Optimization of PI Controller using PSO for Power Electronic Converter

Transcription

1 IOSR Journal of Eletral and Eletrons Engneerng (IOSR-JEEE) e-issn: ,p-ISSN: , Volume 9, Issue 2 Ver. VI (Mar Apr. 214), PP 36-4 Optmzaton of PI Controller usng PSO for Power Eletron Converter B.Ahammal 1, R.Kayalvzh, 2 1 Eletrons and Instrumentaton Engneerng, Annamala Unversty, Inda. 2 Eletrons and Instrumentaton Engneerng, Annamala Unversty, Inda. Abstrat: DC-DC onverters are wdely used n applaton suh as omputer perpheral power supples, ar auxlary power supples and medal equpment s. Postve output elementary Luo onverter performs the onverson from postve soure voltage to postve load voltage. Due to the tme- varyng and swthng nature of the power eletron onverters, ther dynam behavor s hghly non-lnear. Conventonal ontrollers are napable of provdng good dynam performane and hene optmzed tehnques have been developed to tune the PI parameter. In ths work, Partle Swarm Optmzaton (PSO) s developed for PI optmzaton. Smulaton results show that the performanes of ontrollers are better than those obtaned by the lassal ontroller. Keywords: PI ontroller, DC-DC onverter, postve elementary Luo onverter, partle swarm optmzaton and soft omputng tehnque I. INTRODUCTION Many ndustral applatons requre power from varable DC voltage soures. DC-DC onverters onvert fxed DC nput voltage to a varable DC output voltage for use n suh applatons. DC-DC onverters are also used as nterfae between DC systems of dfferent voltage levels. Postve output elementary Luo onverter s a reently developed subset of the DC-DC onverters. Ths onverter provdes postve load voltage for postve supply voltage. Luo onverters overome the effets of the parast elements that lmt the voltage onverson rato. These onverters n general have omplex non-lnear modes wth parameter varaton problems. PI ontrollers do not provde satsfatory response for these onverters whh are tme varyng systems. Hene optmzed tehnques are used for regulatng the postve output elementary Luo onverter. In ths work, PI ontroller, PSO based PI ontroller s desgned and smulated for the above Luo onverter. The performane ndes used s Integral Squared Error (ISE) and Integral Absolute Error (IAE). II. MODELLING OF POSITIVE OUTPUT ELEMENTARY LUO CONVERTER A postve output elementary Luo onverter (Fg.1) performs step-up/step-down onversons from postve nput DC voltage to postve output DC voltage. The voltage transfer rato of the above onverter s (k/ (1-k)) where k s the duty rato. The ruts (Fg.2 and Fg.3) for the swth-on and swth-off modes of the hosen onverter are developed usng a state-spae approah. At ths pont, these two models are averaged over a sngle swthng perod T usng a state-spae averagng tehnque. The state varables are: X 1 = L1, X 2 = L2, X 3 = V o, X 4 = V o (1) Usng the above state varables, the system matres A 1 and A 2, nput matres B 1 and B 2 and output matres C 1 and C 2 are obtaned. Fg. 1 Postve output elementary luo onverter 36 Page

2 Optmzaton of PI Controller usng PSO for Power Eletron Converter Fg.2 Postve output elementary Luo onverter on mode Fg.3 Postve output elementary Luo onverter off mode III. DESIGN OF PI CONTROLLER The funton of a ontroller s to reeve the measured proess varable (pv) and ompare t wth the set pont (sp) to produe the atuatng sgnal (m) so as to drve the proess varable to the desred value. Therefore the nput to the ontroller s the error (sp-pv). It s also known as proportonal plus reset ontroller. The atuatng sgnal m( s related to the error e( by the equaton. 1 m( K e( ( K / T ) e( dt ms (2) Where T s the ntegral tme onstant or reset tme and 1/T s alled repeats per mnute. After a perod of T mnutes for a onstant error E, the ontrbuton of ntegral term s T1 K / T e( dt ( K / T ) ET K E (3) The ntegral aton has repeated the response of the proportonal aton. Reset tme s the tme needed to repeat the ntal proportonal aton hange n ts output. The ntegral aton auses the ontroller output m( to hange as long as an error exsts the proess output. The transfer funton of a PI ontroller G (s)=k [1+1/T s] (4) IV. PARTICLE SWARM OPTIMIZATION Partle Swarm Optmzaton (PSO) was orgnally developed by Kennedy and Eberhart n 1995 s a populaton-based evolutonary algorthm. It was nspred by the soal behavor of brd and fsh shoolng, and has been found to be robust n solvng ontnuous nonlnear optmzaton problems. In PSO, the swarm s ntalzed wth a populaton of random solutons. Eah partle n the swarm s a dfferent possble set of the unknown parameters to be optmzed. Representng a pont n the soluton spae, eah partle tres to adjust ts flyng toward a potental area aordng to ts own flyng experene and shares soal nformaton among partles. The objetve s to effently searh the soluton spae by swarmng the partles toward the best fttng soluton enountered n prevous teratons wth the ntent of enounterng better solutons through the ourse of the proess and fnally onvergng on a sngle mnmum error soluton. For a multdmensonal problem, the veloty and poston of eah partle n the swarm are updated usng the followng equatons: V k+1 = WV k +C 1 rand(pbest S k ) +C 2 rand(gbest _ _ S k ) (5) X k+1 =X k +V k+1 Where, V k+1 s the veloty of the th partle at (k+1) teraton, X(k+1) s the poston of the th partle at (k+1) teraton, w s the nertal weght fator (weghtng funton), C1 and C2 are aeleraton onstants alled ogntve learnng rate and soal learnng rate respetvely, rand s the random funton n the range [,1], pbest s the ndvdual best poston of the partle, gbest s the global best poston of the swarm of the partles. The flow hart of PSO based PI ontrol algorthm as shown n Fg.4 (6) 37 Page

3 Optmzaton of PI Controller usng PSO for Power Eletron Converter Fg.4 Flow hart of PSO The weghtng funton, w s responsble for dynamally adjustng the veloty of the partles, hene t s responsble for balanng between loal and global searh. Applyng a large nerta weght at the start of the algorthm and deayng to a small value through the PSO exeuton makes the algorthm searh globally at the begnnng and loally at the end of the exeuton. The weghtng funton w s alulated as: w = w max (w max - w mn ) ter (7) ter max Here, w max and w mn are the ntal and fnal weghts, ter s the urrent teraton tme and ter max s the maxmum number of teratons. The proposed Ftness funton for the optmzaton of parameters of PI ontroller s defned as: F(s)=w max (Mp+ISE+IAE)+w mn (T R +T S ) (8) V. Performane Indes The performane of a ontroller s best evaluated n terms of error rteron. In ths work, ontroller performane s evaluated n terms of Integral Square Error (ISE) and Integral Absolute Error (IAE) ISE = (9) IAE (1) The ISE and IAE weght the error wth tme and hene mnmze the error values nearer to zero. VI. Smulaton Results The rut parameters of the postve Output elementary Luo Converter are shown n the Table 1. The ontroller parameter values of the onventonal and ontrollers are obtaned. The responses of postve output elementary Luo ontroller usng onventonal and ontroller are shown n Fgures 5,6,7 and 8. Table 2 shows the performane evaluaton of postve output elementary Luo onverter usng onventonal and ontrollers. Smulaton results shows that ontroller wll drastally redue the overshoot, ISE and IAE values as ompared to the onventonal PI ontroller. 38 Page

4 output voltage n volts output voltage n volts output voltage n volts Optmzaton of PI Controller usng PSO for Power Eletron Converter TABLE. 1 CIRCUIT PARAMETERS OF POSITIVE OUTPUT ELEMENTARY LUO CONVERTER Parameter Symbol Value Input Voltage V n 1 V Output Voltage V o 4V Indutor L 1µH Capator C 5µF Frequeny F 5khz Load resstor R 1Ω Duty rato D tme n ses Fg. 5 Closed loop response of Postve Output Elementary Luo onverter tme n ses Fg. 6 Servo response of Postve Output Elementary Luo onverter wth nrease n referene voltage from 4V-45V at.1se tme n ses Fg. 7 Closed loop response of Postve Output Elementary Luo onverter wth sudden lne dsturbane from 1V-11V (1%) at 8 mse. and 1V-9V(1%) at 14 mse 39 Page

5 output voltage n volts Optmzaton of PI Controller usng PSO for Power Eletron Converter tme n ses Fg. 8 Closed loop response of Postve Output Elementary Luo onverter wth sudden load dsturbane from 1Ω -11Ω (1%) at 8 mse. and 1 Ω - 9Ω(1%) at 14 mse TABLE.2 PERFORMANCE EVALUATION OF POSITIVE OUTPUT ELEMENTARY LUO CONVERTER Tunng Parameters Controller Controller Rsng tme (m.se).5.45 Startup Transent Settlng tme (m.se) Peak Overshoot % ISE IAE.1.39 Settlng tme (m.se) 3.7 Lne Dsturbane Load Dsturbane Lne Inrease 1% Lne derease 1% Load nrease 1% Load derease 1% VII. Peak Overshoot % ISE IAE.11.4 SETTLING TIME (M.SEC) Peak Overshoot % ISE IAE Settlng tme (m.se) PEAK OVERSHOOT % ISE IAE Settlng tme (m.se) Peak Overshoot % ISE IAE Conluson In ths work, Partle Swarm Optmzaton (PSO) algorthm s developed to tune the PI ontroller parameters whh ontrol the performane of postve output elementary Luo onverter. The smulaton results onfrm that PI ontroller tuned wth PSO algorthm rejets satsfatorly both the lne and load dsturbanes. Also the results proved that ontroller gves the smooth response for the referene trakng and mantans the output voltage of the postve output elementary Luo onverter aordng to the desred voltage. Referenes [1]. Luo,F.L, Postve output Luo- onverter voltage lft Tehnque, IEE-EPAproessdngs,146(4),July 1999,pp [2]. J.F.HUANG, F.B.DONG, Modellng and Control on Isolated DC-DC Converter, Power Eletrons, voi.44, pp.87-89, Aprl 21. [3]. M. Namnabat, M. Bayat Poodeh, S. Eshtehardha, Comparson the Control Methods n Improvement the Performane of the DC-DC Converter, Internatonal Conferene on Power Eletrons 27, (ICPE 7), pp , 27. [4]. Martn Plesnk., Use of the State spae averagng tehnque n fast steady state smulaton algorthms for swthng power onverters, eeexplore.eee.org CCECE 26. [5]. J.You, S.B.Kang,"Generalzed State Spae Averagng based PWM Retfer Modellng", Eletral Measurement &Instrumentaton vo1.46, pp.67-7, Otober 29 [6]. R.Suresh Kumar, J.Suganth, Improvng the Boost Converter PID Controller Performane Usng Partle Swarm Optmzaton,EuropenJournal of Sentf Researh, Vol.85 No3 September,212,pp [7]. Y.L and Z.C.Duan, Optmzaton for parameter of PID based on PSO, Mahnery & Eletrons, Issue: 9 pp , 24. [8]. B.Nagaraj, P. Vjayakumar A omparatve study of PID ontroller tunng usng GA, EP, PSO, and ACO, Journal of Automaton, Moble Robots & Intellgent Systems, volume 5, 211. [9]. B. Nagaraj, S. Subha, B. Ramprya, Tunng Algorthms for PID Controller usng Soft Computng Tehnques, IJCSNS Internatonal Journal of Computer Sene and Network Seurty, vol,8,no.4,aprl 28. [1]. Ian Grffn, On-lne PID Controller Tunng usng Genet Algorthms, Dubln Cty Unversty, 23 4 Page