D.C. Servo Position Control Parameter Estimation

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1 Eng. & Tech. Journl, Vol.28, No. 5, 2010 Dr. Sd T. Kurdi* & Nihd M. Aeen** Received on:1 /3 /2009 Accepted on:3 / 12/2009 Abstrct Open-loop nd closed-loop position control systes re obtined using dc otor. The open-loop uses n estition of controller preters to perfor the position control where the closed loop position control systes uses cscde controller to intin the desired position. Controllers re designed using Mtlb/Siulink siultion pckge. The objective is to design position controller which will be ble to drive the otor t specified constnt velocity which ight gives the otor soe constnt torque. The results obtined fro the open-loop position control syste preters estition shows better perfornce specifiction in the control tsks, such s rise tie nd overshoot. The cscde closed-loop position control syste shows n iproveent in perfornce when use the vlues of estited preters. ايجاد قيم المعاملات لنظام سيطرة الموقع باستعمال محركات السيرفو الخلاصة نظام السيطرة ذوالحلقة المفتوحة وا نظمة سيطرة ذات التغذيه الخلفيه تم اختيارها لتصميم منظومة سيطرة تقوم بتحديد موقع توقف محرك التيار الثابت. ت ستعمل الحلق ة المفتوح ة تقديرمعاملات جهاز السيطرة لتوجيه المحرك الى الموقع المطلوب بينما تستعمل ا نظمة السيطرة ذات التغذيه الخلفيه سيطرة تتابعيه لا ب قاء المحرك على الموقع المطلوب. نظام السيطرة صم م با ستعمال رزمة محاكاة ماتلاب. الهدف هو تصميم جهاز سيطرة موقع الذي سيكون قادرا على قي اد ة المحرك في حدود سرعة ثابتة التي ق د تعطي المحر ك ب ع ض عزم اللي الثابت. الن تاي ج التي تم الحصول عليها بايجاد قيم المعاملات لنظام السيطرة ذوالحلقة المفتوحة اعطت مواصفات افضل في ا داء مهام السيطرة مثل زمن الاستجابة والقيمة القصوى للاستجابة. تم تحسين اداء نظام السيطرة ذوالتغذيه الخلفيه باستعمال قيم المعاملات المستنبطه من نظام السيطرة ذوالحلقة المفتوحة. 1.Introduction Insted of using sophisticted feedbck control, they re often run open loop using echnicl stops or liit switches. Sophisticted robots use closed loop position systes for ll joints. The robot position is controlled by dedicted coputerbsed controller where this unit is lso cpble of trnslting hun instructions into the robot progr during the teching phse [1]. In 2002 Corrdo Gurino presents n inversion-bsed pproch to the design of dc otor-position servo syste using the recently developed trnsition polynoils, dynic inversion procedure is estblished to deterine feed forwrd cond signl to chieve high-perfornce position trnsfers. It is shown how to iprove the servo perfornces. Moreover, the ethodology cn esily coply with voltge sturtion voidnce constrint. Experientl results on stndrd test bench highlight the effectiveness of the dynic inversion ide [2]. * Electroechnicl Engineering Deprtent, University of Technology/Bghdd **Electricl nd Electronic Engineering Deprtent, University of Technology/Bghdd 1014

2 The preters re djusted by the sttic odel in such wy tht the error becoes sll. The proble is to deterine the djustent echnis which brings the error to zero for ll cond signls. The plnt with lrge preter vritions re difficult to control nd y hve soe unstble behvior or will not respond. By using the optiiztion of the controller preters the perfornce cn be iproved. The open-loop control lw hs no ide wht the output is doing, nd it rches on s if everything is working ccording to n idelized ode. The novel ethod is to use feedbck. Here the output is red by sensors, which y theselves be odeled by differentil equtions. 2.Mechtronic Actution Modules A echtronic syste spns over echnicl engineering, electricl engineering, nd control engineering nd coputer science. Mechtronic ctution odule is defined s self contined physiclly integrted syste tht consists of n electric chine, trnsission (e.g. gers or screw), sensors, low level otion controller nd otor drive unit. In order to rech n optil design of n integrted echtronic syste, first the electric chine odel is presented nd nlyzed. Then physicl coponent odels of otor driver re presented. Finlly the dynic spects re investigted nd the low level controller nd position sensor re integrted into the ethodology. The ethodology is bsed on two types of coponent odels, dynic nd sttic odels. The sttic odels re lgebric expressions which ke it possible to derive the optil physicl preters of ll the coponents without hving to siulte the. This optil preters set is then used in the dynic siultion odel. The dynic syste odel is bsed on differentil equtions needs to be siulted to describe the coponent behvior s function of tie [3]. The optiiztion ethods hve been bsed on n nlytic technique where the optiu either is siply red directly out of grph or clculted with the help of differentil clculus. When nonliner dynic phenoen nd control perfornce evlution included into the nlysis it is necessry to introduce ore dvnced nuericl optiiztion ethods such s the integrl of squre error (ISE) [3]. Mny of the preters used in the dynic siultions re derived with the sttic coponent odels. So the sll errors cn ffect the results fro the dynic siultions gretly. It is possible to obtin ore correct results fter few itertions of the design cycle, hving prototype or previous version of the syste tht y be used for preter identifiction. 3. Modeling of DC Mchine nd Mechnicl Lod Cobintions DC otors hve speed-control cpbility, which ens tht speed, torque, nd even direction of rottion cn be chnged t ny tie to eet new conditions. Control otors re not usully operted t single voltge becuse vrying the voltge is wy of controlling the power (nd therefore speed). As the voltge increses, the stll torque nd nolod speed lso rise. The theticl odel of dc otor t fixed position of the otor shft cn be expressed by these equtions [4].

3 di v = e + i R + L...(1) dt R is the rture resistnce (Ω); L is the rture inductnce (H) nd e is the bck EMF which is dependent on the otor ngulr velocity e ( t) k w ( t)...(2) = E k E is the bck EMF constnt (V/rd/s); w is the ngulr velocity (rd/s) V ( s) = E ( s) + ( R L S) I ( s)..(3) + V ( s) E ( s) I ( s) = M ( R + L S) Dynic eqution T ( s) k I ( s) e = eq T J = J + J T e = J eq + B w + dw dt L T L...(4)...(5)..(7) T e is the internlly generted torque, k T is the torque constnt (N./A), J is the otor oent of inerti nd J L is the lod oent of inerti J = J + J is the rotor eq inerti (kg. 2 ), nd ( B w ) is the viscous friction torque. Assue tht the lod torque ( T L ) is equl to zero. Then the eqution 7 becoes Te( s) w ( s) =...(8) J S + B eq L The block digr for dc otor is shown in figure (1)....(6) 4.Cscde closed loop position control syste In closed loop control position syste the feedbck signl is subtrcted fro the set point t the coprtor, by subtrcting the ctul position fro the desired position we get the syste error. The controller iniizes the error [5]. A control strtegy used is enbles the controller to turn the ctutor on or off. Figure (2) shows the Mtlb/Siulink for the cscde closed loop position control syste. The response of the closed loop syste is shown in figures (3) nd (4), where KT = KE = 0.1, R = 2 Ω, L = 5.2 H, Jeq = 1.5 x 10-4 kg. 2, B = Fro the result obtined it is noticed tht the ctul position cn follow the desired position with soe oscilltion round the desired position tht cn cuse true proble where the overshoot is reltively high (bout 30 %) nd the speed of the otor is vried which cuses n unstble torque. The desired perfornce of the closed-loop syste with no overshoot should be concerned. To provide stble control syste the controller is designed with perfect estition of the process preters. 5.Open-Loop Control Syste with preter estition In Open-Loop Control Systes shown in figure (5), the controller never ctully knows wht the ctutor did becuse there is no feedbck. This syste bsolutely depends on the controller knowing the operting chrcteristics of the ctutor [6]. 6.DC Motor drive unit To drive the otor, n interfce circuit is required to convert the lowlevel otor control signl fro the controller into signl strong

4 enough to run the otor. The clssicl wy to do this is with n nlog drive. In this ethod, liner power plifier plifies the drive signl fro the controller nd gives the otor strengthened nlog voltge. Figure (6) shows otordriver circuit. Insulted Gte Bipolr Trnsistor (IGBT) used to drive the otor in tlb/siulik design. IGBT hs high switching frequency, lower conduction losses thn MOSFET nd high current nd voltge rting. The reference input signl cn produce the on-off tie nd the direction of the control tsk, while the plitude of output signl is proportionl to the DC voltge source. The open-loop control design y well work, but it hs soe inherent probles. The first proble is the disturbnce; which y cuse the output of the plnt to devite significntly fro the reference trjectory. Another proble rises with plnt uncertinties [4]. To overcoe these probles; one odels the plnt, typiclly vi differentil equtions nd ke n ideliztion of the plnt s ctul behvior. of the ctutor preters with suitble optiiztion strtegy re one of the best ethods for ideliztion of the plnt s ctul behvior. 7. of Actutor Preters Servo syste onitors the condition of output vribles nd copring it to n input cond nd king djustents to intin equlity, the ost coon controlled output vribles re position, speed nd torque. It is possible to hve ore thn one controlled vrible or to switch fro one vrible to nother during opertion. Optiiztion strtegy uses n integrl of squre error (ISE) for djusting the preters in which the djustent rte not depends on the gnitude of the test signl. The design preters selected nd initil vlues re obtined ssuing tht the controlled vribles re continuous (the input cused the controlled vribles is ble to reins constnt or to chnge in liner or step ode). The following equtions represent the integrl of squre error (ISE) optiiztion procedure [7]. 2 f ( x, t) = e ( t, b. β ) dt...(9) e = y y b = process preter preter β = the corresponding odel t 2 E e BE = = 2 e( t, b, β ) dt..(10) β β t1 nd Vlidtion test signls is shown in figure (7) is chosen s n input signls for the controller. The first itertion shows the desired nd ctul response in figure (8). The correction of the otor position rottion is iproved fter the first itertion figure (9) where the esured nd siulted response becoes closer [8]. After few itertions ore correct results obtined. The estition of controller preters fter the 7 th itertion shows tht the esured nd siulted responses re identicl, figure (10). The trjectories of estited preters re shown in figure (11). The estited preters re illustrted in tble (1). 8.Siultion Results The siultion result shown in figure (12), shows the syste

5 response to unit step input for one second tie period, the result shows tht the dc otor is rottes 3.9 rd with n ngulr velocity 3.9 rd/sec nd 0.03 N. torque. By incresing the tie to two seconds tht will cuse n incresing of ngulr position by 3.9 rd while the plitude of the ngulr velocity nd the corresponding torque wont effect. This ens tht we obtin position controller with constnt velocity which leds to constnt torque. It is noticed tht the otor speed effected directly by the plitude of the dc voltge source of the drive unit. We cn reverse the otor ngle of rottion by reversing the input signl which cuse rottion of dc otor in opposite direction with the se vlue of ngulr velocity, the ngulr velocity nd torque will reins t the se vle but in ve sign. Figure (13) shows the response with 1.5 second step input in forwrd nd reversed direction of rottion with corresponding ngulr velocities nd torque. With constnt velocity of rottion we cn rech ny position directly or with ny desired tie dely by vrying the frequency of input signl. The input signl cn produce sequence of tsks t the se nner. It is noticed tht the plitude of the input signl will not ffect the speed of rottion. Assue tht the controller is directed to ove fro 0 to 10 rd, by knowing the chrcteristics of the process, desired pulses send to the otor; the otor will rotte exctly 10 rd t the rted speed nd stop. We cn lso control the reverse position by send negtive input signls, s shown in figure (14) which shows the ngulr position, otor speed nd otor torque for two different input signls. The other ethod is to use feedbck by dding feedbck sensor. The syste response for unit step input is shown in figure (15). The siultion results for controller by dding feedbck sensor shows the fst nd stble trnsient response. The ctul position rech the desired vlue t reltively low rise tie, with no overshoot nd zero stedy stte error tht ke it good response nd cn be used in different control pplictions such s grinding, hndling nd gripping. The ngulr velocity of the rotting shft will be stble nd hve no oscilltion tht will cuse constnt torque (Te). Conclusions DC Servos re ttrctive for use in echtronics, becuse they re reltively inexpensive, hve controllble torque, esily be odified to produce continuous shft rottion t reltively slow speeds, decent ount of ccurcy nd they cn esily be controlled by icrocontroller. Copring the controller with the cscde controller, the siultion shows iproveent in syste behvior cused by optiiztion procedure using preters estition in sttic odel. References [1]Alcherio Mrtinoli, "Swr Intelligence in Autonoous Collective Robotics", Ph. D. Thesis, [2]Corrdo Gurino Lo Binco, nd Aurelio Pizzi, "A servo control syste design using dynic inversion", University of Pr, Itly, copyright by Elsevier Science Ltd [3]Fredrik Roos, "Towrds Methodology for Integrted Design of Mechtronic Servo Syste",

6 Royl Institute of Technology, Stockhol, [4]An Engineering Hndbook by Electro-Crft Corportion, "DC Motors Speed Controls Servo Systes", First published by Pergon Press Ltd. United Stte of Aeric, [5]Ire Benyo, "Cscde Generlized predictive control ", oulu university, Finlnd, ct university press, [6]Rolnd S. Burns, "Advnced Control Engineering", university of Plyouth. Jordn Hill Inc, UK, [7] Thos R. Cuthbert, JR., "Optiiztion using Personl Coputers ", John Wiley & Sons, United Stte of Aeric, 1987 [8]Pieter Eykhoff, "Syste Identifiction preter nd stte estition", Gret Britin by J.W. Arrowsith Ltd, Tble (1) Estited preters fter the 7 th itertion Preters Estite Initil d guesses vlues Units Bck ef constnt (V/rd/s) (KE) Motor torque constnt (N./A) (KT) Rotor Inerti 0.57 e e-6 (kg. 2 ) (J) Arture Resistnce (Ω) (R) Arture Inductnce e e-3 (H) (L) Viscous friction (B)

7 Figure (1) Block digr for dc Motor Figure (2) Cscde closed loop Position control syste Figure (5) DC Servo position control syste

8 Figure (6) DC Motor drive unit Figure (7) nd Vlidtion test

9 Figure (12) Syste Response to unit step input Figure (13) Positive nd Negtive step input response

10 Figure (14) the ngulr position, otor speed nd otor torque for Two different input signls Figure (15) Closed-loop position control syste response