Abstract
Output voltage regulation of DC–DC converters has recently gained an increasing attention to face the many system nonidealities. The fast switching behavior is nonlinear time varying, the presence of model and measurement uncertainties, and large variations, are all inherited challenges. The aim of the present work is to design a robust nonlinear controller that ensures satisfactory and robust output voltage regulation for a proton-exchange membrane fuel cell (PEMFC) based on a DC–DC Interleaved Boost Converter (IBC). A state-space model of the DC–DC IBC is first derived using the state-space averaging technique, and a mathematical model is constructed for the PEFMC. In this regard, a robust nonlinear controller and a proportional integral controller are proposed. The controllers are tuned though particle swarm optimization algorithm to estimate their good parameters assuring the desired performance is met. The integral of absolute error criterion is used to improve the dynamic performance of the overall controlled system. Furthermore, the closed-loop stability is analyzed using the Lyapunov stability theorem, and the effectiveness of the closed-loop system is validated under various operating conditions of the PEMFC and load perturbations. Compared to other methods, the obtained results demonstrate a superior performance of the proposed control strategy in terms of its robustness to variations and uncertainties, smooth tracking of a varying set-point and faster transients.
Similar content being viewed by others
Abbreviations
- PEMFC:
-
Proton-exchange membrane fuel cell
- IBC:
-
Interleaved boost converter
- PI:
-
Proportional integral
- PSO:
-
Particle swarm optimization
- IAE:
-
Integral of absolute error
- FCs:
-
Fuel cells
- EVs:
-
Electric vehicles
- MPC:
-
Model predictive control
- LTI:
-
Linear time-invariant
- PSO-PIC:
-
PSO-tuned PI controller
- PSO-RNC:
-
PSO-tuned robust nonlinear controller
- \( V_{c} \) :
-
The output voltage
- \( V_{\text{fc}} \) :
-
The fuel cell source voltage
- L :
-
The inductance
- C :
-
The capacitance
- \( D_{1} ,D_{2} \) :
-
The duty cycles of each phase
- \( I_{{L_{1} }} ,I_{{L_{2} }} \) :
-
The inductors current
- \( I_{\text{fc}} \) :
-
The fuel cell current
- \( I_{\text{R}} \) :
-
The resistor load current
- \( I_{\text{c}} \) :
-
The capacitor current
- \( u \) :
-
The average duty cycle
- \( z \) :
-
Number of moving electrons (z = 2)
- \( E_{\text{n}} \) :
-
Nernst voltage (V)
- \( \alpha \) :
-
Charge transfer coefficient
- \( P_{{{\text{H}}2}} \) :
-
Partial pressure of hydrogen inside the stack (atm)
- \( P_{{{\text{O}}2}} \) :
-
Partial pressure of oxygen inside the stack (atm)
- k :
-
Boltzmann’s constant (1.38 × 10 − 23 J/K)
- h :
-
Planck’s constant (6.626 × 10 − 34 J s)
- ΔG:
-
Activation energy barrier (J)
- T :
-
Temperature of operation (K)
- \( Kc \) :
-
Voltage constant at nominal condition of operation
- \( P_{\text{fuel}} \) :
-
Absolute supply pressure of fuel (atm)
- \( P_{\text{air}} \) :
-
Absolute supply pressure of air (atm)
- \( V_{\text{fuel}} \) :
-
Fuel flow rate (l/min)
- \( V_{\text{air}} \) :
-
Air flow rate (l/min)
- \( P_{{{\text{H}}_{2} {\text{O}}}} \) :
-
Partial pressure of water vapor (atm)
- \( w \) :
-
Percentage of water vapor in the oxidant (%)
- \( E \) :
-
The controlled voltage source
- \( E_{\text{oc}} \) :
-
Open circuit voltage (V)
- \( N \) :
-
Number of cells
- \( A_{f} \) :
-
Tafel slope (V)
- \( i_{0} \) :
-
Exchange current (A)
- \( T_{d} \) :
-
The response time (at 95% of the final value)
- \( R_{\text{ohm}} \) :
-
Internal resistance (Ω)
- \( i_{\text{fc}} \) :
-
Fuel cell current (A)
- \( V_{\text{fc}} \) :
-
Fuel cell voltage (V)
- \( x_{h} \) :
-
Percentage of hydrogen in the fuel (%)
- \( y_{h} \) :
-
Percentage of oxygen in the oxidant (%)
- \( V_{\text{cref}} \) :
-
Desired voltage
- \( I_{\text{fcd}} \) :
-
Desired fuel cell current
- \( k_{1} , k_{2} ,k_{3} \) :
-
Parameters of the proposed controller
- \( K_{p} ,K_{i} \) :
-
Parameters of the PI controller
- \( t \) :
-
The iteration number
- \( j \) :
-
The particle number
- \( p_{j} \) :
-
The individual best solution of particle \( j \) at a given stage
- \( p_{g} \) :
-
The global best solution
- \( C_{1} ,C_{2} \) :
-
The acceleration parameters
- \( r_{1} ,r_{2} \) :
-
Random numbers uniformly distributed
References
Abbaspour A, Khalilnejad A, Chen Z (2016) Robust adaptive neural network control for PEM fuel cell. Int J Hydrogen Energy 41(44):20385–20395
Abdelmalek S, Barazane L, Larabi A, Bettayeb M (2016) A novel scheme for current sensor faults diagnosis in the stator of a DFIG described by a TS fuzzy model. Measurement 91:680–691
Abdelmalek S, Barazane L, Larabi A (2017) An advanced robust fault-tolerant tracking control for a doubly fed induction generator with actuator faults. Turk J Electr Eng Comput Sci 25(2):1346–1357
Abdelmalek S, Azar AT, Dib D (2018a) A novel actuator fault-tolerant control strategy of DFIG-based wind turbines using Takagi–Sugeno multiple models. Int J Control Autom Syst 16(3):1415–1424
Abdelmalek S, Dali A, Bettayeb M (2018b) An improved observer-based integral state feedback (OISF) control strategy of flyback converter for photovoltaic systems. In: 2018 international conference on electrical sciences and technologies in Maghreb (CISTEM). IEEE, pp 1–6
Bakdi A, Bounoua W, Mekhilef S, Halabi LM (2019a) Nonparametric Kullback-divergence-PCA for intelligent mismatch detection and power quality monitoring in grid-connected rooftop PV. Energy 189:116366. https://doi.org/10.1016/j.energy.2019.116366
Bakdi A, Kouadri A, Mekhilef S (2019b) A data-driven algorithm for online detection of component and system faults in modern wind turbines at different operating zones. Renew Sustain Energy Rev 103:546–555
Bankupalli PT, Ghosh S, Kumar L, Samanta S (2018) Fractional order modeling and two loop control of PEM fuel cell for voltage regulation considering both source and load perturbations. Int J Hydrogen Energy 43(12):6294–6309
Barhoumi E, Ben Belgacem I, Khiareddine A, Zghaibeh M, Tlili I (2018) A neural network-based four phases interleaved boost converter for fuel cell system applications. Energies 11(12):3423
Bendoukha S, Abdelmalek S, Abdelmalek S (2018) A new combined actuator fault estimation and accommodation for linear parameter varying system subject to simultaneous and multiple faults: an LMIs approach. Soft Comput 23(20):10449–10462
Choe SY, Lee JG, Ahn JW, Baek SH (2007) Integrated modeling and control of a PEM fuel cell power system with a PWM DC/DC converter. J Power Sources 164(2):614–623
Dali A, Bouharchouche A, Diaf S (2015) Parameter identification of photovoltaic cell/module using genetic algorithm (GA) and particle swarm optimization (PSO). In: 2015 3rd international conference on control, engineering & information technology (CEIT). IEEE, pp 1–6
Dali A, Abdelmalek S, Bettayeb M (2018) A new combined observer-state feedback (COSF) controller of PWM buck converter. In: 2018 international conference on electrical sciences and technologies in Maghreb (CISTEM). IEEE, pp 1–6
Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: MHS’95. Proceedings of the sixth international symposium on micro machine and human science. IEEE, pp 39–43
El-Hay EA, El-Hameed MA, El-Fergany AA (2018) Improved performance of PEM fuel cells stack feeding switched reluctance motor using multi-objective dragonfly optimizer. Neural Comput Appl 31(11):6909–6924
Fernandes D, Almeida R, Guedes T, Sguarezi Filho AJ, Costa FF (2017) State feedback control for DC-photovoltaic systems. Electr Power Syst Res 143:794–801
Grötsch M, Mangold M, Kienle A (2009) Analysis of the coupling behavior of PEM fuel cells and DC–DC converters. Energies 2(1):71–96
Guilbert D, Gaillard A, N’Diaye A, Djerdir A (2016) Power switch failures tolerance and remedial strategies of a 4-leg floating interleaved DC/DC boost converter for photovoltaic/fuel cell applications. Renew Energy 90:14–27
Guilbert D, Collura SM, Scipioni A (2017) DC/DC converter topologies for electrolyzers: State-of-the-art and remaining key issues. Int J Hydrogen Energy 42(38):23966–23985
Habib M, Khoucha F, Harrag A (2017) GA-based robust LQR controller for interleaved boost DC–DC converter improving fuel cell voltage regulation. Electr Power Syst Res 152:438–456
Hossain MZ, Rahim NA (2018) Recent progress and development on power DC–DC converter topology, control, design and applications: a review. Renew Sustain Energy Rev 81:205–230
İnci M, Türksoy Ö (2019) Review of fuel cells to grid interface: configurations, technical challenges and trends. J Clean Prod 213:1353–1370
Kirubakaran A, Jain S, Nema RK (2009) The PEM fuel cell system with DC/DC boost converter: design, modeling and simulation. Int J Recent Trends Eng 1(3):157
Kolli A, Gaillard A, De Bernardinis A, Bethoux O, Hissel D, Khatir Z (2015) A review on DC/DC converter architectures for power fuel cell applications. Energy Convers Manag 105:716–730
Komathi C, Gopinath UM (2018) Analysis and design of genetic algorithm-based cascade control strategy for improving the dynamic performance of interleaved DC–DC SEPIC PFC converter. Neural Comput Appl 32:5033–5047
Li Q, Chen W, Wang Y, Liu S, Jia J (2011) Parameter identification for PEM fuel-cell mechanism model based on effective informed adaptive particle swarm optimization. IEEE Trans Ind Electron 58(6):2410–2419
Navarro-López EM, Cortés D, Castro C (2009) Design of practical sliding-mode controllers with constant switching frequency for power converters. Electr Power Syst Res 79(5):796–802
Ogungbemi E, Ijaodola O, Khatib FN, Wilberforce T, El Hassan Z, Thompson J, Ramadan M, Olabi AG (2019) Fuel cell membranes—pros and cons. Energy. https://doi.org/10.1016/j.energy.2019.01.034
Oshaba AS, Ali ES, Elazim SA (2017) PI controller design via ABC algorithm for MPPT of PV system supplying DC motor–pump load. Electr Eng 99(2):505–518
Ramakumar R, Chiradeja P (2004) Distributed generation and renewable energy systems. In: IECEC’02. 2002 37th intersociety energy conversion engineering conference, 2002. IEEE, pp 716–724
Reddy KJ, Natarajan S (2018) Energy sources and multi-input DC-DC converters used in hybrid electric vehicle applications—a review. Int J Hydrogen Energy 43(36):17387–17408
Rezazi S, Hanini S, Si-Moussa C, Abdelmalek S (2016) Modeling and optimization of the operating conditions of Marrubium vulgare L. essential oil extraction process: Kinetic parameters estimation through genetic algorithms. J Essent Oil Bear Plants 19(4):843–853
Romero A, Martínez-Salamero L, Valderrama H, Pallás O, Alarcón E (1998) General purpose sliding-mode controller for bidirectional switching converters. In: ISCAS’98. Proceedings of the 1998 IEEE international symposium on circuits and systems (Cat. No. 98CH36187), vol 6. IEEE, pp 466–469
Sedraoui M, Abdelmalek S, Gherbi S (2011) Multivariable generalized predictive control using an improved particle swarm optimization algorithm. Informatica 35(3):363–374
Somkun S, Sirisamphanwong C, Sukchai S (2015) A DSP-based interleaved boost DC–DC converter for fuel cell applications. Int J Hydrogen Energy 40(19):6391–6404
Su JT, Liu DM, Liu CW, Hung CW (2009) An adaptive control method for two-phase DC/DC converter. In: 2009 international conference on power electronics and drive systems (PEDS). IEEE, pp 288–293
Subasi A, Kevric J, Canbaz MA (2017) Epileptic seizure detection using hybrid machine learning methods. Neural Comput Appl 31(1):317–325
Tremblay O, Dessaint LA (2009) A generic fuel cell model for the simulation of fuel cell vehicles. In: 2009 IEEE vehicle power and propulsion conference. IEEE, pp 1722–1729
Wang CM, Lin CH, Hsu SY, Lu CM, Li JC (2014) Analysis, design and performance of a zero-current-switching pulse–width–modulation interleaved boost DC/DC converter. IET Power Electron 7(9):2437–2445
Wang WY, Ding YH, Ke X, Ma X (2017) Sliding mode control of direct coupled interleaved boost converter for fuel cell. In: IOP conference series: earth and environmental science, vol 100, no 1. IOP Publishing, p 012170
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Communicated by V. Loia.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Abdelmalek, S., Dali, A., Bettayeb, M. et al. A new effective robust nonlinear controller based on PSO for interleaved DC–DC boost converters for fuel cell voltage regulation. Soft Comput 24, 17051–17064 (2020). https://doi.org/10.1007/s00500-020-04996-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-020-04996-4