Modeling and Simulation of Buck-Boost Converter with Voltage Feedback Control

Transcription

1 MATE Web of onferene 3, 0006 ( 05) DOI: 0.05/ mateonf/ Owned by the author, publihed by EDP Siene, 05 Modeling and Simulation of BukBoot onverter with oltage Feedbak ontrol Xuelian Zhou, Qiang He,a ollege of omputer and Information Siene, Southwet Univerity in No., Tianheng Street,Beibei,hongqing, hina Abtrat. In order to deign the ontrol ytem, it i neeary to have an exat model of bukboot onverter. Thi paper put forward the tranfer funtion model of bukboot onverter by the tatepae average method. The openloop tranfer funtion model of unompenated ytem i dedued aording to the mathemati model of the bukboot onverter, the ontroller i deigned aording to frequeny domain. The phae and magnitude margin of the openloop ytem of the bukboot onverter with ompenator have both been inreaed. After ompenating, thi ontrol ytem ha the advantage of mall overhoot and hort ettling time. It an alo improve ontrol ytem' real time property and antiinterferene ability. Introdution With the development of power eletroni, withing power upplie are widely ued in variou oaion, uh a ar, hip, airraft and omputer []. In many appliation uh a eletroni devie in ar, portable devie, et, where the output voltage range of the battery i oniderably large, bukboot onverter are required. BukBoot onverter with imple truture, eay to implement, et, ha been widely ued in variou oaion. BukBoot onverter i a bai topology of DD withing onverter. There are numerou type of bukboot onverter uh a the SEPI onverter [], the noniolated uk onverter, the Zeta onverter [3] and the SheppardTaylor topologie [4].A bukboot onverter provide an output voltage that may be le than or greater than the input voltage. In order to ahieve a proper deign and ontrol, it i neeary to have an exat model of onverter. By modelling the d d onverter, the operation of onverter in different operational mode an be invetigated in both tranient and teady tate. High auray and low repone time are major feature of the good modelling. The voltage mode ontroller i deigned to improve the ontrol performane of bukboot onverter Sytem model building The power tage of a bukboot onverter i hown a Fig.. It i ompoed of the diode D, the with tranitor Q, the output moothing apaitane the output moothing indutane and the atual load. a orreponding author: heq@wu.edu.n. Priniple of BukBoot onverter The iruit of BukBoot onverter operation an be divided into two ditintive mode: diontinuou ondution mode (DM) and ontinuou ondution mode (M). The ritial value of the indutor an be expreed a Eq.. If the value of the indutor i le than the ritial value, the bukboot onverter work in diontinuou ondution mode (DM). Otherwie, it work in ontinuou ondution mode (M). ( ) T () Where T i the with yle. The output voltage i determined by Eq..Aording Eq., it allow the output voltage to be lower or higher than the input voltage, whih i determined by the duty ratio. When le than 0.5, output voltage will le than input voltage. Otherwie, output voltage will higher than input voltage. o g () Where g i the input voltage and i the duty ratio. The ripple voltage an be expreed a Eq.3 o o T (3) When bukboot onverter operate in M, it an be divided into two mode in every withing period [5]. During mode, the diode D i revered biaed and tranitor Q i turn on. The input urrent flow into Thi i an Open Ae artile ditributed under the term of the reative ommon Attribution iene 4.0, whih permit ditribution, and reprodution in any medium, provided the original work i properly ited. Artile available at or

2 MATE Web of onferene Bukboot onverter Drive irule g Q D oad Figure. The topology for bukboot onverter O g Q Drive irule D oad u d PWM G () e ompenator v ref v o y x H() ontroller g on r i v oad Figure 4. The diagram of loedloop ytem of bukboot onverter the apaitor voltage. When written in tatepae form, thee equation beome a Eq.5. Figure. The equivalent iruit for mode g r i v oad Figure 3. The equivalent iruit for mode indutor and tranitor Q. The indutor urrent will raie and the Indutor will tore energy. At the ame time, apaitane upplie the load. It equivalent iruit i hown a Fig.. AS hown in Fig., i and v are the indutor urrent and the apaitor voltage repetively. on i onreitane of tranitor Q. r i onreitane of the Indutor. During mode, tranitor Q i turn off and the urrent, whih wa flowing through indutor, will flow through,, D and the load. At the ame time, the indutor urrent will fall until the tranitor Q i withed on. It equivalent iruit i hown a Fig.3. Building model of tranfer funtion for BukBoot onverter The theory of tatepae averaging applied in the withmode power onverter wa oneived in the early 970 and well developed in the early 980 [6]. Dr. obert Middlebrook and hi graduate tudent Dr. Slobodan uk were redited with the onept and tehnique aoiated with it. Therefore, the withmode onverter model generated on the bai of the theory have oftentime been named Middlebrook model [7]. Mode. While the with Q i in open poition, the equivalent wa hown a Fig.. Applying Kirhoff voltage law(k), the indutor urrent, apaitor voltage are deribed a Eq.4. di ( on r ) g i dt dv v dt The linear iruit i deribed by mean of the tatevariable vetor x oniting of the indutor urrent and (4) x Ax B y x g on r 0 ( i A, B, x v 0 0 [0 ], y v ) O Mode. While the with Q i in loe poition, in a imilar manner, thee equation beome a Eq.6. x Ax B y x g r 0 i ( A, B, x v [0 ], y v ) The averaged matrix A i a Eq.7. O AA( ) A ( on r ) ( ) r ( ) ( ) In a imilar manner, the averaged matrie B and are evaluated, with the following reult: BB( ) B B ( ) The teadytate i hown a Eq.9. X ( ) ( on r ) A Bg ( ) g g (5) (6) (7) (8) ( ) r ( on r ) ( ) r ( ) (9) 0006p.

3 IMEE 05 The tranfer funtion from the ontrol input (duty ratio ) to output (the apaitor voltage v ) expree a Eq.0. G I A B A A X vd () ( ) [( ) ( B B ) ] ( ) X g (0) Beaue on and r i very mall, they an be ignored. G vd () wa implified a Eq.. Figure 8. Simulation diagram of bukboot onverter G vd () g[ ( ) ] ( ) [ ( ) ] () The tranfer funtion from input voltage g to output v wa hown a Eq. Gvg () ( ) ( ) () The tranfer funtion of the pulewidth modulator i deribed a Eq.3 Figure 9. Simulation reult of bukboot onverter with voltage diturbane G d () (3) m i the maximum of the aw tooth wave of the pulewidth modulator. For pulewidth modulator SG355A, m i 3. [8]. m 3 Deign of ontrol ytem Figure 5. Bode plot of bukboot onverter without ompenator SG355A pin 3 SG355A pin 3 Figure 6. ompenator SG355A pin 9 The peifiation of bukboot onverter withing power upply deign are a follow: Swith yle T i 50μ. voltage i between 0 and 64. Maximum output ripple i no greater than Output voltage i 6±0.0. A hown Fig.4, Independent of variou operating ondition, uh a the output loading, input voltage, and the ambient temperature, the value of voltage of bukboot onverter mut remain ontant. To perform uh a tak, a portion of the iruit mut be inenitive to any of the above variation. Thi portion i alled the referene, uually a voltage oure, ref, whih i preie and well table over temperature. The load reitor i varied from 0 ohm to 00 ohm. The ritial indutor wa deribed a Eq.. Aording to Eq., the value of indutor i mh. onidering the margin of ontinuou ondution mode, the value of indutane i 5mH Aording to Eq., the duty ratio i 0.. Aording to Eq.3, the value of apaitane i 00μ F.onidering the margin of apaitor, the value of apaitor i 600μ F.The value of x i 90k ohm. The value of y i 0k ohm. Aording to Eq.4, H() i 0.. H () /( ) 0. (4) y x y G () G () G () H() o vd d (5) Figure 7. Bode plot of bukboot onverter with ompenator 0006p.3

4 MATE Web of onferene AS hown in Eq.5, the unompenated ytem ha a zero and two loe pole. The zero i deribed a Eq.6. It ha a right halfplane zero (HP), whih i alo alled nonminimum phae ytem (NMP).The two loe pole i deribed a Eq.7. ( ) 3840 (6) zz 3.6 (7) pp pp The openloop tranfer funtion of the unompenated ytem wa hown a Eq.5. It bode plot i hown a Fig.5. A hown a Fig.5, the phae margin of the openloop ytem only reahe to The magnitude margin of the openloop ytem i above 4.65db. Both of them are too maller. The phae margin of ontrol ytem mut be greater than 30. The magnitude margin of ontrol ytem mut be greater than 6db.So, one mut deign a ompenator to improve the magnitude margin and phae margin of the bukboot onverter. SG355A wa eleted a ontroller. The SG355A, pule width modulator ontrol iruit, an offer lower external part ount and improved performane when implemented for ontrolling all type of withing power upplie [9]. ompenation network i deigned between pin 9 and pin. That i hown a Figure 6. The tranfer funtion of ompenator i deribed a Eq.8. It provide two zero and three pole with one pole loated at the origin hown a Eq.9 and Eq.0. The pole at the origin i ued to improve the D regulation. The other pole i ued to ompenate for the right halfplane zero. ( )[ ( ) ] 3 3 G () [ ( )]( )( ) 3 3 z z 3 (8) /( ), /( ) (9) 0, /( ), /( ) (0) p p 3 3 p3 The two zero of ompenator are deigned to pp /3 hown a Eq.. The pole p of ompenator i deigned to ompenate the zero of the unompenated ytem hown a Eq.. The pole p 3 i deribed a Eq.3.The value of the roover frequeny of the feedbak ytem i deigned to047. / / () z z pp 3 p 3 T The gain A i hown a Eq () p zz (3) 3840 p G ( j ) A 40. (4) The value of i 5000 Ohm. The value of 3 depend on Eq.5.The value of i determined by Eq.6. The value of depend on Eq.7.The value of 3 i determined by Eq.8. The value of depend on Eq.9 4 (5) 3 A /( ).68F (6) z 0.nF (7) p 3 /( ).F (8) 3 p 3 /( ) 6.4k (9) z 3 A hown in Fig.7, the phae margin of the openloop ytem with ompenator reahe to The magnitude margin of the openloop ytem of the bukboot onverter with ompenator i.4db.so the ontrol ytem with ompenator i table 4 Simulation experiment In Fig.8, the imulation model of bukboot onverter i hown baed tatepae averaging method. In Fig.9, the imulation reult were preented. Obviouly, the output voltage follow the etvalue very well. A hown a Fig.9, overhoot of the ontrol ytem wa no more than.3%. The ettling time of it i le than 0. eond. The ripple of the output voltage i no more than 0.0 in tead tate. In Fig.9, the imulation model of bukboot onverter with voltage diturbane baed tatepae averaging method wa hown. At the time 0.3 eond, a voltage diturbane impoed on the ontrol ytem hanged by 30. The voltage drop i no more than.. The diturbane reovery time i no more than 0. eond. Aording to imulation reult, it an reit the upply diturbane very well. Thee model are imulated by uing Matlab 0b. 5 onluion Bukboot onverter i a timevariant and nonlinear dynami ytem. Under the aumption ondition of lowfrequeny mall ripple wave and mall ignal, the mathemati model of bukboot onverter are built up with tatepae averaging method. One ha offered an extremely imple deign olution to the problem of outputfeedbak regulation for bukboot onverter whih i inenitive to unertainty in the voltage diturbane. The experimental reult how that the ontrol ytem ha the advantage of mall overhoot and hort ettling time, whih better meet the requirement of ompliated operation ondition of bukboot onverter. 0006p.4

5 IMEE 05 It an alo improve ontrol ytem' real time property and antiinterferene ability. Aknowledgement Thi work wa upported in part by the eearh Program for the tandardization adminitration of the People' epubli of hina under Grant No T 604. Thi work wa alo upported in part by hongqing Engineering eearh enter for Intrument and ontrol Equipment. eferene.. Samavatian and A. adan, Eletrial and Energy Sytem. 63,6(04). J.N. ou,x.b. Wu,M.. Zhao et al, Miroeletroni Journal. J. E 4,5((0) 3. S. Singh, B. Singh, G. Bhuvanewari et al, 04 IEEE International onferene on Eletroni, Drive and Energy Sytem. 5 (04) 4. H. M. Mahery and E. Babaei, Eletrial and Energy Sytem. 44,8 (03) 5.. T. im, G. B. Joung, and G. H. ho, IEEE Tranation on power eletroni. 5,4 (009) 6. Y.h. Hu and W.P. ao,enewable Energy. 75,8 (05) 7. N. A. Ahmed, Eletri Sytem eearh. 73,4 (03) 8. Q. He, Applied Mehani and Material. 669 (04). 9. M. H. ahid, Eletroni: iruit, Devie and Appliation (03) 0006p.5