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Licensed Unlicensed Requires Authentication Published by De Gruyter March 30, 2019

Fractional Order PID Controller Design for Supply Manifold Pressure Control of Proton Exchange Membrane Fuel Cell

Srinivasarao Divi, Shantanu Das, G. Uday Bhaskar Babu and S.H. Sonawane

Abstract

In this work, fractional order PIλDµ (FOPID) controller designed to enhance the dynamic performance of the Proton Exchange Membrane (PEM) fuel cell. The control objective is to regulate the supply manifold pressure on cathode side to maintain oxygen excess ratio of the PEM fuel cell. The higher order PEM fuel cell model is approximated to First order plus time delay (FOPTD) model for controller design and analysis. The proposed FOPID controller is designed based on minimization of Integral Absolute Error (IAE) with pre specified maximum sensitivity (Ms) as a constraint. Uncertainty and measurement noise analysis is carried out to verify the robustness of the designed controller. The simulation results of proposed FOPID controller is compared with other designing methods. Based on minimization of IAE value, the SP 1.4 FOPID controller produces IAE value of 0.255 where as AMIGO 1.4 tuning method and ZN based FOPID tuning methods produces 0.263 and 3.817 respectively for perfect case. Based on maximum sensitivity Ms is 1.4, the SP 1.4 FOPID controller produces Ms of 1.4 where as AMIGO 1.4 PID and ZN based FOPID tuning methods produces Ms of 1.5 and 1.25 respectively for perfect case, which indicates that the proposed SP 1.4 FOPID controller is robust. The proposed SP 1.4 FOPID provides better values (rise time of 0.331 sec, settling time of 0.692 sec and percentage of peak overshoot of 0.797 for perfect case) when compared with other methods. From simulation results, for the control of supply manifold pressure of PEM fuel cell, the proposed fractional-order PID controllers improves the closed loop performance in terms of rise time, settling time and percentage of peak overshoot when compared to the integer-order PID controllers.

Appendix

A Model parameters and constants

Table 7:

Simulation Parameters of PEMFC system.

ParameterSymbolSI UnitsValue
Atmospheric pressurePatmPa101,325
Saturation pressurePsatPa3140.4
Average ambient air relative humidityatm0.5
Atmospheric temperatureTatmK298. 15
Air-specific heat ratioγ1. 4
Stack temperatureTstK353. 15
Specific heat of airCPJ/kg/K1004
Universal gas constantRJ/mol/K8. 31451
Molar mass of oxygenMO2kg/mol32×103
Molar mass of nitrogenMN2kg/mol28×103
Molar mass of vaporMvkg/mol18×103
Molar mass of airMa,atmkg/mol29×103
Faraday’s constantFC/mol96,485
Cathode volumeVcam30.01
Supply manifold volumeVsmm30. 02
Compressor motor mechanical efficiencyηcp%0.8
Compressor efficiencyηcm%0.98
Compressor and motor inertiaJcpN.m5×105
Compressor motor resistanceRcmohm0. 82
Motor constantKtNm/A0. 0153
Motor constantKvV/(rad/sec)0. 0153
Cathode inlet orifice constantKca,inkg/sec/Pa0.36×105
Cathode outlet throttle discharge co efficientCD0.0124
Cathode outlet throttle areaATm20.002
Number of cells in fuel cell stackn381
Oxygen mole fractionyO2,atm0.21

Table 8:

Constants of the PEMFC system model.

c1=RTstKca,inMO2VcaxO2,atm1+ωatmc7=RTstn4FVcac13=ηcmKtJcpRcm
c2=Psatc8=RTstKca,inMN2Vca1xO2,atm1+ωatmc14=RTatmγMa,atmVsm
c3=RTstVcac9=ηcmKtKvJcpRcmc15=1ηcp
c4=MO2c10=CpTatmJcpηcpc16=Kca_in
c5=MN2c11=Patmc17=CDATRTst2γγ1
c6=MvPsatc12=γ1γc18=1γ
xO2,atm=yO2,atmMO2Ma,atmωatm=MvMa,atmϕatmPsatPatmϕatmPsat

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Received: 2018-09-18
Revised: 2019-02-25
Accepted: 2019-03-17
Published Online: 2019-03-30

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