Indonesian J our nal of Electrical Engineering and Computer Science V ol. 36, No. 3, December 2024, pp. 1421 1429 ISSN: 2502-4752, DOI: 10.11591/ijeecs.v36.i3.pp1421-1429 r 1421 Adv anced contr ol and optimization strategies f or a 2-phase interlea v ed boost con v erter Muhammad Adnan Samad 1 , Usmono v Shukurillo Y ulbarso vich 1 , Sultono v Ruzimatjon An v arjon Ugli 1 , Saima Siddiqui 2 1 Department of Electrical Engineering, Electrical Mechanics and Electrical T echnologies, Fer g ana Polytechnic Institute, Fer g ana, Uzbekistan 2 Department of Mathematics, Fer g ana Polytechnic Institute, Fer g ana, Uzbekistan Article Inf o Article history: Recei v ed Feb 28, 2024 Re vised Aug 14, 2024 Accepted Aug 26, 2024 K eyw ords: Boost con v erter Interlea v ed boost con v erter Model predicti v e control Sliding mode control ABSTRA CT Reno wned for their adeptness in smoothing current flo w and maintaining balanced operation, 2-phase interlea v ed boost con v erters (IBC) demonstrate remarkable ef ficienc y , especially when confronted with demanding loads. This mak es them a preferred choice for high-po wer applications such as rene w able ener gy systems, hi gh-po wer supplies, and electric v ehicle po wer trains. In con- trast, standard boost con v erters are typically f a v ored in lo w-po wer , lo w-demand scenarios. The control of a 2-phase IBC in v olv es running tw o boost con v erters in paral lel b ut with a phase shift to reduce ripple currents, impro v e ef ficienc y , and increase po wer handling capabilities. T o ensure stability and optimal perfor - mance, the control strate gies for these con v erters foc us on achie ving balanced operation between the phases. Hence, the control of 2-phase IBC presents a sig- nificant challenge due to their non-minimum phase beha vior . The core focus of this article is the implementation of a composite model predicti v e cont rol (MPC) technique to re gulate a 2-phase interlea v ed boost con v erter . It introduces a no v el approach, model predicti v e sliding mode control (MPSMC), which le v erages the strengths of both MPC and sliding mode control (SMC). The benefits of this h ybrid method, termed MPSMC, are thoroughly de v eloped and simulated using MA TLAB/Simulink. The results, as discussed in the respecti v e section, pro vide an in-depth understanding of its ef fecti v eness in practical applications. This is an open access article under the CC BY -SA license . Corresponding A uthor: Muhammad Adnan Samad Department of Electrical Engineering, Electrical Mechanics and Electrical T echnologies Fer g ana Polytechnic Institute Fer g ana, Uzbekistan Email: samad.muhammad@ferpi.uz 1. INTR ODUCTION A boo s t con v erter is mainly used to increase the unre gulated v oltage to a re gulated one. Its applicat ions can v ary from battery-po wered de vices, rene w able ener gy systems to automoti v e applications. Although there are fe w limitations, including v oltage range, ef ficienc y , EMI, current limitation, and control comple xity . In this paper a tw o-phase interlea v ed boost con v erter is presented that has v arious adv antages o v er a single-phase boost con v erter , including lo wer ripple current, increased ef ficienc y , and superior po wer handling capabilities, especially in rene w able and electric v ehicle applications, as discussed in [1]–[4]. Moreo v er , a 2-phase inter - lea v ed boost con v erters (IBC) using a coupled i nd uc tor is in v estig ated, especially for fuel cell applications, in J ournal homepage: http://ijeecs.iaescor e .com Evaluation Warning : The document was created with Spire.PDF for Python.
1422 r ISSN: 2502-4752 [5]–[7]. In addition, a phase shift switching scheme for the DC-DC boost con v erter with parallel switches is sho wn in [8]. A 2-phase IBC has tw o boost con v erter stages running in parallel b ut out of phase. This design com- prises tw o boost con v erter stages operating in tandem, each phase-shifted for the other , ensuring concurrent operation during their switching c ycles as sho wn in F igure 1. F or simplicity , the continuous conduction mode (CCM) is being tak en into consideration and the parasitic resi stances for both the inductor and capacitor are also included. The phase functions are out of phase, which means that when one phase is conducting (on), the other is in the non-conducting (of f) state, and vice v ersa. By lo wering the ripple current in each indi vidual inductor , the interlea v ed operation impro v es current sharing across phases and lo wers the ripple current i n the o v erall output v oltage. Interlea ving the phases minimizes ripple currents, which leads to a smoother output v oltage and less stress on the components. The interlea v ed con v erter can handle greater currents more ef fi- ciently by distrib uting the load throughout the phases, reducing losses and boosting total con v erter ef ficienc y . Ensures balanced current sharing between phases, distrib uting the load equally and pre v enting one phase from carrying the entire load. Higher po wer handling capacities are possible wi th the interlea v ed arrangement than with a single-phase boost con v erter . After elucidating the benefits of a 2-phase IBC, its imperati v e to e xamine its control mechanisms, gi v en the inherent non-minimum phase beha vior characteri stic of these type of con- v erters, which mak es the control more challenging. Figure 1. 2-phase interlea v ed DC-DC boost con v erter Muktiadji et al. [9] sho w the control of the boost con v erter using observ er -based backstepping SMC for the DC microgrid. Cunha and P ag ano [10] sho ws some limitations in the control of the boost con v erter , especially in its transient beha vior . This art icle presents an inno v ati v e model predicti v e sliding mode control (MPSMC) strate gy to re gulate a 2-phase interlea v ed boost con v erter , emplo ying sliding mode control (SMC) within the inner loop and model predicti v e control (MPC) within the outer loop. This inte grated control strat- e gy substantially enhances the performance and reliability of po wer electronic con v erters, making it ideal for demanding applications such as electric v ehicles, rene w able ener gy systems, and high-performance po wer sup- plies. Samad et al. [11] introduced the control strate gies for boost and 2-phase IBC us ing MP ADRC that combines the adv antages of MPC and acti v e disturbance rejection control (ADRC). A proportional-inte gral based MPC adapti v e approach w as proposed for boost con v erters in [12], follo wed by the introduction of a composite adapti v e MPC method in [13], designed to address model mismatches a rising from parameter un- certainties and disturbances in DC-DC boost con v erter control designs. Furthermore, in [14], an inno v ati v e SMC coupled with a proportional inte gral (PI) controller w as implemented to re gulate a DC-DC boost con- v erter . Although the e xisting literature has laid some groundw ork, there remains significant uncharted territory , particularly concerning multiphase IBC. The rest of the article is or g anized as follo ws. In secti o n 2, we ha v e presented the mathemati cal modeling of a 2-phase IBC. In section 3, we present the control and design methodology . Section 4 is about the results and discussion of our w ork. Finally , we ha v e concluded the results in section 5. 2. MA THEMA TICAL MODELING OF A 2-PHASE INTERLEA VED BOOST CONVER TER Additionally , the distinct states that characterize a 2-phase IBC are depicted in Figures 2 to 5 each representing one of the four states as follo ws. In Figure 2 both switches Q1 and Q2 are on, while in Figure 3 Q1 is on and Q2 is of f. In addition, Q1 is on and Q2 is of f in Figure 4 and finally , Q1 and Q2 are of f in Figure 5. Indonesian J Elec Eng & Comp Sci, V ol. 36, No. 3, December 2024: 1421–1429 Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 r 1423 Figure 2. 2-phase interlea v ed DC/DC boost con v erter: Q1 and Q2 are on Figure 3. 2-phase interlea v ed DC/DC boost con v erter: Q1 is on and Q2 is of f Figure 4. 2-phase interlea v ed DC/DC boost con v erter: Q1 is on and Q2 is of f Figure 5. 2-phase interlea v ed DC/DC boost con v erter: Q1 and Q2 are of f Then using the basic rules of KCL and KVL and depending upon switch states, the current and v oltage equation of all states ha v e been formulated and for simplicity the only a v erage state space is modeled and presented as follo ws, while the matrices A 1 , A 2 , A 3 , A 4 and B of all four states respecti v ely are gi v en by , A 1 = 2 4 r L 1 L 1 0 0 0 r L 2 L 2 0 0 0 1 R 0 C 3 5 Advanced contr ol and optimization str ate gies for a 2-phase interleaved ... (Muhammad Adnan Samad) Evaluation Warning : The document was created with Spire.PDF for Python.
1424 r ISSN: 2502-4752 A 2 = 2 4 r L 1 L 1 0 0 0 r L 2 L 2 1 C 0 1 L 2 1 R 0 C 3 5 A 3 = 2 4 r L 1 L 1 r L 2 L 2 1 C 0 0 0 1 L 1 0 1 R 0 C 3 5 A 4 = 2 4 r L 1 L 1 0 1 C 0 r L 2 L 2 1 C 1 L 1 1 L 2 1 R 0 C 3 5 B = 1 L 1 1 L 2 0 0 0 0 Finally , a v eraging and combining the state space representation for all the states using, A = ( A 1 + A 3 ) d + ( A 2 + A 4 ) (1 d ) yeilds A = 2 4 r L 1 L 1 0 1 2 L 1 d r L 2 L 2 ( d 1) r L 2 L 2 ( d 1) 1 L 2 1 C (2 d + 1) 1 C 1 R 0 C 3 5 (1) B = 2 4 1 L 1 0 1 L 2 0 0 0 3 5 (2) where, v in is the input v oltage, d represent s the duty c ycle, r L1 and r L2 are the parasitic resistances of the inductors L 1 and L 2 respecti v ely , D 1 and D 2 are the diodes, while C is the capacitance and r c is the parasitic resistance of the capacitor , and R o is the load resistance. 3. CONTR OL AND DESIGN METHODOLOGY Controlling DC con v erters is particularly chal lenging due to their non-minimum phase beha vior [15]. Historically , methods such as proportional inte gral deri v ati v e (PID), h ysteresis control, v oltage control, and current control ha v e been emplo yed. Ho we v er , these techniques ha v e limitations, including dif ficulty han- dling non-linearities and lar ge disturbances, EMI issues, increased losses in high-frequenc y applications, slo w response to load changes, limitations in handling v arying input v oltages, comple x design, and e xcessi v e chat- tering. In contrast, the proposed method combines MPC and SMC to capitalize on the strengths of both ap- proaches while mitig ating their indi vidual weaknesses. The k e y adv antages of this inte grated control strate gy include enhanced rob ustness, reduced chattering, impro v ed transient response, superior capability in handling constraints, and increased o v erall stability . The amalg amation of MPC and SMC as depicted in Figure 6. The strate gic utilization of MPC in the outer loop, combined with SMC in the inner loop, underscores a sophisticated approach aimed at optimizing system performance. Central to this design, the outer MPC loop is responsible for the generation of a precise reference current. Meanwhile, operating in tandem, the inner SMC loop cautiously tracks the current to its designated reference point, finally arranging control techniques in a w ay to achie v e the best possible system performance. T o control a 2-phase IBC using MPC and SMC, the choice of using control techniques in the inner and outer loop depends on se v eral f actors, including control objecti v es, system dynamics, and computational requirements. This particul ar research uses MPC in the outer loop due to the inherent adv antages lik e handling multi v ariable control objecti v es and constraints ef fecti v ely , enabling the interlea v ed con v erters to operate in unison and producing the required system performance. Meanwhile, the characteristics lik e rob ust tracking Indonesian J Elec Eng & Comp Sci, V ol. 36, No. 3, December 2024: 1421–1429 Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 r 1425 and disturbance rejection, particularly in systems with uncertain dynamics or disturbances, mak e the SMC the best suitable choice to track the current in the inner loop. Before designing a controller an objecti v e function is required, in this particular case we took the current re gulation problem as a control problem formulated as, i L;er r ( ) = i L;r ef i L ( ) (3) The said objecti v e function can be optimized by minimizing the error as follo ws, minimize J ( ) ; (4) subject to the ma thematical model of a 2-phase IBC. Moreo v er , T able 1 sho ws the initial and tar get v alues of the parameters used in this research w ork. Figure 6. The proposed controller design T able 1. P arameters used and their v alues V ariable V alue Input v oltage 12 V Output v oltage 24 V Duty ratio 0.5 Switching frequenc y 20 kHz Load resistance 100 Inductance 50 mH Conductance 1 ; 000 F 3.1. Model pr edicti v e contr ol A finite-horizon and optimum control issue based on a process linear prediction model is solv ed by the standard MPC technique [16], [17]. Because of its simplicity in managing multi v ariable systems, ability to introduce input/output constraints, and user -friendly design process, MPC is becoming more and more popular in the field of po wer supply [18], [19]. Furthermore, the MPC is a highly ef fecti v e control method based on the receding horizon control concept [20], [21]. The basic steps included are depicted as a flo wchart in Figure 7. 3.2. Slide mode contr oller Gi v en its rob ustness and resilience, the SMC has emer ged as a dependable control technique for attaining desired system performance, e v en in the presence of uncertainties and disturbances for DC-DC boost con v erters [22]–[26]. As suggested, the SMC is incorporated into the inner loop, where the control signals are produced using the SMC la w , which adapti v ely modifies the duty c ycles of the switches in t he con v erter . As en visioned, the SMC can be seamlessly inte grated into each phase of the 2-phase interlea v ed con v erter , adeptly re gulating the inductor current and steadf astly maintaining it at the reference le v el, particularly within the inner loop. The control la w ensures that both phases operate in synchronization, maintaining balanced operation and minimizing output v oltage ripple. Advanced contr ol and optimization str ate gies for a 2-phase interleaved ... (Muhammad Adnan Samad) Evaluation Warning : The document was created with Spire.PDF for Python.
1426 r ISSN: 2502-4752 Figure 7. Flo w chart illustrating the process 4. RESUL TS AND DISCUSSION Due to the non-minimum phase beha vior , the control of these types of con v erters is al w ays challeng- ing. This particular research focuses on a no v el technique that combines the adv antages of MPC and SMC. The ef fecti v eness of the proposed technique is sho wn in Figure 8 as compared to the step response of a 2-phase IBC without an y controller in Figure 9. In addition, it is e vident from T able 2, which compares the step response parameters for both sce- narios, that the proposed controller significantly impro v es performance. Moreo v er , the limitations associated with the tw o-phase interlea v ed boost con v erter can be ef fecti v ely mitig ated by impl ementing additional stages of interlea ving i n future w ork. Finally , the pro v en results in this paper demonstrate the pro v en ef fecti v eness of adv anced control strate gies by inte grating MPC and SMC. Furt h e rmore, the ef fecti v eness of the proposed controller is also v erified by sho wing the response of the con v erter without and with controller in the presence of a disturbance as depicted in Figures 10 and 11. Figure 8. Step response using MPSMC controller Figure 9. Step response without controller T able 2. Comparison of step response parameters Step response parameter W ithout controller W ith proposed controller Rise time (seconds) 0.000554 0.0008 Settling time (seconds) 0.0171 0.0032 Percentage o v ershoot (%) 0.74 0.9200 Final v alue 1.67 0.9909 Indonesian J Elec Eng & Comp Sci, V ol. 36, No. 3, December 2024: 1421–1429 Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 r 1427 Figure 10. Disturbance as a square w a v e Figure 11. Disturbance as a unit step 5. CONCLUSION In this paper , we proposed a no v el method t hat combines the characteristics of MPC and SMC for the proper control of a 2-phase interlea v ed boost con v erter . 2-phase IBC is widely used in dif ferent applications because it can share current load between phases and ripple the output v oltage. Control strate gies for such con- v erters are, ho we v er , v ery challenging as the y ha v e non-minimum phase beha vior . The h ybrid control method we propose combines the predicti v e ability of MPC to predict future beha vior and optimize performance, with SMC that pro vides rob ust stability ag ainst uncertainty/disturbance. The results of our study demonstrate that the inte grated MPSMC approach ef fecti v ely mitig ates the control dif ficulties associated with the 2-phase IBC. This frame w ork inte grates inner -loop SMC and outer -loop MPC, sho wcasing the rob ustness and adaptability of the de vised control strate gy . The combined technique of fers an impro v ed dynamic response, impro v ed stabil- ity , and superior handling of parameter v ariations and e xternal disturbances compared to con v entional control methods. In conclusion, the proposed MPSMC technique represents a significant adv ancement in the control of int erlea v ed boost con v erters. Future w ork will focus on further optimization and v alidation of the proposed control strate gy in real-w orld applicat ions, ensuring its rob ustness and ef fecti v enes s in di v erse operational en- vironments. REFERENCES [1] D. J. S. Ne wlin, R. Ramalakshmi, and S. Rajasekara n, “ A performance comparison of interlea v ed boost con v erter and con v en- tional boost con v erter for rene w able ener gy application, ” in 2013 International Confer ence on Gr een High P erformance Computing (ICGHPC) , Mar . 2013, pp. 1–6, doi: 10.1109/ICGHPC.2013.6533924. [2] A. Thiyag arajan, S. G. Pra v een K umar , and A. Nandini, “ Analysis and comparison of con v entional and interlea v ed DC/DC boost con v erter , ” in Second International Confer ence on Curr ent T r ends In Engineering and T ec hnolo gy - ICCTET 2014 , Jul. 2014, pp. 198–205, doi: 10.1109/ICCTET .2014.6966287. [3] A. Alzahrani, G. De v araja n, S. Subra mani, I. V aira v asundaram, and C. U. Ogb uka, “ Analysis and v alidation of multi-de vice inter - lea v ed DC-DC boost con v erter for electric v ehicle appl ications, ” IET P ower Electr onics , v ol. 16, no. 9, pp. 1548–1557, Jul. 2023, doi: 10.1049/pel2.12494. [4] D. Ra vi, S. L. Shimi, B. M. Reddy , and P . Samuel, “ Analysis and modelling of tw o-phase interlea v ed DC to DC boost con v erter with lifting capacitor for fuel cell h ybrid electric v ehicle, ” in Applications of Computing , A utomation and W ir eless Systems in Electrical Engineering: Pr oceedings of MARC 2018 , 2019, v ol. 553, pp. 689–699, doi: 10.1007/978-981-13-6772-4 59. [5] N. Selv araju, P . Shanmugham, and S. Somkun, “T w o-phas e interlea v ed boost con v erter using coupled inductor for fuel cell applica- tions, ” Ener gy Pr ocedia , v ol. 138, pp. 199–204, 2017, doi: 10.1016/j.e gypro.2017.10.150. [6] M. Phattanasak et al. , “Study of tw o-phase interlea v ed boost con v erter using coupled inductors for a fuel cell, ” in 2013 10th Interna- tional Confer ence on Electrical Engineering/Electr onics, Computer , T elecommunications and Information T ec hnolo gy , May 2013, pp. 1–6, doi: 10.1109/ECTICon.2013.6559613. [7] P . Thounthong, P . Sethakul, S. Rael, and B. Da v at, “Design and implementation of 2-phase interlea v ed boost con v erter for fuel cell po wer source, ” in 4th IET International Confer ence on P ower Electr onics, Mac hines and Drives (PEMD 2008) , 2008, pp. 91–95, doi: 10.1049/cp:20080489. [8] Y .-J. Le e and A. Emadi, “Phase shift switching scheme for DC/DC boost con v erter with switches in parallel, ” in 2008 IEEE V ehicle P ower and Pr opulsion Confer ence , Sep. 2008, pp. 1–6, doi: 10.1109/VPPC.2008.4677615. [9] R. F . Muktiadji et al. , “Control of boost con v erter using observ er -based backstepping sliding mode control for DC microgrid, ” F r ontier s in Ener gy Resear c h , v ol. 10, p. 828978, Mar . 2022, doi: 10.3389/fenr g.2022.828978. Advanced contr ol and optimization str ate gies for a 2-phase interleaved ... (Muhammad Adnan Samad) Evaluation Warning : The document was created with Spire.PDF for Python.
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[25] N. Boujelben, M. Djemel, and N. Derbel, “ Analysis of a quadratic boost con v erter using sliding mode controller , ” in 2020 17th Inter - national Multi-Confer ence on Systems, Signals & De vices (SSD) , Jul. 2020, pp. 969–973, doi: 10.1109/SSD49366.2020.9364205. [26] C. S. Sachin and S. G. Nayak, “Design and simulation for sliding mode control in DC-DC boost con v erter , ” in 2017 2nd International Confer ence on Communication and Electr onics Systems (ICCES) , Oct. 2017, pp. 440–445, doi: 10.1109/CESYS.2017.8321317. BIOGRAPHIES OF A UTHORS Muhammad Adnan Samad recei v ed his BSEE and MSEE from P akistan in the year 2011 and 2015 respecti v ely . He is a Ph.D. scholar of Beijing Institute of T echnology , Beijing, China. His research interests include po wer electronics, DC-DC con v erters and their control, image and signal processing and optimization techniques especially MPC. He is w orking with the Electrical Engineering, Electrical Mechanics and Electrical T echnologies Department at the Fer g ana Polytech- nic Institute (FerPI), Fer g ana, Uz bekistan since No v ember , 2023. He can be contacted at email: samad.muhammad@ferpi.uz. Usmono v Shukurillo Y ulbarso vich is a head of Electrical Engineering, Electrical Me- chanics and Electrical T echnologies Department at the Fer g ana Polytechnic Institute (Fer PI), Fer - g ana, Uzbekistan. He recei v ed his B.Eng., M.Eng., and Ph.D. de grees in po wer supply of industrial enterprises, cities, and agriculture from Fer g ana Polytechnic Institute in 1988, 1991, and 2017, re- specti v ely . He has been an associate professor in FerPI, Fer g ana, Uzbekistan since 2018. His research interests include the field of ener gy audit, industrial applications, industrial electronics, industrial in- formatics, po wer electronics, motor dri v es, applications, engineering systems, artificial intelligence, intelligent control, and digital library . He can be contacted at email: shusmono v1976@gmail.com. Indonesian J Elec Eng & Comp Sci, V ol. 36, No. 3, December 2024: 1421–1429 Evaluation Warning : The document was created with Spire.PDF for Python.
Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 r 1429 Sultono v Ruzimatjon An v arjon Ugli is a lecturer in Electrical Engineering, Electrical Mechanics and Electrica l T echnologies Department at the Fer g ana Polytechnic Institute (FerPI), Fer - g ana, Uzbekistan since 2017; and he has been a senior lecturer since 2019. She recei v ed the B.Eng. De gree in Industrial Heat Ener gy and the M.Eng. de gree in industrial heat ener gy , Ph.D. de gree in electrical dri v ers from Fer g ana Polytechnic Institute (FerPI), Fer g ana, Uzbekistan in 2015, 2017, and 2023, respecti v ely . He w as an assi stant of the Department of Electr ical Engineering, Electri- cal Mechanics and Electric al T echnologies of Fer g ana Polytechnic Institute from 2017. He is good at MA TLAB programming language. His research interests i nclude the field of po wer electronics, motor dri v es, and industrial applications. He can be contacted at email: ruzimatjonsultono v@gmail.com. Saima Siddiqui is w orking as an associate professor in the Department of Mathemat- ics at the Fe r g a na Polytechnic Institute (FerPI), Fer g ana, Uzbekistan. She c ompleted her Ph.D. in Mathematics from Beijing Institute of T echnolgy in 2022. While her M.Phil, Master’ s and Bach- elor’ s de gree is from the Uni v ersity of the Punjab, Lahore, P akistan in the yea r 2011, 2008, 2006 respecti v ely . Her research interests are fourier transform, fractional fourier transform, linear canoci- cal transform, and quantum signal processing, especially in the field of signal and image processing. She can be contacted at email: saimasiddiqui07@gmail.com. Advanced contr ol and optimization str ate gies for a 2-phase interleaved ... (Muhammad Adnan Samad) Evaluation Warning : The document was created with Spire.PDF for Python.