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A new effective robust nonlinear controller based on PSO for interleaved DC–DC boost converters for fuel cell voltage regulation

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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.

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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

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Authors and Affiliations

  1. Department of Electrical Engineering, Faculty of Technology, University of Medea, Medea, Algeria

    Samir Abdelmalek

  2. Renewable Energy Development Center (CDER), Algiers, Algeria

    Ali Dali

  3. Department of Electrical Engineering, University of Sharjah, Sharjah, United Arab Emirates

    Maamar Bettayeb

  4. Center of Excellence in Intelligent Engineering Systems (CEIES), King Abdulaziz University, Jeddah, Kingdom of Saudi Arabia

    Maamar Bettayeb

  5. Department of Mathematics, University of Oslo, 0851, Oslo, Norway

    Azzeddine Bakdi

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  1. Samir Abdelmalek
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  2. Ali Dali
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Correspondence to Samir Abdelmalek.

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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

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