2016 Published in 4th Intenational Symposium on Innovative Technologies in Engineeing and Science 3-5 Novembe 2016 (ISITES2016 Alanya/Antalya - Tukey) An Efficient Contol Appoach fo DC-DC Buck-Boost Convete * 1 Fauk Yalçın and 2 Felix A. Himmelstoss * 1 Faculty of Technology, Depatment of Mechatonics Engineeing Sakaya Univesity, Tukey 2 Depatment of Electonic Engineeing Univesity of Applied Sciences Technikum Wien, Austia Abstact In this pape, an efficient contol stuctue based on a contolle fo DC-DC buck-boost convete opeation is poposed. By the poposed appoach, accuate pulse wih modulation (PWM) switching based opeation duty atio of the buck-boost convete is achieved by the closed-loop contolle. The contol law based on instantaneous values of the input voltage and the desied output voltage is used to suppot the contolle to achieve an efficient and fast opeation duty atio. So the efficiency of the convete is impoved to gain the desied high quality output voltage when the paametes of the convete opeation ae changed. Simulation studies have been done in MATLAB-Simulink to pove the efficiency of the poposed contol appoach based on the contolle suppoted by the contol law. The obtained esults have shown that the poposed contol appoach achieves accuate and efficient opeation fo the buck-boost convete unde diffeent system conditions. Key wods: Buck-boost convete, contol law, contolle, PWM 1. Intoduction The impoving technology needs continuously vaious foms of the electical enegy. So, diffeent types of convetes wee developed based on the impovements in powe electonics. DC-DC convetes ae used to convet a DC souce fom one voltage level to anothe. These convetes ae widely used in many industial applications whee diect voltage egulation is equied [1-3]. The DC-DC buck-boost convete poduces an output diect voltage value lowe o highe than the input voltage value [4]. The voltage tansfomation is achieved by pulse wih modulation PWM. The duty atio contols the buck-boost convete as is the case in othe DC-DC convetes e.g. in buck and boost convetes [5, 6]. Consideing ideal devices and continuous inducto cuent mode conditions, the elation between the convete input and output voltages in steady state can be deived as an algebaic equation which depends on the PWM duty atio alone. But in pactice, discontinuous cuent mode convete opeation and non-ideal convete components pevent to achieve a cetain duty atio fo convete opeation fo the elated opeating point though mathematical computation. Thus, a feedback contol stuctue fo pactical convete opeation depending on the actual and the efeence output voltage values is obviously equied fo accuate convete opeation [7]. The eseaches have studied the contol of the DC-DC buck-boost convete on many diffeent contolles. The contolle pocesses the eo between the convete efeence and the eal output *Coesponding autho: Addess: Faculty of Technology, Depatment of Mechatonics Engineeing Sakaya Univesity, 54187, Sakaya TURKEY. E-mail addess: faukyalcin@sakaya.edu.t, Phone: 902642956473
F. YALCIN et al./ ISITES2016 Alanya/Antalya - Tukey 1093 voltage and eliminates the eo by geneating the necessay duty cycle. The conventional and D contolles ae geneally used to contol DC-DC buck-boost convetes [8, 9]. Moden contol techniques such as the Sliding Mode Contolle ae also successfully applied to many studies, whee the and D contolles ae not sufficient fo the equied convete esponses [10]. The designs of these mentioned contolles ae achieved though the mathematical models fo the defined convete opeating points. So, any change of the convete system paametes foces the change of the mathematical model of the convete. As the mathematical model of the convete is changed, it is impossible to achieve the same pefomance of the system esponse by the designed contolle paametes obtained fo the pevious convete opeating point. This statement is valid fo classical and moden designs. A non-adaptive contolle has to be designed especially fo one woking point, but must be able to contol the system in a pecise and stable way and within a time estiction fo the whole aea of woking points whee the convete is planned to wok. A majo pitfall in contolling the buck-boost convete (and also in the fly-back convete which is a buck-boost with the possibility to get an isolation between input and output) is its ight-side zeo. Diffeent ways wee used to impove the contol [11, 12]. In this study, a novel DC-DC buck-boost convete contol stategy based on the contolle and an open-loop contol law is poposed. In this contol stuctue, the opeating duty atio fo the convete is achieved by the contolle and the poposed open-loop contol law. The open-loop contol law suppots the contolle to eliminate the convete opeating eo in a fast and efficient manne. Thus, the open-loop contol law acceleates the system esponse. So, the contol law pevents the equiement of changing the detemined contolle paametes fo vaious convete opeating points. The contol law is the switching duty atio depending on the convete input voltage and the efeence output voltage and has an algebaic stuctue. So, the contol law can be achieved easily and fast. Thus, it does not cause additional design challenges and complexity. Simulation studies have been done fo the poposed contol appoach fo the DC-DC buck-boost convete in MATLAB-Simulink envionment. The obtained simulation esults fo diffeent opeating points have poved that the poposed contol stuctue based on the open-loop contol law allows a obust and efficient DC-DC buck-boost convete opeation. 2. Design of the Poposed Convete Contol Stuctue 2.1. The open-loop contol law The DC-DC buck-boost convete topology is given in Fig. 1 [13]. In Fig. 1, Vi () t, Vo () t, S, D, L and C epesent the input diect voltage, the output diect voltage, the switch that is one way conductive and capable of being tuned on and tuned off, the diode, the inducto, and the capacito, espectively.
F. YALCIN et al./ ISITES2016 Alanya/Antalya - Tukey 1094 S D Vi (t) L C V o (t) Load Figue 1. The topology of the DC-DC buck-boost convete An IGBT device is used as switch S in this study. The DC-DC buck-boost convete cicuit using a contollable IGBT as switching device is demonstated in Fig. 2. In Fig. 2, Io () t, IL() t and I () t epesent load cuent, inducto cuent, and capacito cuent, espectively. C Vi (t) S D I L (t) I C (t) I o (t) L C V o (t) Figue 2. The DC-DC buck-boost convete cicuit using IGBT as switching device The opeation of the DC-DC buck-boost convete can be claified by the convete cicuit given in Fig. 2. When S is tuned on, diode D is off because of evese biasing. In this case, convete input voltage supplies the inducto, thus the inducto is enegized. When S is tuned off, the diode is fowad biased and tuned on. In this case, the enegized inducto supplies both the capacito and the load. Thus, a voltage value lowe o highe than the input voltage value is obtained at the output of the convete depending on the switching duty atio of S [14]. By assuming the continuous cuent mode (CCM) and ideal convete components, the elation between the convete input and output voltages can be given as [15]: Load () Vo( t) Vi( t), 1 ( ) (1) whee () detemines the PWM switching duty atio of S. It is defined as the atio of the tunon time of S to the switching peiod of S : t on ( ). (2) T The open-loop duty atio that povides the convete opeation can be achieved though (1) consideing the mentioned ideal conditions above. Thus, the open-loop duty atio, which is used as contol law and can be given as:
F. YALCIN et al./ ISITES2016 Alanya/Antalya - Tukey 1095 d CL V ( t), V V () t i (3) whee V is the efeence value of the desied convete output diect voltage. 2.2. The poposed closed-loop convete contol stuctue Because of the unideal easons mentioned befoe, the deived open-loop contol law is not enough to achieve the equied convete output voltage value in pactice. Because of the nonideal convete components and discontinuous inducto cuent situation caused by diffeent load values, the duty atio of the convete poviding the equied output voltage is diffeent fom the duty atio obtained by the open-loop contol law. So, the eal convete duty atio that eliminates the eo between the efeence and eal output voltage must be obtained fom the closed-loop contolle. Fo this aim, the contolle is chosen in this study. The poposed contol stuctue fo the contol of the DC-DC buck-boost convete is given in Fig. 3. I o (t) V i (t) DC-DC Buck-Boost Convete V o (t) Load PWM Geneato V Contol Law d CL (t) d (t) d(t) Contolle Figue 3. The poposed closed-loop contol stuctue fo the DC-DC buck-boost convete As can be seen fom Fig. 3, the contolle poduces a feedback duty atio d () t fom the eo between the efeence and actual convete output voltages. The open-loop duty atio d () t given in (3) suppots the feedback duty atio d () t achieved by the contolle. Thus, the effective duty atio () fo accuate convete opeation is poduced by d( t) d ( t) d ( t). (4) CL As seen fom Fig. 3, the PWM geneato poduces the contol signal of the switch S depending on the duty atio deived by (4). 2.3. Mathematical model of the convete fo the contolle The contolle can be designed by the mathematical model of the convete cicuit given in CL
F. YALCIN et al./ ISITES2016 Alanya/Antalya - Tukey 1096 Fig. 2. The mathematical model of the idealized convete (no loss mechanisms included) can be deived fom the equivalent convete cicuits given in Fig. 4. Vi (t) S D I L (t) I C (t) I o (t) L C R V o (t) (a) S D I L (t) I C (t) I o (t) Vi L C R V o (t) (b) Figue 4. Equivalent cicuits of the convete: a) Switch S is on mode I, b) Switch S is off mode II The dynamic equations fo mode I whee S is on in Fig. 4(a) can be given as: di L () t L Vi () t (5) dvo( t) Vo( t) C. R (6) The dynamic equations fo mode II whee S is off in Fig. 4(b) can be witten as: dil() t L Vo () t (7) dvo( t) Vo( t) C I L( t). (8) R The state-space equations fo mode I and mode II can be obtained fom (5)-(8) espectively as: d IL( t) 0 0 IL( t) 1/ L Vi () t Vo( t) 0 1/ RC Vo( t) 0 (9)
F. YALCIN et al./ ISITES2016 Alanya/Antalya - Tukey 1097 d IL( t) 0 1/ L IL( t) 0 Vi ( t). Vo( t) 1/ C 1/ RC Vo( t) 0 (10) and the aveage state-space model of the DC-DC buck-boost convete can be deived fom (9) and (10) as: d IL( t) 0 (1 d) / L IL( t) d / L Vi ( t). Vo( t) (1 d) / C 1/ RC Vo( t) 0 (11) The closed-loop contol block diagam of the system is shown in Fig. 5 accoding to the closedloop contol stuctue given in Fig. 3. V (s) Contolle G (s) PWM (s) V C (s) d CL (s) G D (s) d (s) d(s) G S (s) V o (s) Figue 5. The closed-loop contol block diagam of the system The tansfe function between Vo () s and ds () can be obtained fom Fig. 5 and (11) (the woking point values ae maked with an index W) as: I s V V 1d LW ow iw W Vo s C LC d s 1 1 d 2 2 W s s RC LC (12) The convete tansfe function shows that the buck-boost convete is a non-phase-minimum system. Theefoe, we have an additional phase shift due to the ight half-plane zeo. The model descibed by (12) is a lineaized model, and theefoe enables us to use the linea contol theoy. As seen in Fig. 5, the duty atio of the contol law d () s has an effect upon the opeation duty atio ds. () By consideing d () s is zeo (assuming thee is no suppot fom the contol law), d () s can be deived as: CL d ( s) d( s). (13) CL PWM s is the tansfe function of the PWM stage between d () s and the contol signal () V () C s and can be given as: PWM ds ( ) 1 ( s). (14) V () s V C PWM
F. YALCIN et al./ ISITES2016 Alanya/Antalya - Tukey 1098 Hee, V PWM is the amplitude of the amp in the PWM convesion of the contolle. The PWM stage can be intepeted as a popotional element. So the tansfe function of the system, which the tansfe function of the contolle G () s has to contol, is the poduct of (12) and (14). The influence of the input voltage on the output voltage can be descibed by the distubance model: dw 1 dw Vo s LC Vi s 1 d 1 2 2 W s s RC LC (15) A contolle has a dynamic stuctue. So it equies a esponse time. But the poposed contol law has a static behavio as seen fom its algebaic stuctue. The contol law poduces a duty atio value close to the necessay opeation duty atio simultaneously with the eo change. Thus, the contol law leads the contolle to compensate the system fom the duty atio point obtained by the contol law. So the contol law acceleates the system esponse. Afte that, the contolle takes ove the task fom the contol law to eliminate the system eo. One has to keep in mind, howeve, that a too fast change in the duty cycle leads to an oveshot in the cuent (and also in the voltage) and has theefoe be omitted. This can be done simila to the soft-stat of the system. 3. Simulation Results The poposed contol appoach fo the DC-DC buck-boost convete has been tested in MATLAB-Simulink envionment fo diffeent system opeating conditions. The obtained simulation esults fo the poposed appoach ae given with the esults of the conventional contolle based convete to show the accuacy and the efficiency of the poposed contol appoach fo the DC-DC buck-boost convete opeation. The compaison studies have been done fo thee diffeent opeation conditions: changing the efeence output diect voltage, changing the input diect voltage and changing the load. The switching fequency is chosen as 20 khz fo the simulation studies. The capacitance value of the capacito and the inductance value of the inducto the in the convete cicuit ae detemined as C=330μF and L=50μH, espectively. The paametes of the contolle ae kept constant fo all opeation conditions. The analog constants detemined fo an opeating point ae used as K =1.2 and K =0.053. P I Fo the fist case, the efeence output voltage is changed duing the DC-DC buck-boost convete opeation. The convete input voltage and the load values ae kept constant. The input voltage and the load values ae V =30V and R=20, espectively. The efeence output voltage i
F. YALCIN et al./ ISITES2016 Alanya/Antalya - Tukey 1099 is deceased fom V =40V to V =25V. The compaative esults of the poposed appoach and the conventional contolle based convete opeation fo case 1 ae given togethe in Fig. 6. Figue 6. The compaative convete opeation esults fo the change of the efeence output diect voltage Fig. 6 shows that the convete contolled by the poposed appoach, whee the poposed contol law suppots the contol eaches the new efeence output voltage faste than the convete contolled by the conventional contolle. On the othe hand, the poposed contol appoach pevents the oveshot whee the conventional method can not. Fo case 2, the convete input voltage is changed duing the efeence output voltage and the load values ae kept constant. The efeence output voltage and the load values ae V =30V and R=20, espectively. The input voltage is changed fom V i =20V to V i =35V. The compaative esults of the poposed appoach and the conventional contolle based convete opeation fo case 2 ae given togethe in Fig. 7. Figue 7. The compaative convete opeation esults fo the change of the input diect voltage Fig. 7 shows that the sudden ise of the input voltage affects the incease of the output voltages of both of the two convetes. But it is clea that the poposed appoach povides the convete output voltage to each the efeence value with less oveshot in a less esponse time. In case 3, the load is foced to change duing the convete opeation, while the efeence output voltage and the input voltage of the convete ae kept constant. The efeence output voltage and the input voltage values ae V =30V and V i =45V, espectively. The load is deceased fom R=20 to R=30. The compaative esults of the poposed appoach and the conventional contolle based convete opeation fo case 3 ae given togethe in Fig. 8.
F. YALCIN et al./ ISITES2016 Alanya/Antalya - Tukey 1100 Figue 8. The compaative convete opeation esults fo the change of the load It is clea fom Fig. 8 that the sudden incease in the load value affects the decease of the output voltage in both of the two convete opeations. At the beginning of the load change, the convetes output voltages incease. Afte that, the output voltages decease immediately. The poposed contol stuctue based on contol law povides the convete output voltage to etun to the efeence value with less oveshot in a less esponse time. The esults fo thee diffeent opeation cases show that the poposed contol law appoach impoves the DC-DC buck-boost convete opeation efficiently though suppoting the closedloop contolle stuctue. So a highe quality of the convete output voltage is achieved in compaison with the conventional contolle based system. 4. Conclusions In this study, contay to the contol stuctue based on the conventional contolle, an impoved contol stuctue based on open-loop contol law that suppots the contolle is poposed fo the contol of the DC-DC buck-boost convete. The poposed contol law is obtained as an algebaic one depending on the efeence output voltage and the input voltage of the convete. So it suppots the contolle and thus a bette quality of the convete opeation fo diffeent opeation paametes of the contolle is achieved. The obtained compaative simulation esults have shown that the poposed appoach has impoved the convete opeation. Refeences [1] K.C. Wu, H.H. Wu, and C.L. Wei, Analysis and design of mixed-mode opeation fo noninveting buck-boost DC-DC convetes, IEEE Tans. Cicuits Syst. II-Expess Biefs, vol. 62, pp. 1194-1198, Decembe 2015. [2] H. Zhang, M. Zhao, and X. Wu, Zeo-cuent switching method fo dc-dc buck convete in potable application, Electon. Lett., vol. 51, pp. 1913-1914, Novembe 2015. [3] E. Babaei and O. Abbasi, Stuctue fo multi-input multi-output dc-dc boost convete, IET Powe Elect., vol. 9, pp. 9-19, Febuay 2016. [4] Y. Ma, Integated lossless load cuent sensing method fo buck-boost DC-DC convetes, Electon. Lett., vol. 51, pp. 88-90, Januay 2015.
F. YALCIN et al./ ISITES2016 Alanya/Antalya - Tukey 1101 [5] C.L. Kok, X. Li, L. Siek, D. Zhu, and J.J. Kong, A switched capacito deaime contolle fo DC-DC buck convete, IEEE Int. Symp. Cicuits and Syst., p. 217-220, 2015. [6] M. Heji and H. Mokhtai, Hybid pedictive contol of a DC-DC boost convete in both continuous and discontinuous cuent modes of opeation, Optim. Cont. Appl. Met., vol. 32, pp. 270-284, May/June 2011. [7] Z. Wu and J.H. Zhao, Nonlinea output feedback contol fo DC/DC buck-boost powe convetes, 6th Int. Symp. Test and Meas., p. 491-494, 2005. [8] Z. Wu, J.H. Zhao, and J.Y. Zhang, -adaptive cascade contolle design fo DC/DC buckboost powe convetes, 7th Int. Conf. Electon. Meas. Instum., p. 426-430, 2005. [9] Z. Wu and W. Chou, Adaptive-D cascade contolle design fo DC/DC buck-boost PWM powe convetes, 3d Int. Conf. Impul. Dynam. Syst. Appl., p. 896-901, 2006. [10] M. Salimi, J. Soltani, A. Zakipou, and N.R. Abjadi, Hype-plane sliding mode contol of the DC-DC buck/boost convete in continuous and discontinuous conduction modes of opeation, IET Powe Elect., vol. 8, pp. 1473-1482, August 2015. [11] F.A. Himmelstoss, J.W.Kola, and F.C.Zach, A Bidiectional DC-DC Convete - Analysis and Contol Design, Jounal of Electonics and Telecommunication Enginees, Vol.37, No.1 1991, pp. 124-132. [12] F.A. Himmelstoss, J.W. Kola, and F.C. Zach, Analysis of a Smith-Pedicto Based Contol Concept Eliminating the Right-Half Plane Zeo of Continous Mode Boost and Buck-Boost DC/DC Convetes, Poceedings of the IEEE Industial Electonics Confeence IECON'91, Kobe, Oct.28 - Nov.1, 1991, pp. 423-428. [13] A. Ajami, H. Adi, and A. Faakho, Design, analysis and implementation of a buck-boost DC/DC convete, IET Powe Elect., vol. 7, pp. 2902-2913, Decembe 2014. [14] M.R. Banaei, H. Adi, and A. Faakho, Analysis and implementation of a new singleswitch buck-boost DC/DC convete, IET Powe Elect., vol. 7, pp. 1906-1914, July 2014. [15] J. Dey, T.K. Saha, and S.N. Mahato, Robust voltage egulation of DC-DC PWM based buck-boost convete, IEEE Int. Conf. Ind. Tech., p. 229-234, 2014. Fauk Yalçın was bon in Sakaya, Tukey in 1984. He eceived M.Sc. and Ph.D. degees in electical and electonics engineeing fom Sakaya Univesity, Tukey, in 2009 and 2013, espectively. He is assistant pofesso at the Depatment of Mechatonics Engineeing at the Faculty of Technology at Sakaya Univesity, Tukey. His cuent eseach inteests ae powe systems, smat gids, powe electonics and contol systems. Felix A. Himmelstoss was bon in 1956 in Moedling, Austia. He eceived the Dipl.-Ing. and D. (PhD) degees fom Technical Univesity of Vienna, in 1981 and 1990, espectively. Since 1982 he has been woking on diffeent pojects fo Austian companies developing powe supplies and electical dives. He is autho and coautho of numeous technical and scientific papes and patents. D. Himmelstoss is pofesso and head of the Industial Electonics section of the Univesity of Applied Sciences Technikum Wien.