Applications of Modern Optimization Methods for Controlling Parallel Connected DC-DC Buck Converters

Transcription

1 IJCSI Internatonal Journal of Computer Scence Issues, Volume 3, Issue 6, November Applcatons of Modern Optmzaton Methods for Controllng Parallel Connected DC-DC Buck Converters Al S. Al-Dmour Assocate Professor n Electrcal Engneerng Department Engneerng College Mu tah Unversty Mu tah-karak Jordan Abstract Ths paper presents the applcaton of on-lne Partcle Swarm (PSO) and Ant Colony Optmzaton (ACO) technques basedstate feedback controllers for adjustng and tunng the output voltage and current of parallel DC-DC buck convectors. The objectve of control system s to balance the current of each converter and to hghly mprove the output voltage performance of the parallel buck converter. Gven a system wth large varatons of nput voltage and load, t s necessary to guarantee good performance of the controller for large varatons of operatng pont. The smulaton results of PSO and ACO-based controllers systems are compared. The results were obtaned show how PSO and ACO can effectvely and effcently optmze the dynamc performance of the adopted converter under varatons n load and nput voltage as well as n reference voltage. Keywords: Partcle Swarm Optmzaton (PSO), state feedback controller, Optmzaton, Ant Colony Optmzaton (ACO), DC-DC converters, parallel buck system.. Introducton DC-DC converters are electronc devces used to change DC electrcal power effcently from one voltage level to another. These converters are wdely used n swtched-mode power supples, adjustable speed drves, unnterruptble power supples, telecommuncaton equpment, spacecraft power system, and many other applcatons to change the level of an nput voltage to fulfl requred operatng condtons. In addton, the converters are usually subjected of large load varatons when operated n these applcatons. Therefore, the man objectve of a good control strategy to be developed for such converters must be to acheve an output voltage regulaton, under large load varatons, as fast as possble wthout havng any stablty problem []. Usually, the output voltage s regulated by varyng the duty cycle of the power MOSFET drvng sgnal. The mode of operaton of the converter s smply vared from swtch (ON) to (OFF) state and the Krchhoff s law s appled to obtan the dfferental equaton of each state of the converter [2]. The swtchng power converters n general are nherently non-lnear and tme nvarant and therefore, the control approach requres effectve modellng and analyss of the converters [3]. Controller desgn for any system needs knowledge about system behavour. Usually ths nvolves a mathematcal descrpton of the relaton among nputs to the process, state varables, and output. Ths descrpton n the form of mathematcal equatons whch descrbe behavour of the system (process) s called model of the system. In recent years, varous researches was performed on applyng the non-lnear methods to control parallel DC/DC converters [4]; however, the controller desgn approaches based on the lnearzed state-space average model, due to the smplcty of mplementaton and generalty. Generally, the parallelng of lower-power converter modules offers a number of advantages over a sngle, hgh power, centralzed power supply. Some of these advantages nclude hgher effcency, better dynamc response due to a hgher frequency of operaton, and better load regulaton. The major concern of parallel-connected converters s to share the load current among the converters. To do ths, some form of control has to be used to equalze the currents n the ndvdual converters. A varety of approaches, wth varyng complexty and current-sharng performance, have been proposed [4], [5]. Today, many researchers have adopted the ntellgent desgn technques for dfferent applcatons whch proven success n mprovng the performance. Among the varous technques of artfcal ntellgence, the most popular and wdely used technques n control systems are the fuzzy logc, Neural Network (NN) and the Partcle Swarm Optmzaton (PSO) [6], [7], [8]. Such an ntellgent controller desgned may even work well wth a system wth an approxmate model.

2 IJCSI Internatonal Journal of Computer Scence Issues, Volume 3, Issue 6, November In ths paper, the basc crcut and theory s utlzed to dentfy the basc structures and nvestgate the control problem of parallel buck converter usng PSO and ACO methods. Ths s because of ther proved performance n dfferent applcatons and because of ther smplcty, snce nether expensve computatons nor specalzed methods are needed. The parallel-connected converters has been deployed here because of several factors such as growng consumer power demands, mportance of dynamc power management, growng requrements for system relablty, and decreasng overall system cost [ 4]. Consequently, t s wdely known that parallelng converters when carefully desgned may accommodate the load sharng capablty requred by the hgh current applcatons. However, a conventonal controller whch ncorporates load sharng at any load level suffers the drawback of poor converter s effcency especally at low output current. Hence, a more advanced controller wll be needed to manage the number of converters n parallel requred based on the load current whch n turn wll keep the effcency of the converter relatvely hgh. It s found that PSO outperforms random search through and at the end of the search process, showng better convergence behavour and over-fttng avodance. In addton, the ACO s based on the cooperatve behavour of real ant colones, whch are able to fnd the shortest path from ther nest to a food source. In many practcal systems, the objectve functon, constrants, and the desgn data are known only n vague and lngustc terms [9]. In ths work, the resultant output load voltage and load sharng current of ndvdual converter s analyzed. These results gve evdence that the ACO or PSO-based state feedback controllers can work as an any-tme method for controllng the swtchng operaton of the DC-DC converters. Consequently, the smulaton results of the adopted converter system behavour and the effectveness of the controller for optmzaton and regulaton purposes s an mportant feature of ths paper. 2. Small Sgnal Analyss of the Ideal Converter The small sgnal averaged state-space method s a generalzed analyss tool whch s readly applcable to ether smple crcuts or complex structures []. The lnear averaged tme-nvarant models acheved by usng ths method are relatvely smple, but a lot of mathematcal efforts are needed to derve the fnal results. To obtan such models, the step-by-step procedure proposed n [], [2], s adapted to our problem. 2. Parallel connected buck converters Paralleled DC-DC converters are used n telecommuncaton ndustry wdely and operated under closed loop control to regulate the output voltage and allow hgh current to be delvered to loads wthout the need to employ devces of hgh power ratng. The desgn wth these standard converter modules nfluences the costs of development n a postve manner and the system relablty and operatonal redundancy are mproved. In addton, the supply system can be extended qute easly by addng another converter module nstead of replacng the converter by a stronger one. The parallel connecton of swtch mode converter s a well known strategy. It nvolves phase shftng of two or more buck converters connected n parallel and operatng at the same swtchng frequency. Two buck converters are connected n parallel feedng a common resstve load wth a swtchng perod T and duty cycle D s shown n Fgure. Fg. : System contanng two parallel connected buck converters For the purpose to obtan the relaton between changes n the converter duty cycle (the swtchng control sgnal) and the system states, the followng perturbatons can be appled [2],[3]: D D dˆ d ˆ vˆ for n, vn vn vˆ n for, D v v c ˆ vˆ c vc vˆ c for, and ˆ for v. c In order to provde examnng the response of the converter to load changes, a current source generator I o s added n parallel wth load resstor; therefore, ths leads to followng assumpton: n

3 IJCSI Internatonal Journal of Computer Scence Issues, Volume 3, Issue 6, November I o I o Iˆ I ˆ o o for I After averagng and applyng the perturbatons as descrbed n the current secton, the state space representaton of the open loop two-module parallel connected buck converters s gven by: dˆ dt dˆ 2 d dt vˆ c dt 2C 2C o vn ˆ ˆ 2 vˆ c RC 2 vn D D2 dˆ d ˆ vˆ Iˆ 2C 2 n o () 3. Ant colony optmzaton Algorthm Ant colony optmzaton (ACO) s based on the cooperatve behavour of real ant colones, whch are able to fnd the shortest path from ther nest to a food source. The method was developed by Dorgo and hs assocates n the early 996s [4], [5]. The ant colony optmzaton process can be explaned by representng the optmzaton problem as a multlayered object, where the number of layers s equal to the number of desgn varables and the number of nodes n a partcular layer s equal to the number of dscrete values permtted for the correspondng desgn varable. Thus each node s assocated wth a permssble dscrete value of a desgn varable. The PSO procedure, whch s used here for optmzng the state feedback controller gans, s as shown n the flowchart n Fgure 2 [6]. The ACO method procedure starts when an ant k, that located at node, uses the pheromone tral to compute the probablty of choosng the next node j by applyng the followng probablstc transton rule: (2) J k () s a set of nodes whch reman to be vsted when the ant k s at node. α and β are two adjustable postve parameters that control the relatve weghts of the pheromone tral and of the heurstc vsblty. After each ant completes ts tour, the pheromone amount on each path wll be adjusted accordng to followng equaton: (3) where (-ρ) s the pheromone decay parameter (<ρ<) where t represents the tral evaporaton when the ant chooses a node and decdes to move. where k s the length of the tour performed by ant k and Q s an arbtrary constant constant related to the qualty of pheromone trals lad by ants. Here n ths work, the algorthm s tested for dfferent values of parameters by smulatng the model for dfferent operatng condtons. Accordng to the trals, the optmum parameters used for verfyng the performance of the ACO-state feedback controller s lsted n Table. Table : ACO Parameters ACO Parameters Number of ants Number of nodes 2 Number of teraton 3 Evaporaton rate.7 α and β.7 and.2 respectvely Fg. 2: Flow Chart of ACO Algorthm 4. PSO Algorthm The PSO algorthm was orgnally proposed by Kennedy and Eberhart n 995 [7].The PSO algorthm s an evolutonary computatonal technque, but t dffers from other well-known evolutonary computaton algorthms such as the genetc algorthms. Although a populaton s used for searchng the search space, there are no operators appled on the populaton. Instead, n PSO, the populaton dynamcs smulates a brd flock s behavour, where socal sharng of nformaton takes place and ndvduals can proft from the dscoveres and prevous experence of all the other

4 IJCSI Internatonal Journal of Computer Scence Issues, Volume 3, Issue 6, November companons durng the search for food. Thus, each companon, called partcle, n the populaton, whch s called swarm, s assumed to fly over the search space n order to fnd promsng regons of the landscape. Optmzaton methods based on swarm ntellgence are called behavourally nspred algorthms as opposed to the genetc algorthms, whch are called evoluton-based procedures. In the context of multvarable optmzaton, the swarm s assumed to be of specfed or fxed sze wth each partcle located ntally at random locatons n the multdmensonal desgn space. Each partcle s assumed to have two characterstcs: a poston and a velocty. In addton, t wanders around n the desgn space and remembers the best poston (n terms of the food source or objectve functon value) t has dscovered. The partcles communcate nformaton or good postons to each other and adjust ther ndvdual postons and veloctes based on the nformaton receved on the good postons. Thus the PSO model smulates a random search n the desgn space for the maxmum value of the objectve functon. As such, gradually over much teraton, the brds go to the target (or maxmum/mnmum of the objectve functon). et x and v denote a partcle poston and ts correspondng flght velocty n a search space, respectvely. Therefore, the th partcle s represented 54 the nerta weght factor; c and c2 are acceleraton constants; r and r2 are two random numbers between d d and ; x k and v k are the velocty and the current of th partcle n the d -dmensonal search space at teraton k, respectvely. Start Intalze the partcle wth random poston velocty vectors x and v For each partcle:. evaluate ftness f(x) 2. If new partcle s best set pbest=x For the whole populaton:. Identfy global best gbest Update x and v accordng to Equatons (5) and (6) as x ( x, x,..., x ) n the d-dmensonal search 2 d space. The best remembered of the th partcle ndvdual partcle poston s recorded and represented as pbest ( pbest, pbest 2,..., pbest d ). The ndex No Is convergence obtaned? of best remembered swarm poston among all the partcles n the group s represented by 2 d) the gbest ( gbest, gbest,..., gbest. The flght velocty for partcle s represented Yes as v (v, v,..., v ). The modfed velocty and 2 d Stop poston of each partcle can be calculated usng the current velocty and the dstance from pbest to gbest as presented n the followng flow chart shown n Fgure 3. The modfed velocty and poston of each partcle can be calculated usng the current velocty and d d the dstance from pbest to gbest as presented n the followng formulas [26]: v kd wv kd c r ( pbest kd x kd ) c 2 r2 ( gbest d x kd ), =,2,...,n and d=,2,,m x kd x kd v kd (5) (6) where w, c and c2. n s the number of partcles n a group; m s the number of members n a partcle; w s Fg. 3: Flow chart of PSO In general, PSO shares many smlartes wth evolutonary computaton technques. The man dfference between the PSO and other approaches s that PSO does not have operators and the partcles update themselves wth the nternal velocty; they also have a memory that s mportant to the algorthm. In addton, the PSO s easy to mplement and there are few parameters to adjust. Furthermore, PSO s computatonally nexpensve snce ts memory and speed requrements are low [7].In ths work, PSO

5 IJCSI Internatonal Journal of Computer Scence Issues, Volume 3, Issue 6, November algorthm s used to fnd the optmal values of the state feedback gans to mprove the behavour of a Buck converter. The objectve of the optmal controller desgn s to mantan constant output voltage and reduce the overshoots. To nvestgate the effectveness of the PSO-based controller on the performance of the parallel Buck converters, the evoluton procedure of PSO Algorthms, whch was shown n Fg. 3, has been consdered. Moreover, the tme responses are chosen as the performance ndces to be obtaned. Snce computatonal tme s one of the mportant factors to be consdered n an optmzaton process, nvestgatons on the number of ndvduals/partcles were carred out by varyng those numbers from 4 to 6. Fewer ndvduals/partcles resulted n hgh values of errors but faster computatonal tme, whle a hgh number of ndvduals/partcles resulted n smaller values of the mean error wth very slow executon tme. In order to get compromse values between the mean error and computatonal tme, the best number of ndvduals/partcles was found to be 4 for all algorthms The other parameters consdered for PSO algorthm are C = 2, and C 2 = 2. Moreover, the number of dmensons (Nod) s=5 and the maxmum teraton number (No) equal 2 and are used for checkng termnaton crteron n ths algorthm. Consequently, the nerta weght factor (w) s selected accordng to the followng equaton: w = * ( /No) (7) where s the th teraton. The decreasng of w through the search process, called adaptve nerta weght s a process smlar to that of smulated annealng n whch temperature s decreased exponentally, allowng global and local search [8],[9]. As n most search algorthms, n PSO a cost functon s needed to evaluate the apttude of canddate solutons. Generally, the defnton of a cost functon depends on the problem at hand, but n general should reflect the proxmty of the solutons to the optma. The cost functon that s adopted n ths work s selected to be based on the mean squared error between the system output voltages as well as nductors currents and the related reference values. 5. Smulaton results usng ACO and PSO algorthms Smulaton results of parallel buck converter are presented n ths secton where the buck converter parameters are V n =24V, =69 mh, C=22 uf, R=3, wtchng frequency f s = KHz, and Vo=2. For smulatons purposes, the buck converter system was smulated n C++ envronment usng numercal technque based on forth order Runge-Kutta method wth tme step sze of 2 µsec. The smulaton envronment s used to test the transent and steady-state response of the system to varous dsturbances from the nput source, reference voltage and load sde. The smulaton results are then used to compare the openloop response of the system wth the compensated closed-loop responses of the controlled systems wth dfferent schemes. In ths work, a lnear feedback control law s desgned to actvely control the behavour of the converters system. Ths law s desgned usng the state vector determned by the state equaton () of the system descrbed Secton 2.. Snce the states are composed of output voltage and nductors currents, the control law wll depend on these for varous smulatons tests. The control sgnals based on state feedback deas [2], takes the followng form (f two control nputs for both converters are utlsed): Vˆ ( ) c t u u c c2 ( t) f ( t) f 3 f f 2 4 f f 3 6 Iˆ Iˆ 2 where the scalars f, f2,..., f6 are the feedback gans for the desgned control law. Snce there s a complete smlarty between the two desgned converters, t s assumed that, for smplcty, f4 f, f5 f 2, and f6 f 3. In the presented work, t s adopted, for the purpose of fndng the sutable control law for ACO and PSO controllers, the followng command duty rato algorthm for PWM controller as [5]: Vref C D uc (k) (9) V V n n (8) Actually t s thought when usng the off-lne optmzed parameters (gans) of the state controllers, a rough approxmaton to the desred control law should be performed frst,.e., drect optmzng. In ths manner, the state controller would be capable of drvng the system over the operatng range wthout nstablty problems. Then on-lne specalsed optmzng would be used to mprove the control provded by the state controller. Here, both suggestons s used; the off-lne parameters optmzng usng the drect manner and a fxed-gan controller so as to stablse the system and also to provde an approxmate control. In off- lne learnng, the state controller based- PSO or ACO takes as ts nputs ether or the system output, or both, and the controller system parameters are optmzed to reproduce the needed control sgnal.

6 IJCSI Internatonal Journal of Computer Scence Issues, Volume 3, Issue 6, November The optmzed parameters should then be able to produce the approprate control sgnal, makng the actual system output approach the reference one. In the other hand, on-lne parameters optmzaton s an teratve procedure, whch attempts to mnmze the error between the system output, and the reference as data becomes avalable. Here, the controller parameters are optmzed to fnd the system nput that drves the system output to reach the gven target. Ths control system can specfcally work n the regon of nterest, and t may be worked on-lne to tune tself whle performng the desred work. For successful and accurate workng of the controller, the nput data must be rch enough to reveal all the mportant controlled parameters of the system. Ths s called on-lne knd of optmzng as "specalzed optmzng" snce the ACO or PSO-based state controller s desgned to operate n regons of specalzaton only. In ths work, a parallel buck converter controller usng ACO based-state feedback controller was ntally appled. The goal of the controller s to mantan the output voltage constant at 2 V n spte of the changes n the load or nput voltage. Here, the ACO algorthm s used to optmze the gans values of the state feedback gans K, K 2, and K 3 tll the desred output s obtaned. The values of gans were found to be equal k =., K 2 =.255, and k 3 = respectvely as llustrated n Fgure 4. K of open loop and closed loop system are gven n Table 2. Fg. 5: Tme responses of open-loop and closed-loop system to 24 V DC power source The performance comparson of the controllers s made n terms of peak overshot, rse tme, settlng tme and steady state error. Both controlled responses have slghtly zero steady-state error and the open-loop response has a percentage maxmum overshoot of 32.7% whle the controlled responses nearly have a zero maxmum overshoot. In addton, the rse tme has been reduced from 3. msec to 2.8 msec for ACO and to 2.4 msec for PSO. However, the settlng tme has been decreased by approxmately 6% for both controller schemes from the open loop case. K 2 K 3 Table 2: The undsturbed system transent specfcatons wth open loop and closed loop system Method Rse Tme(msec) Settlng Tme(msec) Maxmum Overshoot % Steady State Error (V) Open loop ACO-Based Controller PSO-Based Controller Fg. 4: Feedback gans of the state based-aco controller The responses of the open-loop system and the system compensated by an on-lne ACO and PSO based-state controller for a 24 V D.C. power source and.5 duty cycles usng the proposed specalzed optmzaton are llustrated n Fgure 5. The response performance parameters of the output voltage results after smulaton In the followng, performance of proposed of the ACO and PSO based-controllers n three dfferent condtons ncludng of change n the reference voltage, nput voltage, and output load are studed.

7 IJCSI Internatonal Journal of Computer Scence Issues, Volume 3, Issue 6, November Performance assessment of varous algorthms based on system performance The smulaton s ntally carred out by varyng the output voltage and nductors currents wth the varaton n the reference voltage usng ACO and PSO-based controllers as shown n Fgure 6. Fg. 7: System responses of ACO and PSO controlled buck converter wth the changes n the nput voltage Fg. 6: System responses of ACO and PSO controlled buck converter wth the reference voltage s changed from 2V to 8V. The reference voltage s changed from 2 V to 8 V at moment t=.5 sec. where t can be seen that the correspondng output voltage has been changed and followed the reference. In ths case, the controller adopts the change n reference, vary the duty cycle of the converter and produce the reference as the output voltage wthn a fracton of mllsecond. In the present case, the nput voltage s vared from 24 to 8V at.33 sec and from 8V to 3V at.66 sec. The tme response of the output voltage and nductor current n a closed-loop system compensated by a ACO and PSO-controller s llustrated n Fgure 7. The changes n the nput voltage do not make any clear varatons n the output voltage and current snce the controller adopt the varatons n the parameters and contnuously track the reference voltage. Consequently, the duty cycle of gate pulse to the MOSFET s changed so that to mantan the output voltage at the same desgned value wthn a fracton of mllsecond. Ths proves the effectveness and the robustness of the controllers as well as that the controller respond very well under ths change. Fgure 8 shows the smulaton results when the proposed ACO and PSO-based controller are appled to the converter under load varaton. The load resstor (R) s suddenly changed from 3 Ω (nomnal value) to 9 Ω and agan to 6 Ω. By changng the value of resstance load, t has been seen that as load resstance ncrease, the output voltage s followed the reference value (2V) whle the nductors current are changed accordng to the load values. Fgure 9 shows the behavour of the controlled system when a falure n one of the converters s occurred after.5 sec. from the startng smulaton tme. Fg. 8: System responses of ACO and PSO controlled buck converter wth the changes n the nput voltage

8 IJCSI Internatonal Journal of Computer Scence Issues, Volume 3, Issue 6, November References Fg. 9: System responses of ACO and PSO controlled buck converter wth sudden falure n converter 2 Ths Fgure llustrates that a satsfactory performance s obtaned where the output voltage resumes ts reference value (of 2V) mmedately after the transent varaton caused by the sudden falure n one of the converters. Smulaton results verfy that the control schemes n ths secton gve stable operaton of the power supply and the output voltage and load current can return to the steady state even when t s affected by sudden changes or any falure n the controlled system. 6. Conclusons The desgn of on-lne ACO and PSO-based state feedback controllers for the parallel converters were adopted as an optmzaton task and the controller gans are optmzed through evolutonary search algorthms. Performance of proposed controllers n dfferent condtons, ncludng of change n reference voltage, the output load and the nput voltage as well as the sudden falure n the one of the converters were nvestgated. By observng the rse tme, settlng tme, and peak overshoot from the step response responses, whch are obtaned by usng the on-lne state controllers, t can be concluded that PSO-based parameter optmzaton s good and robust as compared to other method. The PSO controller gves the better performance and was more robust for model naccuraces and dsturbances n comparson wth the ACO-based controller. The obtaned smulated results valdate the effectveness of the proposed PSO control strategy. Consequently, the controlled converters systems work fne and behave very well wth very less overshoot and settlng tme. Ths leads to that the overall speed of the system s ncreased as seen by the decrease of the settlng tme when the converter s connected to the power source [ ] H. Guldemr, Modellng and sldng control of DC-Dc buck-boost Converter, 6th Internatonal Advanced Technologes Symposum (IATS ), 6-8 May, Elazığ, Turkey, 2. [2 ] R. D. Mddebrok and S, Cuk, "A general unfed approach to modellng swtchng converter power stages", IEEE Power Electroncs Specalst (PESC) Conf. Proc., 976, pp [3 ] F. H. eung, P. K. Tam, C.K., The control of swtchng dc-dc converters-a general QR problem, IEEE Transactons on Industral Electroncs, Vol. 38, No.,99, pp [4 ] S. M. Derakhshana, and M. Sedghzadeh, New ntellgent controller for parallel DC/DC converters, Internatonal Journal of Engneerng, TRANSACTIONS A: Bascs Vol. 27, No.,24, pp [5 ] Wang -l, Study of Intermttency n ParallelConnecton Buck Converters, Internatonal Conference on Advances n Engneerng, Proceda Engneerng 24, 2, pp [6 ] G. Seshagr Rao, S. Raghu, N. Rajasekaran, Desgn of Feedback Controller for Boost Converter Usng Optmzaton Technque, Journal homepage, Vol. 3, No.,23, pp [7 ] K. W. Seo and H. H. Cho, Smple Fuzzy PID Controllers for DC-DC Converters, Journal of Electrcal Engneerng and Technology Vol. 7, No. 5,22 pp [8 ] P. Mattavell,. Rossetto, G. Spazz, and P. Tent, General-purpose fuzzy controller for dc dc converters, IEEE Transactons on Power Electroncs, Vol. 2, No., 997, pp [9 ] M. Bozorg, V. Fereshtehpoor, M. Monfared, and N. Namjoo, Controller desgn usng ant colony algorthm for a non-nvertng Buck Boost chopper based on a detaled average model, Electrc Power Components and Systems, 43(2), 25, pp [ ] J. Mahdav, A. Emad, and H. A. Tolyat, (997), Applcaton of state space averagng method to sldng mode control of PWM DC/DC converters, IEEE Industry Applcatons Socety, 997. [ ] Hassanzadeh, M. Monfared, S. Golestan, and R. Dowlatabad, Small sgnal averaged model of DC choppers for control studes, Internatonal Conference on Electrcal Engneerng and Informatcs, Bandung, Indonesa, 2.

9 IJCSI Internatonal Journal of Computer Scence Issues, Volume 3, Issue 6, November [2 ] M. S. Reddy, Ch. Kalyan, M. Uthra and D. Elangovan, A Small sgnal analyss of DC-DC boost converter, Indan Journal of Scence and Technology, Vol. 8(S2),25, pp. -6. [3 ] Bhowate and S. Deogade, Comparson of PID tunng technques for closed loop controller of DC-DC boost converter, Internatonal Journal of Advances n Engneerng and Technology, Vol. 8, Issue, pp , 25. [4 ] Colorn, M. Dorgo, and V. Manezzo, Dstrbuted optmzaton by ant colones, n Proceedngs of the Frst European Conference on Artfcal fe, F. J. Varela and P. Bourgne, Eds., MIT Press, Cambrdge, MA,992, pp [5 ] Dorgo, M., Manezzo, V., and Colorn, A., Ant system, optmzaton by a colony of cooperatng agents, IEEE Trans. Syst., Vol. 26, 996, pp [6 ] M. Bozorg, V. Fereshtehpoor, M. Monfared and N. Namjoo, Controller Desgn Usng Ant Colony Algorthm for a Non-nvertng Buck Boost Chopper Based on a Detaled Average Model, Electrc Power Components and Systems, 43(2), 25, [7 ] J. Kennedy, and R. Eberhart, Partcle swarm optmzaton. Proc. IEEE Int. Conf. on Neural Network, 995, pp [8 ] S. K. Sngh and M. Borah, A Comparatve performance of swarm ntellgence optmzaton method and evolutonary optmzaton method on some nosy numercal benchmark test problems, Internatonal Journal of Computatonal and Appled Mathematcs, ISSN Volume 4 Number ),29, pp. 9. [9 ] J. F. Schutte, and A. A. Groenwold, A study of global optmzaton usng partcle swarms, J Global Optmum, 25. [2 ] Vetgte J V, Feedback Control System, PrentceHall, Inc., concepts based on neural networks, fuzzy logc, Partcle Swarm Optmzaton, and genetc algorthms. Al S. Al-Dmour an assocate professor n the Electrcal Engneerng Department at Mutah Unversty n Jordan. He completed hs BSc n Electrcal Engneerng at Mousel Unversty, Iraq, n 984 and hs PhD n Control Systems at Bradford Unversty, UK, n 996. Hs man nterest s real-tme control applcaton, wth partcular emphass on vbraton suppresson n flexble structures and n controllng electrcal machnes. In partcular, the control laws utlzng ntellgent desgn