Fractional Order PID Controller Design for Supply Manifold Pressure Control of Proton Exchange Membrane Fuel Cell
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Srinivasarao Divi
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
Simulation Parameters of PEMFC system.
| Parameter | Symbol | SI Units | Value |
|---|---|---|---|
| Atmospheric pressure | Pa | 101,325 | |
| Saturation pressure | Pa | 3140.4 | |
| Average ambient air relative humidity | – | 0.5 | |
| Atmospheric temperature | K | 298. 15 | |
| Air-specific heat ratio | – | 1. 4 | |
| Stack temperature | K | 353. 15 | |
| Specific heat of air | J/kg/K | 1004 | |
| Universal gas constant | J/mol/K | 8. 31451 | |
| Molar mass of oxygen | kg/mol | ||
| Molar mass of nitrogen | kg/mol | ||
| Molar mass of vapor | kg/mol | ||
| Molar mass of air | kg/mol | ||
| Faraday’s constant | C/mol | 96,485 | |
| Cathode volume | m3 | 0.01 | |
| Supply manifold volume | m3 | 0. 02 | |
| Compressor motor mechanical efficiency | % | 0.8 | |
| Compressor efficiency | % | 0.98 | |
| Compressor and motor inertia | N.m | ||
| Compressor motor resistance | ohm | 0. 82 | |
| Motor constant | Nm/A | 0. 0153 | |
| Motor constant | V/(rad/sec) | 0. 0153 | |
| Cathode inlet orifice constant | kg/sec/Pa | ||
| Cathode outlet throttle discharge co efficient | — | 0.0124 | |
| Cathode outlet throttle area | m2 | 0.002 | |
| Number of cells in fuel cell stack | — | 381 | |
| Oxygen mole fraction | — | 0.21 |
Constants of the PEMFC system model.
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- Computational Fluid Dynamics Studies of Gas-Solid Flows in a Horizontal Pipe, Subjected to an Adiabatic Wall, Using a Variable Gas Properties Eulerian Model
- Enhanced PID Controller for Non-Minimum Phase Second Order Plus Time Delay System
- Fractional Order PID Controller Design for Supply Manifold Pressure Control of Proton Exchange Membrane Fuel Cell
Articles in the same Issue
- Research Articles
- A Simplified One-Dimensional Mathematical Model to Study the Transient Thermal Behavior of an Oxidation Catalyst with Both Low and High Levels of CO Concentration at the Inlet
- Control of Integrating Process with Time Delay
- Moisture Content and Oil Uptake Variations and Modeling in Deep-Fried Hamburger Slices
- Modelling of Thermodynamic Pressure – Composition – Temperature Relationships in the Systems of Metallic Hydride Forming Materials with Gaseous Hydrogen Using C++ Software
- CFD Investigation of Al2O3 Nanoparticles Effect on Heat Transfer Enhancement of Newtonian and Non-Newtonian Fluids in a Helical Coil
- Computational Fluid Dynamics Studies of Gas-Solid Flows in a Horizontal Pipe, Subjected to an Adiabatic Wall, Using a Variable Gas Properties Eulerian Model
- Enhanced PID Controller for Non-Minimum Phase Second Order Plus Time Delay System
- Fractional Order PID Controller Design for Supply Manifold Pressure Control of Proton Exchange Membrane Fuel Cell
