Improvement of Buck Converter Performance Using Artificial Bee Colony Optimized-PID Controller

Transcription

1 Journal of Automaton and Control Engneerng Vol. 3, No. 4, August 2015 Improvement of Buck Converter Performance Usng Artfcal Bee Colony Optmzed-PID Controller Yusuf Sonmez1, Ozcan Ayyldz1, H. Tolga Kahraman2, Ugur Guvenc3, and Serhat Duman3 1 Department of Electrcal and Energy, Gaz Vocatonal College, Gaz Unversty, Turkey Department of Software Engneerng, Technology Faculty, Karadenz Techncal Unversty, Turkey 3 Department of Electrcal and Electroncs Engneerng, Technology Faculty, Duzce Unversty, Turkey Emal: {ysonmez, oayyldz}@gaz.edu.tr, htolgakahraman@yahoo.com, {ugurguvenc, serhatduman}@duzce.edu.tr 2 Abstract In ths study, Artfcal Bee Colony (ABC) algorthm s proposed to determne gan parameters of the PID algorthm for controllng a desgned buck converter. Study ams to mprove the performance of buck converter va ABC-PID. Genetc Algorthm (GA) based PID s used also to control the converter n order to nvestgate the performance of the proposed algorthm on the system. Experments wth dfferent cases are done va smulatons. In the smulatons, settlng tme, steady-state error and readjustment tme of output voltage n cases of load varaton are analyzed n order to determne the performance of the proposed algorthm. Results obtaned from smulatons are shows that ABC-PID controlled converter has superor performance than GA-PID controlled buck converter. Index Terms artfcal bee colony algorthm, PID, buck converter I. INTRODUCTION Dc-dc converters are wdely used power electroncs components n ndustral area lke swtchng mode power supply (SMPS), personal computer, dc motor drves, etc. The nput of the dc-dc converters s unregulated dc voltage obtaned by the rectfyng lne-voltage and a converter converts ths nput nto a regulated dc output voltage at a desred level. Buck converter s used to decrease the output voltage level n proporton to nput and so t s called or known as step-down converter also. Snce dc-dc converters have power devces, effect of swtchng and passve components lke nductors and capactors, they are non-lnear systems [1], [2]. Therefore, control methods used to control the converters drectly affect the performance of the converter. Varous control methods have used to control the output voltage of dc-dc converters such as pole placement [3], QR [4], feedback loop [5], state space control [6]. A powerful method to control the converters s PID control. Snce t s easy to desgn and mplementaton to a system, most of the tme chosen by practtoners. However, choosng of PID gan parameters s hard because of dc-dc converters contans parastc components and changes n nput voltage and output load by the tme [7]. Therefore, PID gan parameters must be desgned effectvely by usng strong methods n order to obtan a robust transent response. Frst tme, varous classcal methods [8], [9] or Zegler-Nchols (ZN) [10] are used to perform ths operaton. These classcal methods have some dsadvantages such as the necessty of complex mathematcal computaton, producng huge overshoot and unsatsfactory phase and gan margns. In recent years, artfcal ntellgence and optmzaton technques have been used frequently n desgnng of PID dependng on development of these methods. Algorthms lke Fuzzy ogc (F) [11], [12], Partcle Swarm Optmzaton (PSO) [13], [14], Bacteral Foragng Optmzaton (BFO) [15], [16] or Genetc Algorthm (GA) [17], [18] have been mplemented to determnng the PID gan parameters successfully. However, they have had nadequate n some soluton process due to reasons lke dffculty of creatng fuzzy rules n fuzzy logc, premature convergence or long computng tme. Artfcal Bee Colony (ABC) whch was proposed by Karaboğa [19] has a smple structure, less control parameters and gves strong solutons for dfferent ftness functons when compared to other optmzaton algorthms lke GA and PSO [20]. Therefore, n ths study, ABC s used to determne the PID gan parameters for controllng the Buck Converter. The performances of the controller optmzed by ABC are compared n smulaton n accordance wth overshoot, undershoot, rse tme, settlng tme, and steady state error. Results obtaned from ABC are compared the GA n order to evaluate the performance of proposed algorthm. The rest of the paper organzed as follows. In Secton 2, the mathematcal model of the buck converter s presented. In Secton 3, ABC-PID control schema of the converter s expressed. Expermental results are gven n Secton 4, and Secton 5 contans concluson of the study. II. MATHEMATICA MODE OF THE BUCK CONVERTER As the smplest form of a SMPS crcut, a Buck Converter converts the unregulated nput voltage nto Manuscrpt receved July 1, 2014; revsed September 26, do: /joace

2 Journal of Automaton and Control Engneerng Vol. 3, No. 4, August 2015 regulated output voltage whch s lower level than nput. A basc Buck Converter model s shown In Fg. 1. A buck converter contans a swtch, a dode, an nductor, a capactor and a load resstance. Accordng to Fg. 1, the swtch (S) choppers the nput voltage at hgh frequency and converts the nput voltage wth constant ampltude to rectangular waveform. Then average DC output voltage V o s obtaned from ths rectangular waveform by passng through low-pass flter formed from nductor and capactor. The turnng-on tme of the swtch (t on ) durng one swtchng perod (T s ) s called duty rato (D) and V o s controllng by changng D. These formulatons are llustrated n Eq. 1. A buck converter crcut has two operatng mode accordng to cases of the swtch. In frst mode, when the swtch s on, the nput source provdes energy to the, C and R and the nput current passng through these components. S R O + - V C C V C R V O R C Fgure 1. The equvalent crcut of the buck converter t T on D and o s V DV (1) The nductor current s equal to the nput current and shows an ncreasng tendency. In second mode, when the swtch s off, the nductor provdes the own energy stored at prevous mode to the, C and R and the nductor current passng through these components. The nductor current shows a decreasng tendency at ths mode. Mathematcal model of the buck converter can be defned as follows accordng to both modes. When the swtch s on: d V dt When the swtch s off: d dt 1 R RC 1 RC (2) R vc 1 R RC R RC dvc 1 R 1 1 v (3) C dt C R RC C R RC 1 R RC 1 RC R vc 1 (4) R RC R RC dvc 1 R 1 1 v (5) C dt C R RC C R RC where V s the nput voltage, R s the nductor resstance, R c s the capactor resstance, s the nductor current, v c s the capactor voltage, s the nductor, C s the capactor and R s the load resstance. III. ABC-PID BASED CONTRO OF THE BUCK CONVERTER The output voltage of the buck converter can be kept at a stable value by usng the PID controller structure. A basc dagram of PID control model for buck converter s shown n Fg. 2. Dfference between the output voltage of the converter and a desred voltage value are known as error (n Eq. 6) and t s nput of the PID controller. Controller computes a control varable value (PID output, n Eq. 7) by usng ts gan parameters and error value and ths control varable value feds the Pulse Wdth Modulaton (PWM) generator. PWM generator produces the swtchng sgnal for swtch located on the converter by comparng the PID output and a saw-tooth waveform. Ths process can be modeled mathematcally as descrbed n Eq. 6 and Eq. 7. e t V V t (6) u ref t K et K et p t 0 o dt K d det dt where e(t) s the error, V ref s the reference voltage, V o (t) s the converter output voltage, K p s the proportonal parameter, K s the ntegral parameter, K d s the dervatve parameter and u(t) s the output (control varable) of the PID controller. In the PID control, K p effects the rse tme, K reduce the steady state error and K d s used to reduce the overshoot and mprove the stablty.[14, 15].These controller parameters are defned optmally n the control system to make the system stablty and obtan an effectve or robust transent response. As can be seen from Fg. 2, n ths study, ABC algorthm s used to defne the PID parameters optmally. Ths optmzaton process s explaned below. A. Applcaton of Artfcal Bee Colony Algorthm to Optmze the PID Controller ABC s a robust optmzaton method proposed by Karaboğa [19] nsprng by foragng behavor of honey bees. In the ABC, algorthm artfcal bees whch are employed, onlooker and scout search the food source whch has the hghest nectar amount by modfyng the food postons by tme. In the ABC, whle a possble soluton of the problem corresponds to poston of a food source, ftness of the assocaton soluton corresponds to nectar amount of ths source. ABC algorthm works at 10 steps descrbed below [21]. (7) 305

3 Journal of Automaton and Control Engneerng Vol. 3, No. 4, August 2015 TABE I. IMITS OF THE PID PARAMETERS PID controller Range parameters Mnmum Maxmum Kp K 0 10 Kd Step1: Input data mts of PID parameters are read at ths step. In ths study used lmts belong to PID parameters are gven n Table I. Step 2: Intalzaton ABC parameters lke colony dmenson, maxmum cycle number, number of varables and lmt parameter are ntalzed. Artfcal Bee Colony Algorthm K p K K d PID Controller Vref K p Swtchng Pulse e(t) dt + u(t) V O + K + PWM Buck Converter - + V O d dt K d Fgure 2. ABC-PID control model the buck converter Step 3: Intalzaton of populaton A set of ntal populaton wth N solutons x (=1,2, N) s produced randomly and ther ftness are determned. Here each soluton of x represented by D- dmensonal vector corresponded to number of PID parameters optmzed. Step 4: Ftness evaluaton of the populaton Ftness values obtaned from the ftness functon belong to each soluton s evaluated at ths step. The ftness functon used n ths study s descrbed as follows. ft k t1 t 2 e (8) where e(t) s the error value descrbed n Eq. 6 and k s the maxmum teraton number n smulaton of operatng buck converter for determned PID parameters at one cycle of ABC algorthm. Step 5: Set the cycle counter to 1 Step 6: Modfcaton of food source postons (solutons) Food sources are modfed and replaced by a new one va employed bees. Then the nectar amounts of the new sources are tested. If the nectar amount of the new source s better than old one, the new food source are kept the memory, otherwse t dscards. Ths modfcaton process of food sources are descrbed as follows. x x k 1,2,..., N and j 1,2 D vj xj j j kj,..., (9) where v j s the new food source poston, k and j are randomly determned ndexes, β j s a number determned randomly nterval of [-1,1]. Step 7: Employng of onlookers and calculaton of probabltes Employed bees share the nectar amount and poston nformaton of food sources wth onlookers watng at the dance area after completng the search process. Onlooker bees prefer a food source accordng to a probablty value P descrbed as follows. N P j1 ft ft j (10) where ft s the ftness value of the -th soluton descrbed n Eq. 8 and N s the total number of food sources. Then, at ths step, onlooker bees modfy the food sources gven n Eq. 9 and test the nectar amount as n the case of Step 6. Step 8: Abandonng from the exploted source At ths step, f a food source s not mproved further that source s abandoned and t replaced wth a new one by scout bees. In the ABC, ths process s done accordng to the lmt parameter whch s predetermned number of cycles for abandonng the food source. Dscoverng a new food source by a scout s descrbed as follows. x j j mn 1 j j 0, x x x rand (11) x j mn and x j max are mnmum and maxmum lmts of the parameter to be optmzed. Step 9: Memorze the best soluton so far Step 10: Increase the cycle counter Step 11: Stoppng the algorthm Steps between 6 and 10 are repeated untl reach the Maxmum Cycle Number (MCN) determned before. Then, the searchng process s stopped. max IV. EXPERIMENTA RESUTS mn 306

4 Journal of Automaton and Control Engneerng Vol. 3, No. 4, August 2015 In ths study, control of the buck converter s smulated by usng ABC-PID algorthm n order to nvestgate performance of the proposed algorthm. GA based PID algorthm s also mplemented on the same converter and obtaned results are compared wth GA-PID algorthm to show the effectveness of the ABC-PID. Smulaton of experments s done va C# language n Vsual Studo. Buck converter parameters used n smulaton are lsted n Table II, ABC parameters used n smulaton are gven n Table III and PID parameters produced by ABC and GA are gven n Table IV. TABE II. PARAMETERS OF THE BUCK CONVERTER Parameter Value V R R C R 12 V 0.13 Ω 0.03 Ω 2 Ω 270 µh C 1000 µf Fgure 3. Smulaton results of the GA-PID controlled buck converter (c) TABE III. ABC PARAMETERS ABC Parameters Values Colony dmenson 86 Maxmum cycle number 5000 Number of varables 3 mt parameter TABE IV. PID PARAMETERS OBTAINED FROM OPTIMIZATION AGORITHMS Gan Parameters Algorthms P (Proportonal) D (Dervatve) I (Integral) GA ABC In Fg. 3, output waveform of GA-PID controlled buck converter s gven. Fg. 3 and Fg. 3(c) are zoomed verson of Fg. 3. The settlng tme s 0.01 ms as seen n Fg. 3 and steady-state error s 12 mv as seen n Fg. 3(c) for GA-PID control. In Fg. 4 output waveform of ABC-PID controlled buck converter s gven. Fg. 4 and Fg. 4(c) are zoomed verson of Fg. 4 also. The settlng tme s ms as seen n Fg. 4 and steady-state error s 3.9 mv as seen n Fg. 4(c) for ABC-PID control. It s clearly seen that these results ABC-PID algorthm produces more robust results to control the buck converter from the pont of settlng tme and steady-state error. In the experment, the load resstor s changed 2 Ω to 10 Ω at 0.5 ms. Fg. 5 shows the output waveform of GA-PID controlled converter n ths case. Fg. 5 s zoomed verson of Fg. 5. The GA-PID controller regulates the voltage ncrease wth 0.14 V n ms for ths case. Fg. 6 shows the output waveform of ABC- PID controlled converter for the same case. 307

5 Journal of Automaton and Control Engneerng Vol. 3, No. 4, August 2015 (c) Fgure 4. Smulaton results of the ABC-PID controlled buck converter Fgure 5. Smulaton results of the GA-PID controlled buck converter; R=2 Ω to R=10 Ω at 0.5 ms Fgure 6. Smulaton results of the ABC-PID controlled buck converter; R=2 Ω to R=10 Ω at 0.5 ms 308

6 Journal of Automaton and Control Engneerng Vol. 3, No. 4, August 2015 Fg. 6 s zoomed verson of Fg. 6. The ABC-PID control regulates the voltage ncrease wth 0.11 V n ms for ths case. As can be seen from these results, ABC-PID gves superor results than GA-PID n the case of beng an ncrease n the output load. In an another expermental case, the load resstor s changed 10 Ω to 2 Ω at 0.5 ms. Fg. 7 shows the output waveform of GA-PID controlled converter for ths case. Fg. 7 s zoomed verson of Fg. 7. The GA- PID controller regulates the voltage decrease wth 0.1 V n ms. Fg. 8 shows the output waveform of ABC-PID controlled converter for the same case. Fg. 8 s zoomed verson of Fg. 8. The ABC-PID control regulates the voltage ncrease wth 0.09 V n ms for ths case. ABC-PID controller gves better soluton agan than GA-PID for ths case also. V.CONCUSION ABC-PID controller algorthm s desgned and mplemented to buck converter n ths study. Fgure 7. Smulaton results of the GA-PID controlled buck converter; R=10 Ω to R=2 Ω at 0.5 ms Fgure 8. Smulaton results of the ABC-PID controlled buck converter; R=10 Ω to R=2 Ω at 0.5 ms The effects of the proposed algorthm on system performance of the buck converter are nvestgated. Experments are done va smulatons to analyze the responses obtaned. In order to verfy the effectveness of the proposed algorthm, GA based PID s used to control the same converter for same expermental cases. Results show that ABC-PID produces better results than GA-PID to control the buck converter n the way of settlng tme, steady-state error and load change cases. When ABC-PID compared to GA-PID, ABC-PID mproves the settlng tme wth ms and steady-state error wth 8.1 mv. Moreover, n the cases of load change, ABC-PID has a faster dynamc response wth ms. ACKNOWEDGMENT Ths work s supported by Gaz Unversty, Department of Scentfc Research Projects wthn the Project /05. REFERENCES [1] D. M. M. S. Prabha, S. P. Kumar, and G. G. Devadhas, "An optmum settng of controller for a dc-dc converter usng bacteral ntellgence technque," n Proc. PES Innovatve Smart Grd Technologes Conf., 2011, pp [2] M. Namnabat, M. B. Poudeh, and S. Eshtehardha, "Comparson the control methods n mprovement the performance of the DC- DC converter," n Proc. Power Electroncs Conf., 2007, pp [3] M. Khermand, M. Mahdavan, M. B. Poudeh, and S. Eshtehardha, "Intellgent modern controller on DC-DC converter," n Proc. IEEE Regon 10 Conf., 2008, pp [4] K. We, Q. Sun, B. ang, and M. Du, "The research of adaptve fuzzy PID control algorthm based on QR approach n DC-DC converter," n Proc. Computatonal Intellgence Conf., vol. 1, 2008, pp [5] P. Gupta and A. Patra, "Hybrd sldng mode control of DC-DC power converter crcuts," n Proc. Convergent Technologes for the Aca-Pacfc Regon Conf., vol. 1, 2003, pp

7 Journal of Automaton and Control Engneerng Vol. 3, No. 4, August 2015 [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] G. Keller, D. ascu, and J. M. A. Myrzk, "State-space control structures for buck converters wth/wthout nput flter," n Proc. Power Electroncs and Applcatons Conf., 2005, pp İ. Atacak and Ö. F. Bay, "Tunng gan parameters of a PI controller usng genetc algorthm for boost dc-dc converter," n Proc. Internatonal Advanced Technologes Symp., 2009, pp H. N. Kovo, "Tunng of a multvarable PID-controller for unknown systems," n Proc. IEEE Decson and Control Includng the Symposum on Adaptve Processes Conf., vol. 19, 1980, pp D. M. Ban and G. D. Martn, "Smple PID tunng and PIDclosed loop smulaton," n Proc. Amercan Control Conference Conf., 1983, pp J. G. Zegler, N. B. Nchols, and N. Y. Rochester, "Optmum settngs for automatc controllers," Transactons of the ASME, vol. 64, pp , A. Dordev, O. Ursaru, M. ucanu, and. Tgaeru, "A hybrd fuzzy-pid controller for dc-dc converters," n Proc. Sgnals, Crcuts and Systems Conf., vol. 1, 2003, pp , Guo, J. Y. Hung, and R. M. Nelms, "Evaluaton of DSP-based PID and fuzzy controllers for dc dc converters," IEEE Transactons on Industral Electroncs, vol. 56, no. 6, pp , O. T. Altnoz and H. Erdem, "Evaluaton functon comparson of partcle swarm optmzaton for buck converter," n Proc. Power Electroncs, Electrcal Drves, Automaton and Moton conf., 2010, pp M. R. Yousef, M. B. Poudeh, and S. Eshtehardha, "Improvement performance of step-down converter through ntellgent controllers," n Proc. IEEE Intellgent Systems Conf., vol. 4, 2008, pp A. Jallvand, H. Vahed, and A. Bayat, "Optmal tunng of the PID controller for a buck converter usng bacteral foragng algorthm," n Proc. Intellgent and Advanced Systems Conf., 2010, pp D. M. M. S. R. Prabha, S. P. Kumar, and G. G. Devedhas, "An optmum settng of controller for a dc-dc converter usng bacteral ntellgence technque," n Proc. Innovatve Smart Grd Technologes Conf., 2011, pp C. Ou and W. n, Comparson between PSO and GA for parameters optmzaton of PID controller, n Proc. IEEE Mechatroncs and Automaton Conf., 2006, pp C. H. Cheng, P. J. Cheng, and M. J. Xe, "Current sharng of paralleled DC DC converters usng GA-based PID controllers," Expert Systems wth Applcatons, vol. 37, pp , D. Karaboga, "An dea based on honey bee swarm for numercal optmzaton," Techncal Report-TR06, Ercyes Unversty, Engneerng Faculty, Computer Engneerng Department, D. Karaboga and B. Akay, "A comparatve study of artfcal bee colony algorthm," Appled Mathematcs and Computaton, vol. 214, pp , Y. Sönmez, "Estmaton of fuel cost curve parameters for thermal power plants usng ABC," Turksh Journal of Electrcal Engneerng and Computer Scence, vol. 21, pp , Yusuf Sönmez was born n Ankara, Turkey n He receved the BS degree n electrcal and electroncs educaton and the MSc degree n electrcal educaton from Gaz Unversty, Ankara, Turkey, n 2002 and 2005, respectvely, and the PhD degree n electronc and electrcal engneerng from the Gaz Unversty, Ankara, 310 Turkey, n He s a research assstant wth Gaz Unversty, Gaz Vocatonal College from Hs research nterests nclude power systems, electrcal machnes and drves, ntellgent control, artfcal ntellgence and optmzaton technques. Ozcan Ayyıldız receved the BS degree n electrcal and electroncs educaton from Fırat Unversty, Elazığ, Turkey, n He s a lecturer wth Gaz Unversty, Gaz Vocatonal College. from Hs research nterests nclude power electroncs, electrcal machnes and drves. H. Tolga Kahraman was born n Trabzon, Turkey, n He receved the B.Sc. degree n electrcal educaton from Gaz Unversty, Ankara, Turkey n 2002, M.Sc. degree from Gaz Unversty, Turkey n 2005 and the Ph.D. degree from Gaz Unversty, Turke y n He s currently an Assstance Professor n the Department of Software Engneerng, Faculty of Technology, Karadenz Techncal Unversty, Turkey. Hs man nterests are n artfcal ntellgent, object orented programmng and numercal analyss. Ugur Guvenc was born n Zle, Turkey, n He receved the B.Sc. degree n electrcal educaton from Abant İzzet Baysal Unversty, Bolu, Turkey n 2002, M.Sc. degree from Gaz Unversty, Turkey n 2005 and the Ph.D. degree from Gaz Unversty, Turkey n He s currently an Assstance Professor n the Department of Electrcal Educaton, Faculty of Techncal Educaton, Duzce Unversty, Turkey. Hs man nterests are n artfcal ntellgent, power system and mage processng. Serhat Duman was born n Bandırma, Turkey, n He receved the B.Sc. degree n electrcal educaton from Abant Izzet Baysal Unversty, Bolu, Turkey, n 2008 and M.Sc. degree from the Department of Electrcal Educaton, Duzce Unversty, Duzce, Turkey n He s currently student of Ph.D. n the Department of Electrcal Engneerng, Kocael Unversty, Turkey. Hs areas of research nclude power system transent stablty, power system dynamc stablty, FACTS, optmzaton technques, voltage stablty, optmzaton problems n power systems and artfcal ntellgent.