Interntionl Journl of Reserch Studies in Science, Engineering nd Technology Volue 2, Issue 11, Noveber 215, PP 12-19 ISSN 2349-4751 (Print) & ISSN 2349-476X (Online) Differentil Evolutionry Algorith Bsed PID Controller Design for Antenn Aziuth Position Control Syste G.Srvnn, R.Revthi, R.Jeevith Deprtent of EEE, PR Institute of Engineering nd Technology, Til Ndu, Indi Abstrct: In this pper, ntenn ziuth position control syste with PID controller ws proposed. PID controllers re inly used becuse of its siplicity, robustness nd successful prcticl ipleenttions. Mny PID controllers tuning ethods re vilble like Ziegler-Nichols (ZN) ethod, Modified Ziegler-Nichols without overshoot (MZN-NOOS) ethod, Modified Ziegler-Nichols with overshoot (MZN-OS) ethod nd Tyreus- Luyben (TL) ethod. All the ethods re siulted in MATLAB environent nd the results re copred with differentil evolutionry lgoriths bsed PID controller which hs less overshoot nd sooth response. eywords: Ziegler-Nichols (ZN), Modified Ziegler-Nichols without overshoot (MZN-NOOS), Modified Ziegler-Nichols with overshoot (MZN-OS), Tyreus- Luyben (TL), Differentil Evolution (DE, Proportionl Integrl Controller (PID). 1. INTRODUCTION The Aziuth Position control syste obtins n output response fro input cond signl. This control syste is used inly used in ntenns, robot rs, rocket fire nd coputer disk drives. The position of ntenn is inly controlled by using gers nd feedbck potentioeter. For better response PID controller is used before the preplifier but fter the power plifier. Output ngle of the ntenn θ o (t) is get fro the input ngle of the potentioeter θ i (t). Fig 1 shows the pictoril view of ziuth control syste. In this syste ngulr displceent is n input cond signl. The potentioeter converts the ngulr displceent in to voltge. In the se wy potentioeter in the output pth converts the output ngulr displceent into the voltge. The signl nd power plifiers boost the difference between the input nd output voltges. The plified ctuting signl drives the plnt [1]. Fig1. Lyout of Antenn Aziuthl position control syste Fig 2 shows the coponents of ntenn ziuth control syste. In this the potentioeter which is plced t the top ost position is controlled by the operting personnel. The signl is first received by the differentil preplifier nd then it goes to the power plifier. The output signl fro the power plifier goes to the otor nd then to the ger. This ger is connected to nother ger for the oveent of ntenn. Finlly the ntenn s signl is connected to potentioeter nd nother ger. The feedbck signl is going fro the potentioeter bck into the differentil plifier. After tht differentil plifier check how uch the obtined signl is different fro the given signl nd lso find the error. Power plifier plifies the input signl. Motor will run until the error pproches to zero. Interntionl Journl of Reserch Studies in Science, Engineering nd Technology [IJRSSET] 12
Differentil Evolutionry Algorith Bsed PID Controller Design for Antenn Aziuth Position Control Syste Fig2. Coponents of Antenn Aziuthl position control syste 2. MODELING OF AZIMUTH POSITION CONTROL SYSTEM Block digr of Aziuthl position control syste consists of two potentioeters one t input side nd other t the output side, preplifier, power plifier, otor, lod nd gers. Trnsfer function of oor nd lod is E ( s) ( s) s( s ) The eqution for inerti nd dping coponents re given s J J A J L ( g 2 ) D D A DL( g 2 ) In below eqution, N1 nd N2 represent the ger teeth rtio g N N 1 2 Motor nd lod block s pole nd zero is represented s D R JR bt t JR Where R is the resistnce of the otor, b nd t re the bck EMF nd torque constnt of the otor respectively. Fig3. Block digr of Azhiuthl position control syste Interntionl Journl of Reserch Studies in Science, Engineering nd Technology [IJRSSET] 13
G.Srvnn et l The closed loop control syste for controlling the ziuthl position control is given by ( s) 1 g ( s) s( s )( s o i Tble1. Shows the preters of block digr ) Preters Vlue 1 1 1 1.8 1.32 g.2 3. PID CONTROLLER A PID controller is control loop feedbck echnis coonly used in industril control systes. PID controller involves three seprte constnt preters nd therefore it is sid to be three-ter control. They re P stnds for the proportionl ter I for the integrl ter nd D for the derivtive in the controller. An error vlue is clculted by the PID controller s the difference between esured process vrible nd desired set point. The error is iniized by PID controller by djustent of control vrible, such s the position of control vlve, dper, or the power supplied to heting eleent, to new vlue deterined by weighted su: Where p, i nd d ll non-negtive, denote the coefficients for the proportionl, integrl, derivtive nd ters, respectively. PID controllers perfor well for brod rnge of processes nd they will give resilient presenttion for wide rnge of working conditions nd re esy to execute using nlog or digitl hrdwre. Fig 4 shows the block digr of PID controller. The syste odel is given by, G ( s) c d s 2 s p s I Fig4. Block digr of PID controller 4. TUNING METHODS The PID controller tuning ethods re clssified into two in ctegories such s closed nd open loop ethods. The closed loop tuning ethods re Ziegler-Nichols ethod, Modified Ziegler-Nichols with nd without overshoot ethod, Tyreus- Luyben ethod nd Dped oscilltion ethod. Tble 2 shows the tuning rules for vrious closed loop tuning ethods of PID controllers. Tble2. Vrious tuning rule of PID controller P T i T D ZN.6 u P u /2 P u /8 MZN-NOOS.2 u P u /2 P u /2 MZN-OS.33 u P u /2 P u /3 TL.45 u 2.2 P u P u /6.3 Interntionl Journl of Reserch Studies in Science, Engineering nd Technology [IJRSSET] 14
Differentil Evolutionry Algorith Bsed PID Controller Design for Antenn Aziuth Position Control Syste 5. DIFFERENTIAL EVOLUTION ALGORITHM Differentil Evolution (DE) lgorith is siple evolutionry lgorith for optiiztion of ultidiensionl rel vlued functions. DE optiizes proble by intining popultion of cndidte solutions nd creting new cndidte solutions by cobining existing ones ccording to its siple forule, nd then keeping whichever cndidte solution hs the best score or fitness on the optiiztion proble t hnd. The optiiztion process is preceded by ens of three in opertions: uttion, crossover nd selection. DE ws heuristic optiiztion lgorith nd the pseudo-code of DE [4-5] ws given below in section 5.1 5.1. DE Algorith 1: Select P, F nd CR nd Set G= 1 2: P G = initilize popultion rndoly 3: while terintion criteri not stisfied do 4: for ech individul in P G do 5: Select uxiliry prents 6: Crete offspring using uttion nd crossover 7: 8: end for 9: Set = + 1 1: end while 5.2. Objective Function The proble of PID controller preter selection is forulted s n optiiztion proble, the objective function of which is given by The bove optiiztion proble is subjected to the following constrints PID controller is tuned by tuning ethods nd the vlues of P, I, D, t r, t s, t p, re shown in tble 3. Tble3. Bound vlue of PID controller Preters Min.Vlue Mx.Vlue P 3 I 1 D 3 Tble4. P I D Vlue of vrious ethods nd esured vlue of syste response Preters P I D t r t s t p Pek vlue % Pek vlue ZN 157.7151 579.7789 1.7815.163 3.716.4987 1.6767 67.641 MZN-NOOS 52.5717 192.2596 14.3753.161 3.283.8325 1.3354 33.5359 MZN-OS 86.7433 317.2284 15.81279.1274 2.493.8285 1.3782 37.8167 TL 118.2863 98.3146 1.2681.131 1.3984.8758 1.4171 41.789 DE 2.577.1686 1.3572 1.8891 2.595.921 1.657 6.5739 6. RESULTS AND DISCUSSION The rise tie, settling tie, pek tie nd pek vlue re considered in rel tie opertions but ll this specifictions re not chieving in ny conventionl ethods nd ny optiiztion techniques. In this work, pek vlue is only considered nd the iniu vlue is chieved in DE lgorith but it Interntionl Journl of Reserch Studies in Science, Engineering nd Technology [IJRSSET] 15
Pek vlue Rise tie in sec Pek tie in sec Settling tie in sec G.Srvnn et l hs high settling tie, Pek tie nd rise tie s copred with conventionl ethods. Fig 5 shows the coprison of settling tie of vrious ethods. Of tht TL hs fst settling tie. Fig 6 shows the coprison of pek tie of vrious tuning ethods nd it is observed tht ZN hs iniu pek tie. Fig 7 shows Rise tie coprison of vrious ethods nd it is cler tht ZN hs low rise tie copred to other ethods. Fig 8 nd 9 shows the coprison of pek vlue nd its percentge vlue nd it is proven tht DE hs inil vlue copred to other conventionl ethods. Fig 1. Shows the Bode plot of different ethods which re used to find the gin rgin. Fig 11 nd 12 shows the step response chrcteristics. 4. 3. 2. 1.. ZN MZN-NOOS MZN-OS TL Fig5. Settling tie coprison of vrious ethods.5.4.3.2.1. ZN MZN-NOOS MZN-OS TL Fig6. Pek tie coprison of vrious ethods.16.14.12.1 ZN MZN-NOOS MZN-OS TL Fig7. Rise tie coprison of vrious ethods 2. 1.5 1. Step input.5. Fig8. Pek vlue coprison of vrious ethods Interntionl Journl of Reserch Studies in Science, Engineering nd Technology [IJRSSET] 16
Aplitude Aplitude Phse (deg) Phse (deg) Phse (deg) Mgnitude (db) Mgnitude (db) Mgnitude (db) % of pek vlue Differentil Evolutionry Algorith Bsed PID Controller Design for Antenn Aziuth Position Control Syste 7. 6. 5. 4. 3. 2. 1.. Fig9. % Pek Vlue coprison of vrious ethods Bode Digr Bode Digr Bode Digr 2 2 2 ZN MZN-NOOS TL -2-2 -2-4 -4-4 -6-6 -6-8 -8-8 -1-1 -1 45 45 ZN MZN-NOOS TL -45-45 -45-9 -9-9 -135-135 -135-18 1 1 1 1 2 1 3 1 4 Frequency (rd/s) -18 1 1 1 1 2 1 3 1 4 Frequency (rd/s) -18 1-1 1 1 1 1 2 1 3 1 4 Frequency (rd/s) Fig1. Bode plot for ZN, MZN-NOOS nd TL ethods 1.8 Step Response 1.4 Step Response 1.6 1.2 1.4 1.2 MZN-NOOS ZN TL 1 1.8.8.6.6.4.4.2.2 1 2 3 4 5 6 Tie (seconds) Fig11. Step response of vrious tuning ethods 5 1 15 2 Tie (seconds) Interntionl Journl of Reserch Studies in Science, Engineering nd Technology [IJRSSET] 17
Aplitude G.Srvnn et l esponse 1.4 Step Response 1.2 DE MZN-NOOS ZN TL 1.8.6.4.2 3 4 5 6 seconds) 5 1 15 2 25 3 35 Tie (seconds) 7. CONCLUSION Fig12. Step response of Differentil lgorith bsed PI controller ethod Antenn ziuth position control syste with DE bsed PID controller provided iniu pek vlue nd sooth response s copred with conventionl tuning ethods. All the works re crried out in MATLAB environent. The optiiztion technique provides p, i nd d vlues re iniu s copred with conventionl tuning which leds esy to ipleent the PID controller for rel tie pplictions. REFERENCES [1] Nise, Norn S.: Control Syste Engineering, 6th ed., John Wiley & Sons, Inc, New York, 211. [2] Bobn Teelkovski nd Jugoslv Achkoski Modeling nd Siultion of Antenn Aziuth Position Control Syste Interntionl Journl of Multidisciplinry nd Current Reserch 4, Vol.2 (Mrch/April 214 issue). [3] Ashish Tewri, 23, Modern Control Design with Mtlb Siulink, John Wiley & Sons Inc., U. [4] Mohd Shhrokhi nd Alirez Zoorrodi, Coprison of PID Controller Tuning. [5] Musrrt Ali, Millie Pnt, nd V. P. Singh, An Iproved Differentil Evolution Algorith for Rel Preter Optiiztion Probles, AMAE Interntionl journl on Production nd Industril Engineering, Vol. 2, No. 1, June 211. [6]. Price, An Introduction to DE, In: Corne, D., Mrco, D., Glover, F.(eds.), New Ides in Optiiztion, McGrw-Hill, London (U), 1999, pp. 78-18. [7] i Heong Ang, Gregory Chong, nd Yun Li, PID Control Syste Anlysis, Design, nd Technology IEEE Trnstions Control Syste Technology, Vol.13, No.4, July 25, pp.559-576. [8] H. Ibrhi Okuus Antenn Aziuth Position Control with Clssicl PID nd Fuzzy Logic Controllers 212 IEEE. [9] Xun L., Estrd J. nd Digicondre J.,''Antenn Aziuth Position Control Syste Anlysis nd Controller Ipleenttion'', ter project, 29. [1] Sukhbir Hundl, Bee Tho, Tyrone Trcy: Antenn Aziuth Position Control Syste Verifiction, 27. Interntionl Journl of Reserch Studies in Science, Engineering nd Technology [IJRSSET] 18
Differentil Evolutionry Algorith Bsed PID Controller Design for Antenn Aziuth Position Control Syste AUTHORS BIOGRAPHY Mr.G.Srvnn, is working s Assistnt Professor (Sr.G), Deprtent of EEE, PR Institute of Engineering nd Technology, Coibtore. He hs Bchelor s Degree in Electricl nd Electronics Engineering nd Msters in Applied Electronics. He hs 7 yers of teching experience nd 2.5 yers of industry experience. His reserch nd teching interests includes Control systes, Electrognetic fields, VLSI Design nd Renewble energy sources. He hs published severl reserch ppers in ntionl nd interntionl journls nd conferences. He is life tie eber in ISTE nd lso eber in IEEE. Ms.R.Revthi, is working s Assistnt Professor, Deprtent of EEE, PR Institute of Engineering nd Technology, Coibtore. She hs Bchelor s Degree in Electricl nd Electronics Engineering nd Msters in Power Electronics nd Drives. She hs 5 yers of teching experience. Her reserch nd teching interests includes Power Electronics nd Drives, She hs published severl reserch ppers in ntionl nd interntionl journls nd conferences. She is life tie eber in ISTE. R.Jeevith, received BE degree in EEE fro SSM College of Enginering in 211 nd ME degree in Power Electronics & Drives t urguru College of Technology, Coibtore in 213. Currently, she is working s Assistnt Professor t PR Institute of Engineering nd Technology, Coibtore. Her res of interest re power Electronics nd Electricl Mchines.She hs published severl reserch ppers in ntionl nd interntionl journls nd conferences. She is life tie eber in ISTE. Interntionl Journl of Reserch Studies in Science, Engineering nd Technology [IJRSSET] 19