Fast Model Predictive Control of PEM Fuel Cell System Using the L<sub>1</sub> Norm
This work describes the development of a fast Model Predictive Control (MPC) algorithm for a Proton Exchange Membrane (PEM) fuel cell. The MPC cost-function used considers the sum of absolute values of predicted control errors (the L<inline-formula><math xmlns="http://www.w3.org/1998/M...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-07-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/15/14/5157 |
| _version_ | 1797433589988589568 |
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| author | Robert Nebeluk Maciej Ławryńczuk |
| author_facet | Robert Nebeluk Maciej Ławryńczuk |
| author_sort | Robert Nebeluk |
| collection | DOAJ |
| description | This work describes the development of a fast Model Predictive Control (MPC) algorithm for a Proton Exchange Membrane (PEM) fuel cell. The MPC cost-function used considers the sum of absolute values of predicted control errors (the L<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>1</mn></msub></semantics></math></inline-formula> norm). Unlike previous approaches to nonlinear MPC-L<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>1</mn></msub></semantics></math></inline-formula>, in which quite complicated neural approximators have been used, two analytical approximators of the absolute value function are utilised. An advanced trajectory linearisation is performed on-line. As a result, an easy-to-solve quadratic optimisation task is derived. All implementation details of the discussed algorithm are detailed for two considered approximators. Furthermore, the algorithm is thoroughly compared with the classical MPC-L<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> method in which the sum of squared predicted control errors is minimised. A multi-criteria control quality assessment is performed as the MPC-L<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>1</mn></msub></semantics></math></inline-formula> and MPC-L<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> algorithms are compared using four control quality indicators. It is shown that the presented MPC-L<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>1</mn></msub></semantics></math></inline-formula> scheme gives better results for the PEM. |
| first_indexed | 2024-03-09T10:19:09Z |
| format | Article |
| id | doaj.art-452c6420ec8c4e39a4cda0623268c664 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-09T10:19:09Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-452c6420ec8c4e39a4cda0623268c6642023-12-01T22:07:16ZengMDPI AGEnergies1996-10732022-07-011514515710.3390/en15145157Fast Model Predictive Control of PEM Fuel Cell System Using the L<sub>1</sub> NormRobert Nebeluk0Maciej Ławryńczuk1Institute of Control and Computation Engineering, Faculty of Electronics and Information Technology, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warsaw, PolandInstitute of Control and Computation Engineering, Faculty of Electronics and Information Technology, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warsaw, PolandThis work describes the development of a fast Model Predictive Control (MPC) algorithm for a Proton Exchange Membrane (PEM) fuel cell. The MPC cost-function used considers the sum of absolute values of predicted control errors (the L<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>1</mn></msub></semantics></math></inline-formula> norm). Unlike previous approaches to nonlinear MPC-L<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>1</mn></msub></semantics></math></inline-formula>, in which quite complicated neural approximators have been used, two analytical approximators of the absolute value function are utilised. An advanced trajectory linearisation is performed on-line. As a result, an easy-to-solve quadratic optimisation task is derived. All implementation details of the discussed algorithm are detailed for two considered approximators. Furthermore, the algorithm is thoroughly compared with the classical MPC-L<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> method in which the sum of squared predicted control errors is minimised. A multi-criteria control quality assessment is performed as the MPC-L<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>1</mn></msub></semantics></math></inline-formula> and MPC-L<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula> algorithms are compared using four control quality indicators. It is shown that the presented MPC-L<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>1</mn></msub></semantics></math></inline-formula> scheme gives better results for the PEM.https://www.mdpi.com/1996-1073/15/14/5157proton exchange membrane fuel cellmodel predictive controloptimisationL1 cost function |
| spellingShingle | Robert Nebeluk Maciej Ławryńczuk Fast Model Predictive Control of PEM Fuel Cell System Using the L<sub>1</sub> Norm Energies proton exchange membrane fuel cell model predictive control optimisation L1 cost function |
| title | Fast Model Predictive Control of PEM Fuel Cell System Using the L<sub>1</sub> Norm |
| title_full | Fast Model Predictive Control of PEM Fuel Cell System Using the L<sub>1</sub> Norm |
| title_fullStr | Fast Model Predictive Control of PEM Fuel Cell System Using the L<sub>1</sub> Norm |
| title_full_unstemmed | Fast Model Predictive Control of PEM Fuel Cell System Using the L<sub>1</sub> Norm |
| title_short | Fast Model Predictive Control of PEM Fuel Cell System Using the L<sub>1</sub> Norm |
| title_sort | fast model predictive control of pem fuel cell system using the l sub 1 sub norm |
| topic | proton exchange membrane fuel cell model predictive control optimisation L1 cost function |
| url | https://www.mdpi.com/1996-1073/15/14/5157 |
| work_keys_str_mv | AT robertnebeluk fastmodelpredictivecontrolofpemfuelcellsystemusingthelsub1subnorm AT maciejławrynczuk fastmodelpredictivecontrolofpemfuelcellsystemusingthelsub1subnorm |