel, DC moor Modeling simulaion and analysis using differen mehods and verificaion by MATLAB/Simulink, ( acceped; nernaional Journal of nelligen Sysems and Applicaions (JSA),, 11,1 ). [] Bashir M. Y. Nouri, modeling and conrol of mobile robo,roceeding of he Firs nernaional Conference on Modeling, Simulaion and Applied Opimizaion, Sharjah, U.A.E. February 1-3,. [7] Jamel A. Mohammed, Modeling,analysis and speed conrol design mehod of a DC moor.eng & Tech Journal. Val 9,No.1,11. [] Ahmed A. Mahfouz, Ayman A. Aly, Farhan A. Salem, Mecharonics design of a mobile robo sysem,.j. nelligen Sysems and Applicaions, 13, 3, 3-3 [9] Chun HooAung, hinthandarlwin, and Yin Mon Myin, Modeling Moion Conrol Sysem for Moorized Robo Arm using MATLAB. World Academy of Science, Engineering and Technology [1] Dr. Jamal A. Mohammed, Modeling, Analysis and Speed Conrol Design Mehods of a DC Moor, Eng. & Tech. Journal, Vol. 9, No. 1, 11 [11] HedayaAlasooly, Conrol of DC moor using differen conrol sraegies, Global journal of echnology & opimizaion, Volume,11. [1] JaroslavHanzel, LadislavJurišica, Marian ľúčik, Anon Viko, MaejSrigáč, Experimenal mobile roboic sysem, modeling of mechanical and mecharonics sysems 11. [13] R.C. Dorf and R.H. Bishop, Modern Conrol Sysems,1h Ediion, renice Hall,. Appendix linear Accel., M/s A mahemaical and Simulink models for desired oupu moion -conrol is inroduced. Running - 1 he simulink model 1 for a given moion sysem, will resul in response curves in erms of oupu angular posiion, angular speed, linear speed, curren, orque and acceleraion, when a specific elecric moor, plan parameers, and conrol sraegy are applied. The resuled response curves are used o es and compare overall sysem performance and finally selec he mos suiable acuaor, plans parameers, and conrol sysem for achieving desired oupu moion. The suggesed model can be modified o include oher moion conrol sraegy. Acknowledgmen The auhor is obliged o Taif Universiy, Taif, SA for providing valuable resources o carry ou his sudy. Special hanks are exended o my parens and Dr. Farhan A. Salem for his noble suppor and encouragemen in his paper. REFERENCES [1] Hedaya Alasooly, ''Conrol of DC moor using differen conrol sraegies'' global journal of echnology and opimizaion 11. [] Jamal A. Mohammed,Modeling, Analysis and Speed Conrol Design Mehods of a DC Moor Eng. & Tech. Journal, Vol. 9, No. 1, 11. [3]. Anil Naik and. Srikanh, Sabiliy Enhancemen of DC Moor using MC Tuned D Conroller, inernaional journal of advanced engineering sciences and echnologies,11. [] Ahmad A. Mahfouz, Farhan A. Salem, erformance analysis, conroller selecion and verificaion of elecric moor for mecharonics moion conrol applicaions, using new MATLAB - Symbol Quaniy VALUE UNT V, or Vin The applied inpu 1 Vole, V volage,(moor erminal volage) R a Armaure resisance,( erminal 1 Ohm,Ω resisance) L a Armaure inducance. H Moor orque consan.9 N.m/A e Moor back-elecromoive force.1 V/(rad/s) cons. The moor consan 1.1 N.m/A ω m Moor shaf angular velociy rad/s T m Torque produced by he moor N.m J m Moor armaure momen of. kg.m ineria J oal Toal ineria=jm+jload kg.m L a Armaure inducance. Henry, H bload_arm Viscousdamping of robo arm.9 N.m/rad.s bm Viscousdamping of moor.3 e a,emf: The back elecromoive force, e a,emf: EMF = bdθ/d θ m Moor shaf oupu angular radians posiion ω m Moor shaf oupu angular rad/sec speed V R = R*i The volage across he resisor Volage V L=Ldi/d The volage across he inducor Volage T load Torque of he mechanical load T load Tα Torque du o Tα roaionalacceleraion Tω Torque du o roaionalvelociy Tω T EMF The elecromagneic orque. TEMF

7 NTERNATONAL JOURNAL OF CONTROL, AUTOMATON AND SYSTEMS VOL.1 NO. ARL 13 SSN 1-77 (rin) SSN 1- (Online) hp:// m Mass of robo arm. g L Lengh of robo arm.3 m M Mass of mobile robo g r Wheel radius of mobile robo.7 m L Lengh of mobile robo plaform 1.1 m a widh of mobile robo plaform. m b heigh of mobile robo plaform.9 m Auhor' profile: Ahmed M. Aloaibi: was born in 199 in Jeddah, Saudi Arabia. B.Sc. in Mecharonics Engineering, Taif universiy, 1, Saudi Arabia. Now, from Sepember 1 up o dae, He works as a Demonsraor a Taif universiy, Mecharonics secion 7