Sri Ramakrishna Institute of Technology, Coimbatore, India 6. College of Engineering, Guindy, Chennai, India

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1 DC Position Control System Determintion of Prmeters nd Significnce on System Dynmics C.Gnesh 1, B.Abhi 2, V.P.Annd 3, S.Arvind 4, R.Nndhini 5 nd S.K.Ptnik 6 1,2,3,4,5 Sri Rmkrishn Institute of Technology, Coimbtore, Indi Emil: c.gnesh.mtech72@gmil.com 6 College of Engineering, Guindy, Chenni, Indi Abstrct Physicl systems used for control pplictions require proper control methodologies to obtin the desired response. Controller prmeters used in such pplictions hve to be tuned properly for obtining the desired response from the systems. Tuning controller prmeters depends on the physicl prmeters of the systems. Therefore, the physicl prmeters of the systems hve to be known. Number of techniques hs been developed for finding the mechnicl prmeters of motors. But, no strightforwrd method hs been estblished for estimting the prmeters of the lod so fr. This pper presents method of determining mechnicl prmeters viz. moment of inerti nd friction coefficient of motor & lod. This pper lso stresses tht lod prmeters hve pprecible effect on the dynmic response of systems nd hve to be determined. A DC servo position control system is considered for pplying the method. Moment of inerti nd friction coefficient of the DC servo motor s well s lod re determined using the method. It is evident tht moment of inerti nd friction coefficient cn be determined for ny lod rrngement using the proposed method. Effect of lod on the system dynmics is emphsized by considering the PID controller tuning. It is found tht PID controller when tuned bsed on estimted lod prmeters could yield optimum response. This justifies tht lod prmeters hve to be determined for dynmic lod vritions. Index Terms Inerti, Friction, Bck emf, PID controller without considering the lod prmeters [9]-[13], then such system will not yield desired response in rel time. Precision nd ccurcy re of utmost importnce in tuning controller prmeters to chieve the desired trnsient nd stedy stte responses without scrificing stbility. Hence determintion of mechnicl prmeters of motor nd lod by employing pproprite techniques is of utmost importnce. The controller tuning ws done tking into ccount mechnicl prmeters of motor s well s lod in which inerti nd friction re either lredy known or specified [14]-[19]. However, vrition of lod prmeters under dynmic lod vrition ws not ccounted [14]-[19]. Most of the control pplictions employ motor nd mechnicl lod rrngement. Hence, simple nd stndrd strtegies re the order of the dy to compute the moment of inerti nd friction coefficient of motor nd lod. So fr, no simple strtegies hve been developed to estimte inerti nd friction. Further, the effect of vrition of these prmeters with respect to dynmic lod vrition on the system behvior hs not been highlighted so fr. This pper presents very simple nd stndrd procedure to determine the moment of inerti nd friction coefficient of DC motor nd lod under dynmic lod vritions. Moreover, the effect of lod on the system behvior is lso highlighted with suitble cse studies under dynmic lod vritions. I. INTRODUCTION Identifiction of prmeters of ny physicl system plys vitl role to choose the prmeters of controllers ppropritely. This is essentil to mke sure tht the system controlled stisfies the desired performnce specifictions. Over the yers, gret del of reserch hs been crried out in the estimtion of prmeters of systems using genetic lgorithms, fuzzy logic nd neurl networks. Inerti nd Friction coefficient of motor lone were determined but tht of lod were not considered even though optimiztion, dptive control nd rtificil intelligent techniques were used [1]-[5]. The importnce of estimtion of lod prmeters ws emphsized in [6] but strtegies for estimting inerti nd friction of lod were not highlighted. Even in precise pplictions such s position control, viscous friction of motor ws estimted [7] but tht of lod ws not t ll tken into considertion. In [8], lod model prmeters were obtined using genetic lgorithm but friction coefficient of motor ws not t ll considered. Tuning controller prmeters demnds proper estimtion of physicl prmeters of systems. If controller tuning is done bsed on only motor prmeters 1 II. DETERMINATION OF PARAMETERS A. Importnce of Estimtion of Dynmic Prmeters Prmeters of the DC servomotor such s torque constnt K T, bck emf constnt K b, rmture resistnce R, rmture inductnce L, moment of inerti of motor nd lod J, friction coefficient of the motor nd lod B hve to be estimted properly so tht controller prmeters cn be properly tuned nd the desired response cn be chieved from the DC position control system. K T, K b, R nd L do not vry with lod nd hence these vlues re determined using conventionl method. However, J nd B vry with respect to lod s per the detils given in the subsections C nd D. Hence, their vritions will hve n effect on the dynmics of the system. DC servomotor used for illustrtion of the determintion of prmeters hs the rtings: 24V, 4A, 4000rpm, 12.6&! rmture resistnce (R ) nd 283mH rmture inductnce (L ). B. Determintion of Torque Constnt In rmture control method, the rmture voltge nd

2 hence the rmture current re vried. Bck emf is clculted using the expression E b V i R. (1) The vlue of ngulr speed is determined from the vlue of mesured speed N in rpm. Bck emf is proportionl to speed. E b K b. (2) The slope of the grph obtined by plotting the vrition of bck emf E b ginst speed gives the vlue of K. The b mechnicl equivlent of electricl power nd mechnicl power re equl t stedy stte. Te E bi. (3) Electromgnetic torque T e is proportionl to rmture current i. Therefore, Te K Ti. (4) where K T is the torque constnt. From (2), (3) nd (4), it cn be obtined tht K b K T. (5) Hence, Torque constnt K T is obtined from the slope of the grph obtined by plotting the vrition of E b ginst ω. DC servomotor with the rtings s lredy mentioned bove is switched on t no lod. The rmture voltge nd hence the rmture current re vried by rmture control method nd the corresponding vlues of speed re noted. Vlues of ω nd E b re clculted t ech rmture voltge nd current. They re tbulted in Tble I. From the Tble I, it cn be found tht K T for the servomotor is 0.04 Nm/A. TABLE I. ESTIMATION OF K T C. Estimtion of Friction Coefficient The torque eqution of the motor nd lod rrngement is given by d T e J B. (6) dt where J nd B re inerti nd friction coefficient of the rrngement respectively. When the speed is constnt, the torque eqution becomes T e B. (7) From (4) nd (7), lod current using (8). DC servomotor is switched on t no lod. The motor is loded in steps. At ech lod current, stedy stte vlues of rmture current nd speed re noted. B is determined t ech lod using (8). These vlues re tbulted in Tble II. TABLE II. ESTIMATION OF B D. Determintion of Moment of Inerti When the supply to the rmture is switched off, motor speed reduces to zero from its stedy speed. Hence, the torque eqution becomes d J B 0. (9) dt The solution for (9) obtined using the stedy stte speed s the initil vlue of speed is expressed by T e (B / J)t e. (10) B When t= =J/B, mechnicl time constnt of the motor, the motor speed reduces from stedy stte speed to 36.8% of stedy stte speed. The time tken for speed of the motor to reduce from stedy stte speed to 36.8% of stedy stte speed gives the mechnicl time constnt of the motor nd lod. From the time constnt, the moment of inerti of the motor nd lod is given by, J B. (11) Thus the moment of inerti of motor nd lod J cn be determined by substituting the vlues of B nd mechnicl time constnt in (11). DC servomotor is run t no lod nd two different lod currents. Armture current nd speed re mesured t ech lod current. Whenever the motor is switched off, speed response is cptured on the Digitl Storge Oscilloscope. Speed responses re cptured t no lod nd other two lod currents. They re shown in Fig. 1 nd Fig. 2 respectively. From these responses, time tken (mechnicl time constnt) for the speed to drop from its stedy stte initil speed to 36.8% of its stedy stte initil speed is noted for no lod nd two different lods. J is determined for ech cse using (11). These vlues re tbulted in Tble III. TABLE III. ESTIMATION OF J K T i B. (8) where i is the rmture current mesured t stedy stte for the given lod current. Thus B is determined for the given 2

3 Trnsfer function of DC position control system t no lod is obtined by substituting the estimted prmeters of DC servomotor nd lod rrngement in (12). It is given by Figure 1. Speed response t no lod ( s) 0.04 V ( s) s[( s)(2.26e 5s 2.261e 5) ]. Using the bove expression, step response of the DC position control system is determined by MATLAB simultion nd shown in Fig. 4. Trnsfer function of DC position control system t lod 1 is obtined s ( s) V ( s) s[( s)(1.94e 5s 4.52e 5) ] Using the bove expression, step response of the DC position control system is determined by MATLAB simultion nd shown in Fig. 5. From Fig. 4 nd Fig. 5, it is very cler tht the response of DC position control system depends on the lod current. These simultion results re shown in Tble IV. From the Tble IV, it is cler tht the performnce specifictions depend on the lod current. Hence, prt from mechnicl prmeters viz. inerti nd friction of motor, mechnicl prmeters of the lod lso hve to be determined for evluting the response.(i.e. Inerti nd friction of the lod get dded to tht of motor to obtin the net inerti of the motor nd lod rrngement). Figure 2. Speed response t lod 1 III. EFFECT OF LOAD ON CONTROLLER TUNING AND SYSTEM DYNAMICS DC position control system is considered for this nlysis. Block digrm of DC motor used in position control is shown in Fig. 3. Trnsfer function of the DC position control system [20] is given by (s) KT V (s) s[(r sl )(Js B) K K ]. (12) b T Figure 4. Step response of position control system t no lod Figure 3. Block digrm of DC Motor 3

4 Figure 5. Step response of position control system t lod 1 TABLE I. SIMULATION RESULTS OF DC POSITION CONTROL SYSTEM Figure 7. Step response of PID controlled system t lod1 Response of the DC position control system with the use of PID controller is optimised t no lod by PARR tuning [21] nd shown in Fig. 6. Response of the DC position control system with the use of PID controller is optimised t lod 1 nd shown in Fig. 7. Response of the DC position control system with the use of PID controller is optimised t lod 2 nd shown in Fig. 8. These results re tbulted in Tble V. From the Tble V, it is cler tht PID controller prmeters re different t different lod currents nd hve to be tuned bsed on the mechnicl prmeters of the motor nd lod t prticulr lod setting. Figure 8. Step response of PID controlled system t lod 2 TABLE V. SIMULATION RESULTS OF PID CONTROLLED DC POSITION CONTROL SYSTEM Figure 6. Step response of PID controlled system t no lod 4 Anlysis of the simultion results from Tble IV nd Tble V clerly revel tht lod hs effect on system dynmics becuse mechnicl prmeters J nd B depend on the lod setting nd hve to be ccurtely determined for evluting the system response nd tuning the controller prmeters.

5 CONCLUSIONS Proposed method cn be used for estimtion of moment of inerti nd friction of DC motor nd lod under dynmic lod vritions. From the illustrtive studies mde on DC servo motor, it is found tht inerti nd friction of motor nd lod cn be ccurtely determined using the proposed method. From the study of effect of lod on the performnce of DC position control system, it is found tht these prmeters hve to be determined for ny chnge in lod nd controller prmeters hve to be tuned ccordingly. This method cn be extended to on-line prmeter estimtion of inerti nd friction of DC motors with ny type of lod rrngement. There is no need to hve informtion bout inerti nd friction well in dvnce. Further, controller prmeters cn be tuned from estimted prmeters of inerti nd friction of motor nd lod by employing rtificil intelligent techniques. This will improve the response of the system in rel time whenever there is chnge in lod. This method cn be lso extended to on-line prmeter estimtion of inerti nd friction of induction nd synchronous motors with ny type of lod rrngement, if torque eqution of DC motor is replced by tht of induction or synchronous motor. REFERENCES [1] Rdu Bbu, Ion Bolde, T. J. E. Miller nd Nicole Munten, Complete Prmeter Identifiction of Lrge Induction Mchines from No-Lod Accelertion Decelertion Tests, IEEE Trnsctions on Industril Electronics, vol. 54, pp , August [2] Arif A. Al-Qssr, Mzin Z. Othmn, Experimentl Determintion of Electricl nd Mechnicl Prmeters of DC Motor Using Genetic Elmn Neurl Network, Journl of Engineering Science nd Technology, vol. 3, pp , August [3] Mrin Despltoviæ, Mrtin Jdriæ, Božo Terziæ, Identifiction of Induction Motor Prmeters from Free Accelertion nd Decelertion Tests, Automtik, vol. 46, pp , Jnury [4] A. Kpun, M. Èurkoviè, A. Hce nd K. Jezernik, Identifying dynmic model prmeters of BLDC motor, Simultion Modelling Prctice nd Theory, vol.16, pp , October [5] M. 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