Optimal Tuning of PI Controller using Bacterial Foraging Algorithms for Power Electronic Converter B. Achiammal 1, R.Kayalvizhi 2

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1 Internatonal Journal of Soft Computng and Engneerng (IJSCE) ISSN: , Volume-3, Issue-, November 23 Optmal Tunng of PI Controller usng Bacteral Foragng Algorthms for Power Electronc Converter B. Achammal, R.Kayalvzh 2 Abstract- DC-DC converters are wdely used n applcaton such as computer perpheral power supples, car auxlary power supples and medcal equpments. Postve output element Luo converter performs the converson from postve source voltage to postve load voltage. Due to the tmevaryng and swtchng nature of the power electronc converters, ther dynamc behavour s hghly non-lnear. Conventonal s are ncapable of provdng good dynamc performance and hence optmzed technques have been developed to tune the PI parameter. In ths work, Bacteral Foragng (BF) algorthm and Modfed Bacteral Foragng (MBF) algorthm are developed for PI optmzaton. Smulaton results show that the performances of and M s are better than those obtaned by the classcal. Keywords: PID, DC-DC converter, postve elementary Luo converter, Bacteral Foragng Algorthm, Modfed Bacteral Foragng Algorthm. I. INTRODUCTION Many ndustral applcatons requre power from varable DC voltage sources. DC-DC converters convert fxed DC nput voltage to a varable DC output voltage for use n such applcatons. DC-DC converters are also used as nterface between DC systems of dfferent voltages levels. Postve output Luo converter s a recently developed subset of the DC-DC converters. Ths converter provdes postve load voltage for postve supply voltage. Luo converters overcome the effects of the parastc elements that lmt the voltage converson rato. These converters n general have complex non-lnear modes wth parameter varaton problems. PI s do not provde satsfactory response for these converters whch are tme varyng systems. Hence optmzed technques are used for regulatng the postve Luo converter. In ths work, PI, BF based PI and MBF based PI s desgned and smulated for the above Luo converter. The performance ndces used s Integral Squared Error (ISE) and Integral Absolute Error (IAE) II. MODELLING OF POSITIVE OUTPUT ELEMENTARY LUO CONVERTER A postve output elementary Luo converter (Fg.) performs step-up/step-down conversons from postve nput DC voltage to postve output DC voltage. The voltage transfer rato of the above converter s (k/(-k)) where k s the duty rato. The crcuts (Fg.2 and Fg.3 ) for the swtch-on and swtch-off modes of the chosen converter are developed usng a state-space approach. At ths pont, these two models are averaged over a sngle swtchng perod T usng a state-space averagng technque. The state varables are: X = L, X 2 = L2, X 3 = V o, X 4 = V co () Usng the above state varables, the system matrces A and A 2, nput matrces B and B 2 and output matrces C and C 2 are obtaned. D S Fg. postve output elementary Luo converter Fg.2 Postve output elementary Luo converter mode Fg.3 Postve output elementary Luo converter mode 2 Manuscrpt Receved on November 23 B.Achammal, Assstant Professor of Electroncs and Instrumentaton Engneerng, Annamala Unversty, Inda. 2 Dr. R.Kayalvzh,, Professor of Electroncs and Instrumentaton Engneerng, Annamala Unversty, Inda. III. DESIGN OF PI CONTROLLER The functon of a s to receve the measured process varable (PV) and compare t wth the set pont (sp) to produce the actuatng sgnal (m) so as to drve the process varable to the desred value. Therefore the nputs to the s the error (sp-pv). It s also known as proportonal plus reset the actuatng sgnal m(t) s related to the error e(t) by the equaton. 2

2 Optmal Tunng of PI Controller usng Bacteral Foragng Algorthms for Power Electronc Converter m(t) K c e(t) (K c /T ) e(t)dt ms where T s the ntegral tme constant or reset tme and I/T s called repeats per mnute. After a perod of T mnutes for a constant error E, the contrbuton of ntegral term s (2) T K c / T e( t) dt ( K c / T ) ET K c E (3) The ntegral acton has repeated the response of the proportonal acton. Reset tme s the tme needed to repeat the ntal proportonal acton change n ts output. The ntegral acton causes the output m(t) to change as long as an error exsts the process output. The transfer functon of a PI G c (s)=k c [+/T s] (4) IV. BACTERIAL FORAGING OPTIMIZATION TECHNIQUE Bacteral Foragng algorthm s a new dvson of bo-nspred algorthm. Ths technque s developed by nsprng the foragng behavour of Eschercha col (E.col) bactera. In the bacteral foragng optmzaton process four motle behavour are mmcked:- A. Chemotaxs Chemotaxs process s acheved by through swmmng and tumblng va Flagella. Dependng upon the rotaton of flagella n each bacterum, t decdes whether t should move n a predefned drecton (Swmmng) or altogether n dfferent drectons (Tumblng), n the entre lfetme. To represent a tumble, a unt length random drecton, say (j), s generated; ths wll be used to defne the drecton of movement after a tumble. In partcular ( j,k,l ) ( j,k,l ) C( )* ( j ) () θ (j,k,l) represents the th bacterum, at j th chemotactc, k th reproductve, and l th elmnaton and dspersal step. C() s the sze of the step taken n the random drecton specfed by the tumble(run length unt). B. Swarmng E.col cells can cooperatvely self organze nto hghly structured colones wth elevated envronmental adaptablty usng an ntrcate communcaton mechansm. Overall, cells provde an attracton sgnal to each other so they swarm together. The mathematcal representaton for swarmng can be represented by, J cc (,D(j, k, l)) = J cc(, ( j, k, l) )) = X+Y (6) X s [ D *exp( W * ( m m)2] attract attract m p Y s [ H *exp( W * ( m m)2] repellant repellant m J cc (,D(j, k, l)) s the cost functon value to be added to the actual cost functon to be mnmzed to present a tme varyng cost functon, S s the total number of bactera, P s the number of parameters to be optmzed whch are present n each bacterum and D attract, W attract, H repellant, W repellent are dfferent coeffcents that should be chosen properly. C. Reproducton The least healthy bactera de whle each of the healther bactera (those yeldng lower value of the objectve functon) asexually splt nto two bactera, whch are then placed n the same locaton. Ths keeps the swarm sze constant. D. Elmnaton and Dspersal It s possble that n the local envronment the lfe of a populaton of bactera changes ether gradually (e.g., va consumpton of nutrents) or suddenly due to some other nfluence. Events can occur such that all the bactera n a regon are klled or a group s dspersed nto a new part of the envronment. They have the effect of possbly destroyng the chemotactc progress, but they also have the effect of assstng n chemotaxs, snce dspersal may place bactera near good food sources. From a broad perspectve, elmnaton and dspersal are part of the populaton-level long-dstance motle behavour. V. MODIFIED BACTERIAL FORAGING OPTIMIZATION TECHNIQUE MBFOA emulates the foragng process of bactera E. col as follows: Wthn a cycle called generaton (P) each bacterum performs a chemotactc step N c tmes. After all bactera went through ther chemotactc step, the best bactera are reproduced whle the worst ones are elmnated and new ones are generated at random. It creates a procedure n whch the best bactera among all the chemotactc steps are passed to the subsequent generatons. MBFOA s based on the four processes, combnng the chemotaxs and swarmng nto one loop and smplfyng the reproducton and elmnaton-dspersal. MBFOA uses realencodng to represent a soluton, whch s called bacterum and s represented by ts poston as, θ j, P = x (7) represents the number of bacterum, j represents the chemotactc loop number, P s the cycle number of the algorthm. A. Chemotaxs The chemotactc cycle conssts on tumble (search drecton at random) and swm movements carred out by bactera n the search space wth the am to fnd nutrents. p 236

3 Internatonal Journal of Soft Computng and Engneerng (IJSCE) ISSN: , Volume-3, Issue-, November 23 The attractor movement apples twce n a chemotactc loop, whle n the remanng steps the tumble - swm movement s carred out. The rules work as crtera n the chemotactc loop n the reproducton step and n the elmnaton of the worst bacterum n the swarm. The chemotactc process conssts on tumble-swm movements carred out by bactera n the current swarm. The tumble movement s represented by ( ) ( ) (8) T ( ) ( ) () s a randomly generated vector of sze n wth elements wthn the followng nterval: [, ]. After that, each bacterum modfes ts postons by swmmng and s represented as ( j, p ) ( j,p ) ( ) () (9) θ (j+, P) s the new poston of bacterum (new soluton) at chemotactc step j +, θ (j,p) s the current poston of bacterum at chemotactc step j. In MBFOA the step sze values n vector B() are calculated usng Equaton 7 by consderng the vald lmts per each desgn varables. xk B( ) k S,k,... m () m x k s the dfference between upper and lower lmts for desgn parameter x k : U k L k, m s the number of desgn varables and S s a user-defned percentage of the value used by the bactera as step sze. MBFOA mplements an attractor movement so as to let each bacterum n the swarm to follow the bacterum located n the most assurng regon of the search space and s represented as B ( j, p) ( j, P) ( ( p) ( j, p)) () θ (j +, P) s the new poston of bacterum, θ (j,p) s the current poston of bacterum, θ B (P) s the current poston of the best bacterum n the swarm so far at generaton P, and β defnes the closeness of the new poston of bacterum wth respect to the poston of the best bacterum θ B (P). The attractor movement apples twce n a chemotactc loop, whle n the remanng steps the tumbleswm movement s carred out. The am s to promote a balance between exploraton and explotaton n the search. B. Reproducton The reproducton process conssts of sortng the swarm accordng to the rules of the constrant-handlng technque. The frst half of the populaton s replcated to mantan the same populaton sze for the next generaton. It conssts of elmnatng the second worst bacterum and replacng t wth a copy of the best bacterum n the current populaton, whle the worst bacterum s also elmnated and replaced wth one generated at random. C. Elmnaton and Dspersal The elmnaton - dspersal process elmnates only the worst bacterum, and a new randomly generated bacterum s nserted as ts replacement. A sngle reproducton step and a sngle elmnaton- dspersal step are performed at the end of generaton loop. The elmnaton dspersal step s smplfed because only the worst bacterum n the populaton s elmnated. The lmtatons of BF algorthm have been augmented through the swarmng and reproducton processes. The global searchng of the MBF algorthm has been mproved owng to the fact that t provdes better solutons than the BF algorthm. The MBF algorthm thus has been framed to elmnate the role of complex computatons n the BF algorthm. VI. PERFORMANCE INDICES The performance of a s best evaluated n terms of error crteron. In ths work, performance s evaluated n terms of Integral Square Error (ISE) and Integral Absolute Error (IAE) ISE = t e 2 dt t IAE = e dt (2) (3) The ISE and IAE weght the error wth tme and hence mnmze the error values nearer to zero. VII. SIMULATION RESULTS The crcut parameters of the postve Output elementary Luo Converter are shown n the Table. The parameter values of the conventonal, BF- PI and M s are obtaned. The responses of postve output elementary Luo converter usng conventonal, and M controls are shown n Fgures 4,,6 and 7. Fgures show that M wll drastcally reduce the overshoot, ISE and IAE values as compared to the conventonal PI and. Table 2 shows the performance analyss of postve elementary output Luo converter usng conventonal, BF- PI, and M s. Table : Crcut Parameters of postve output elementary Luo Converter Parameter Symbol Value Input Voltage V n V Output Voltage V o 3V Inductor L µh Capactor C µf resstor R Ω Duty rato D.7 237

4 output voltage n volts output voltage n volts output voltage n volts output voltage n volts Optmal Tunng of PI Controller usng Bacteral Foragng Algorthms for Power Electronc Converter M tme n secs x -3 Fg.4 closed loop responses of Conventonal, and M Controllers 3 M tme n sec x -3 Fg.6 closed loop responses of Conventonal ZN- PI, and M Controllers wth sudden load dsturbance from Ω-Ω (%) at 3msec and Ω- 9Ω (%) at 6msec M tme n secs x -3 tme n secs Fg. Closed Loop responses of conventonal, x -3 and M s wth sudden lne Fg.7 Servo response of Conventonal, dsturbance from V-V (%) at 3msec and V- and M Controllers from 3V-33V at 3msec. 9V at 6msec. Table 2 Performance evaluaton of postve output elementary Luo converter Start up Transent Lne Dsturbance Dsturbance Supply ncrease % Supply decrease % ncrease % decrease % Tunng Parameters M MPF-PI Rsng tme (m. sec) Settlng tme (m. sec).8.8. Peak Overshoot % 8 ISE IAE..2. Settlng tme (m sec).7.2. Peak Overshoot % ISE IAE Settlng tme (m sec) Peak Overshoot %.9.6 ISE IAE Settlng tme (m sec) 2.. Peak Overshoot % ISE IAE Settlng tme (m sec)..2. Peak Overshoot % 3.3 ISE IAE

5 Internatonal Journal of Soft Computng and Engneerng (IJSCE) ISSN: , Volume-3, Issue-, November 23 VIII. CONCLUSION In ths work, Bacteral Foragng algorthm () and Modfed Bacteral Foragng algorthm (M) are developed to tune the PI parameters whch control the performance of postve output elementary Luo converter. The smulaton results confrm that PI tuned wth BF algorthm and MBF algorthm rejects satsfactorly both the lne and load dsturbances. Also the results proved that M gves the smooth response for the reference trackng and mantans the output voltage of the postve output elementary Luo converter accordng to the desred voltage. REFERENCES []. Luo,F.L.: Postve output Luo-converter:voltage lft Technque,IEE-EPAprocessdngs,46(4),July 999,pp [2]. E.Mezura-Montes and B.Hernandez-Ocana, Modfed bacteral foragng optmzaton for engneerng desgn, n proceedngs of the Artfcal Neural Netowrks n Engneerng Conference (ANNIE 29), ser. Intellgent Engneerng Systems Through Artfcal Neural Networks, C.H.Dagl and et al., Eds., Vol.9. St.Lous, MO, USA:ASME Press, November 29, pp [3]. Janardan Nanda, S. Mshra, and Lalt Chandra Saka, Maden Applcaton of Bacteral Foragng-Based Optmzaton Technque n Multarea Automatc Generaton Control, IEEE Transactons on Power systems, Vol.24, No 2, May 29. [4]. J.F.HUANG, F.B.DONG,"Modellng and Control on Isolated DC- DC Converter", Power Electroncs, voi.44, pp.87-89, Aprl 2. []. M.Namnabat, M.Bayat Poodeh, S.Eshtehardha Comparson the Control Methods n Improvement the Performance of the DC- DC Converter, Internatonal Conference on Power Electroncs 27, (ICPE 7), pp.246-, 27. [6]. Martn Plesnk., Use of the State space averagng technque n fast steady state smulaton algorthms for swtchng power converters eeexplore.eee.org CCECE 26. [7]. J.YOU, S.B.KANG, "Generalzed State Space Averagng based PWM Rectfer Modelng", Electrcal Measurement &Instrumentaton vo.46, pp.67-7, October 29. [8]. Vsol A. Optmal Tunng of PID Controllers for Integral and Unstable Processes, IEEE proceedngs-control Theory & Applcaton,2,48(2):pp [9]. R.Suresh Kumar and J.Suganth, Improvng the Boost Converter PID Controller performance usng partcle Swarm Optmzaton, European Journal of Scentfc Research, Vol.8 No.3 September, 22, pp []. Kevn M.Passno, Bommcry of Bacteral foragng for Dstrbuted Operaton and Control, IEEE control systems Magazne, June 22. B. ACHIAMMAL receved her B.E (Electroncs and Instrumentaton) and M.E (Process Control) degrees from Annamala Unversty n 23 and 28 respectvely. She s presently workng as a Assstant Professor n the Department of Instrumentaton Engneerng, Annamala Unversty, where she has put n a total servce of years. She s presently pursung Ph.D n the Department of Instrumentaton Engneerng, Annamala Unversty. Her areas of nterest are: DC-DC converter: modelng, smulaton and mplementaton of optmzaton technques for control of power electronc converters. Dr. R. KAYALVIZHI receved her B.E (Electroncs and Instrumentaton) and M.E (Power Systems) degrees from Annamala Unversty wth dstncton n 984 and 988 respectvely. She s presently workng as a Professor n the Department of Instrumentaton Engneerng, Annamala Unversty where she has put n a total servce of 28 years. She has publshed Natonal and Internatonal journals and attended natonal and nternatonal conferences. Her research nterests are n DC-DC converters: modelng, smulaton, mplementaton of ntellgent control strateges and Dgtal mage processng. She s a lfe member of Indan socety for TechncalEducaton. 239