Design of PI Controller for Angular Velocity Control of Brushed DC Motor plus Neuro Adaptive Control

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1 Seinr Nsionl ke 9: ekys Teknologi Industri dn Inforsi Design of PI Controller for Angulr Velocity Control of Brushed DC Motor plus Neuro Adptive Control Sbt Anwri Deprten of Electrotechnic ITENAS Bndung Abstrk ecently, the DC otor hs been widely used in industry even though its intennce costs re higher thn the induction otor. Although control theory hs de gret dvnce in the lst few decdes, which hs led to ny sophisticted control schees, PID (Proportionl Integrl Derivtive) control still reins the ost populr type of control being useed in industries tody. This populrity is prtly due to the fct tht PID controllers hve siple structures nd very well understood principles. PI controller is essentilly PID controller with the derivtive (D) coefficient set equl to zero. A derivtive coefficient is not essentil nd y hve detrientl effect on syste response chrcteristics especilly in first order syste.generlly, the DC servo otor systes hve uncertin nd nonliner chrcteristics which degrdeperfornce of controllers.to llevite the probles,we dded robustifying dptive gin. Bsed on ypunov synthesis ethod, it ws shown tht the proposed dptive gin gurnteed the convergence of the trcking error to zero nd the globl boundedness of ll signls in the closed-loop syste. eywords : brushed dc otor, PI controller, neurl dptive control, siultion.. Introduction Due to its excellent speed control chrcteristics, the DC otor hs been widely used in industry even though its intennce costs re higher thn the induction otor (Fisher, et. l., 996). As result, speed control of DC otor hs ttrcted considerble reserch nd severl ethods hve evolved. Although ny dvnced control techniques such s robust control (ucukdeirl, et. l., 999), odel reference dptive control (Anwri nd usuh, 6), robust odel reference dptive control (Anwri, 6), ADAINE Bsed Adptive Control (He nd Xu, 8), Fuzzy ogic Control (Akbrzdeh, et. l., 997; Bulut, et. l., ), neurl network (Weersoory nd Al-Shrkwi, 99), nd sliding ode control (Jovnovic nd Golo, 997) hve been proposed to iprove syste perfornces, the conventionl PI/PID controllers re still doinnt in jority of relworld servo systes (Nnd nd Sen, 987). PID controllers re siple in structure, esy for ipleenttion, hve low cost, inexpensive intennce, nd effectiveness. However, they y produce lrge overshoots nd overoscilltory responses. Cobining PID control with other control techniques often results in dvnced hybrid schees tht re ble to iprove pure PID controllers. For exple, i et l proposed fuzzy pre-copensted PID controller for DC otor position servo syste (i, et. l., 994); Mtsung et l presented switching-type hybrid schee in which the syste controller switches between fuzzy controller nd PID controller (Mtsung, 99); i nd Tsng proposed concurrent rely-pid controller (i nd Tsng, 7). PI controller is essentilly n dpttion of PID controller with the derivtive (D) coefficient set equl to zero. PI controller is sipler thn PID controller. Although the forule for the PI coefficients re siple, they re pplicble to DC otor control syste. One of the first pplictions of PI controller to DC otor control syste ws crried out by Zein et l (Zein, et. l., 99). They used switchble ded-bnd PI controller to control DC otor. Ji nd Sul proposed self tuning PI controller using digitl signl processor (Ji nd Sul, 995). Ircleous nd Alexndridis used fuzzy logic to tune PI controller (Ircleous nd Alexndridis, 995). Sundreswrn nd Vsu proposed genetic lgorith to tune PI controller for speed control of DC otor (Sundreswrn nd Vsu, ). Dobr proposed robust PI synthesis, vi MI optiiztion (Dobr, ). In this pper, we propose cobintion of clssicl PI controller nd neurl dptive control to iprove trnsient response. The first is to design PI controller. The second is to dd robustifying dptive neurl controller to intin stbility in the fce of odeling iprecision nd uncertinty. In the siultion experients of this pper, the proposed controller ws pplied on brushed DC otor control to prove its effectiveness. Sekolh Tinggi Teknologi Nsionl (STTNAS) Yogykrt 35

2 Seinr Nsionl ke 9: ekys Teknologi Industri dn Inforsi. Modelling A theory is generl stteent of principle bstrcted fro observtion. A odel is representtion of theory tht cn be used for control nd prediction. For odel to be useful, it ust be relistic nd yet siple enough to understnd nd nipulte. These requireents re not esily fulfilled s relistic odels re seldo siple nd siple odels re seldo relistic. The scope of odel is defined by wht is considered relevnt. Fetures or behviour tht is relevnt ust be included in the odel nd those tht re not cn be ignored. Modelling refers to the process of nlysis nd synthesis to rrive t theticl description tht contins the relevnt dynic chrc-teristics of the prticulr odel (Ong, 998). Figure. Brushed DC Motor Construction The sttor of the DC otor hs poles, which re excited by DC current to produce gnetic fields. The rotor hs ring-shped linted iron-core with slots. Coils with severl turns re plced in the slots. The distnce between the two legs of the coil is bout 8 electric degrees. The coils re connected in series. To keep the torque on DC otor fro reversing every tie the coil oves through the plne perpendiculr to the gnetic field, split-ring device clled couttor is used to reverse the current t tht point. The couttor shown in Figure consists of insulted copper segents ounted in cylinder. The electricl contcts to the rotting ring re clled "brushes" since copper brush contcts were used in erly otors. Modern otors norlly use spring-loded crbon contcts, but the historicl ne for the contcts hs persisted. Two brushes re pressed to the couttor to perit current flow. The brushes re plced in the neutrl zone (gnetic field is close to zero) to reduce rcing (ruse, 989). Figure. Concept of The Couttor In ny electric otor, opertion is bsed on siple electrognetis. A current crrying conductor genertes gnetic field which when plced in n externl gnetic field, it will experience force proportionl to the current in the conductor nd to the strength of the externl gnetic field. The internl configurtion of DC otor is designed to hrness the gnetic interction between current-crrying conductor nd n externl gnetic field to generte rottionl otion. The geoetry of the brushes, couttor contcts, nd rotor windings re such tht when power is pplied, the polrities of the energized winding nd the sttor gnet(s) re isligned, nd the rotor will rotte until it is lost ligned with the sttor's field gnets. As the rotor reches lignent, the brushes ove to the next couttor contcts, nd energize the next winding. To perfor the siultion of syste, n pproprite odel needs to be estblished. For this pper, the syste contins DC otor. Therefore, odel bsed on the otor specifictions needs to be obtined. Figure 3. Schetic Digr of Brushed DC Motor Applying constnt sttor current nd ssuing gnetic linerity, the bsic otor equtions re T I () e () et the switch SW be closed t t =. After the switch is closed, di e I (3) q Fro Eqution () nd (3) di I (4) q d T I J B T (5) The ter Brepresents the rottionl loss torque of the syste. Sekolh Tinggi Teknologi Nsionl (STTNAS) Yogykrt 36

3 Seinr Nsionl ke 9: ekys Teknologi Industri dn Inforsi The stte-spce representtion is given by the equtions: x Ax Bu (6) y Cx Du where x, B / J / J A, i / q / q / J B, u, y, C, / q T nd D. The trnsfer function between ngulr velocity nd voltge is A v (7) V s B s B t The trnsfer function between ngulr velocity nd od Torque is A (8) T s Bs B where A v, A, J q J B B,.nd (B ) B. J J q In ost DC otors, the rotor inductnce nd the vlue of B re sll tht cn be neglected to led to reduced order. If is neglected then Eq. (4) becoes V I (9) t If B is neglected then Eq. (5) becoes d T I J T q () The current-voltge reltionship for the left hnd side of the eqution cn be written nd nipulted to relte between voltge nd ngulr velocity. e I () T V t ( d J T (3) d T J J (4) J The noinl first order liner odel of otor is shown in (5). d T 5.3 (5) x Since T is unknown, it cn be included in the plnt perturbtion, hence trnsfer function of the noinl plnt is 5.3 G (s) (6) s The exct odel nd the noinl odel cn be relted s G G ( ) (7) where G is exct odel, G is noinl odel, nd is ultiplictive perturbtion. 3. Controller Design The PI controller cn be written in this for: p (s i/ p ) C(s) (8) s If we set i nd p then the closed loop 5.3 p trnsfer function is CTF(s) (9) s Uncertnty in processes dynics of the plnt led to poor control perfornces if controller preters re not properly dpted. To overcoe this proble we propose control input s follows C(s) PI(controller) C r () where C is robustifying control ter. r The first stge in designing n dptive controller schee for DC otor, the gol of the control is to drive speed of dc otor ω to the desired speed ω. et us d define e ω ω s trcking error. We firstly define d the error etric s follows: t s e λ e dτ () where λ is positive rel constnt. The gol is n idel condition i.e. s () s (3) If syste sttes rein on the idel condition, the trcking error e will governed fter such finite ount of tie by the first-order differentil eqution e λ e. Thus the trcking error e will converge syptoticlly to s t becuse λ is positive constnt (Slotine nd i, 99). Bsed on PI controller pplied in noinl odel (odel without uncertinty) will iply e e (4) Sekolh Tinggi Teknologi Nsionl (STTNAS) Yogykrt 37

4 Seinr Nsionl ke 9: ekys Teknologi Industri dn Inforsi Bsed on PI controller pplied in rel odel with uncertinty will iply e e (5) where is the error between ppliction of rel odel nd noinl odel. et the control input u cn be chosen s Eqs. will iply e e (6) C r The robustifying control ter C cn be r constructed s function of error etric vribles, s follows C r Ws W (7) where W nd W re dptble weights tht re uped during the opertion. The gol is to push s to zero in finite tie. To chieve this requireent, the following ypunov function is selected V s (8) The function selected is positive definite nd its vnishes only when s. A globl reching condition is its tie derivtive be negtive definite. Choosing its tie derivtive s V γs (9) where, γ is positive constnt, restricts the derivtive to be negtive definite. Substituting (8) into (9), the following eqution is obtined s s γs (3) Going one step further, s (s γ s) (3) Hence, for the ypunov stbility criteri to be held, s γs (3) ust be stisfied for s. A solution to this proble cn be using n dptive weight tht iniizes the function s γ s nd eventully kes it zero, without need for the infortion bout the syste dynics. As stted bove, the gol is to push the function s γ s to zero. To chieve this gol the error function E (s γs) (33) is introduced to the syste nd weights re uped ccordingly. Weights re uped using siple grdient descent pproch in continuous for or bck propgtion : E w j (34) w j where, η is the lerning constnt, generlly chosen between nd. To copute the weight upes, the derivtive of the error function E w.r.t. w should be j found. Using the chin rule, the derivtive cn be written s E E k (35) w j k w j Substituting (33) into (35) nd tking the derivtives, the following eqution is obtined: (s γ s) (s γ s) σ k i E for j (36) w j (s γ s) (s γ s) k for j 4. Siultion esults od torque ws unknown but in the siultion it ws ssued s follows 6 T 9.8 x N (37) In order to vlie the control strtegies s described bove, digitl siultion ws crried out on DC otor drive syste. A coprtive study of the results obtined with Proportionl Integrl Derivtive (PID) controller nd PI Controller plus Neuro Adptive Control (PINAC) ws presented in this section. The control siultion results re shown in Figure 4 nd Figure 5. ngulr velocity (rd/sec) tie (sec) Figure 4. Siultion esult of DC Motorwith PID Controller Sekolh Tinggi Teknologi Nsionl (STTNAS) Yogykrt 38

5 Seinr Nsionl ke 9: ekys Teknologi Industri dn Inforsi ngulr velocity (rd/sec) tie (sec) Figure 5. Siultion esult of DC Motorwith PINAC Controller Figure 4 shows tht the response of the DC otor with Proportionl Integrl Derivtive (PID) controller while Figure 5 depicts the speed of the DC otor using PI Controller plus Neuro Adptive Control (PINAC) controller. Applying PID controller to the syste, the speed chieved is slightly lower thn the PINAC. There is no overshoot when PINAC is pplied while using PID there is little overshoot. esults in Fig. 4 nd Fig. 5 show tht the PINAC perfors slightly better thn the PID controller. 5. Conclusions The control of DC otor ws investigted in this reserch work with PI Controller plus Neuro Adptive Control (PINAC) controller. The conclusion is tht PINAC ws found to be superior, ore robust, fster, flexible, nd less sensitive to the preter vritions s copred with conventionl PID controllers. Siultion results re presented to deonstrte the potentil of the proposed schee. It hd been shown tht the proposed schee hs severl dvntges such s, sll stedy stte error, fst response, nd sll overshoot. eferences Akbrzdeh, T. M.., i, Y.T.,nd Feerouzbkhsh, B. (997).Evolutionry Fuzzy Speed egultion for DC Motor, Proceedings of the 9th Southestern Syposiu on Syste Theory (SSST '97).pp Anwri, S. (6). obust Model eference Adptive Control of Angulr Velocity Control Siultion of Brushed DC Motor, JurnlTeknikElektro.Vol. 6.No.. pp Anwri, S. nd usuh, D. (6).Angulr Velocity Control Siultion of Brushed DC Motor Using Model eference Adptive Control.JurnlItens, Vol. 9. No. 4. pp Bulut, M., Cnsever, G., nd Ustun, S. V. ().Fuzzy Model-Bsed erning for DC Motor Controller.ICSPAT DSP World Conference, Dlls, Texs. USA.6-9 Oct. Dobr, P. ().obust PI Control for Servo DC Motor.Interntionl Conference on Control Applictions.Vol.. pp.. Fisher, M. E., Ghosh, A., nd Shrf, A. M. (996).Intelligent Control Strtegies for Pernent Mgnet DC Motor Drives.Proceedings of the 996 Interntionl Conference on Power Electronics, Drives nd Energy Systes for Industril Growth. New Delhi. Indi.Vol..pp He, S. nd Xu, X. (8). Hrdwre/Softwre Codesign Approch for n ADAINE Bsed Adptive Control Syste.Journl of Coputers.Vol. 3.No., Feb. pp Ircleous, D. P. nd Alexndridis, A. T. (995). Fuzzy Tuned PI Controllers for Series Connected DC Motor Drives.Proceedings of the IEEE Interntionl Syposiu on Industril, Athens. Greece.Vol.. pp Ji, J.. nd Sul, S.. (995).DSP-Bsed Self-Tuning IP Speed Controller with od Torque Copenstion for olling Mill DC Drive.Trns. on Industril Electronics.Vol. 4.No. 4.Aug. pp Jovnovic, Z., nd Golo, G. (997).DC Motor Position Control by Discrete-Tie Vrible Structure Controllers.The Scientific Journl FctUniversittis, Series: Mechnics, Autotic, Control nd obotics. Vol.. No 7. pp i, J. H., i,. C., nd Chong, E.. P. (994).FuzzyPrecopensted PID Controllers.IEEE Trns. Contr. Sys. Tech. Vol.. pp ruse, P. C. nd Wsynczuk, O. (989).Electroechnicl Motion Devices.McGrw-Hill. Singpore. ucukdeirl, I. B., Cnsever, G., nd Gulez,. (999).Design of Dynic nd obust Speed Controller for DC Servo Motor by Using DSP.Proc. nd Interntionl Conference on Mtheticl nd Coputtionl Applictions in Engineering. Bku. Azerbijn. Sep. 3.pp i, G. nd Tsng,. M. (7).Concurrent ely-pid Control for Motor Position Servo Systes.Interntionl Journl of Control, Autotion, nd Systes.Vol. 5.No. 3. June. pp Mtsung, N. (99).Fuzzy Hybrid Control of DC Servootor.Trns. IEE Jpn.Vol.. pp. 5. Nnd, P.. nd Sen, P. C. (987).Anlog nd Digitl Speed Control of DC Drives Using Proportionl Integrl nd Integrl-Proportionl Control Techniques.IEEE Trns. Ind. Electron, Vol. 34. pp Ong, C. M. (998).Dynic Siultion of Electric Mchinery.Prentice Hll Interntionl. New Jersey. Slotine, J.E., nd i., W.(99).Applied Nonliner Control.PenticeHll Interntionl. New Jersey. Sekolh Tinggi Teknologi Nsionl (STTNAS) Yogykrt 39

6 Seinr Nsionl ke 9: ekys Teknologi Industri dn Inforsi Sundreswrn,. nd Vsu, M. ().Genetic Tuning of PI Controller for Speed Control of DC Motor Drive.Proceedings of IEEE Interntionl Conference on Industril technology (ICIT-).Go. Vol.. Jn. pp Weersoory, S. nd Al-Shrkwi, M. A. (99). Identifiction nd Control of DC Motor Using Bck-Propgtion Neurl Networks.IEEE trnsctions on Energy Conversion. Vol. 6, No. 4.Dec. pp Zein, S., sss, M., nd Wells, F. M. (99).A Switchble DB-PI Controller for DC-Motor Drives with Trnsient equireent.proceedings of the IEEESouthestcon '9. New Orlens. A. April.Vol. 3. pp Sekolh Tinggi Teknologi Nsionl (STTNAS) Yogykrt 4