Variable Time Step Algorithm for Transient Response Analysis for Control and Optimization
This work considers an optimization problem based on step response characteristics. We lay a foundation for it by designing a rapid transient response analysis algorithm with variable time steps. This method applies to linear ordinary differential equations with real order. Numerical tests of the al...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-11-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/12/710 |
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| _version_ | 1846104590315945984 |
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| author | Igor Reznichenko Primož Podržaj Aljoša Peperko |
| author_facet | Igor Reznichenko Primož Podržaj Aljoša Peperko |
| author_sort | Igor Reznichenko |
| collection | DOAJ |
| description | This work considers an optimization problem based on step response characteristics. We lay a foundation for it by designing a rapid transient response analysis algorithm with variable time steps. This method applies to linear ordinary differential equations with real order. Numerical tests of the algorithm in the integer case show significant improvement even for higher order systems. This suggests a new method for acquiring step response characteristics for the fractional order case for which we have constructed an explicit expression of the inverse Laplace transform. |
| format | Article |
| id | doaj-art-bad0eb8bbf6949a58588604da83671f6 |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-bad0eb8bbf6949a58588604da83671f62024-12-27T14:27:04ZengMDPI AGFractal and Fractional2504-31102024-11-0181271010.3390/fractalfract8120710Variable Time Step Algorithm for Transient Response Analysis for Control and OptimizationIgor Reznichenko0Primož Podržaj1Aljoša Peperko2Faculty of Mechanical Engineering, University of Ljubljana, 1000 Ljubljana, SloveniaFaculty of Mechanical Engineering, University of Ljubljana, 1000 Ljubljana, SloveniaFaculty of Mechanical Engineering, University of Ljubljana, 1000 Ljubljana, SloveniaThis work considers an optimization problem based on step response characteristics. We lay a foundation for it by designing a rapid transient response analysis algorithm with variable time steps. This method applies to linear ordinary differential equations with real order. Numerical tests of the algorithm in the integer case show significant improvement even for higher order systems. This suggests a new method for acquiring step response characteristics for the fractional order case for which we have constructed an explicit expression of the inverse Laplace transform.https://www.mdpi.com/2504-3110/8/12/710control theoryalgorithmsstep response analysisfractional order systemsinverse Laplace transform |
| spellingShingle | Igor Reznichenko Primož Podržaj Aljoša Peperko Variable Time Step Algorithm for Transient Response Analysis for Control and Optimization Fractal and Fractional control theory algorithms step response analysis fractional order systems inverse Laplace transform |
| title | Variable Time Step Algorithm for Transient Response Analysis for Control and Optimization |
| title_full | Variable Time Step Algorithm for Transient Response Analysis for Control and Optimization |
| title_fullStr | Variable Time Step Algorithm for Transient Response Analysis for Control and Optimization |
| title_full_unstemmed | Variable Time Step Algorithm for Transient Response Analysis for Control and Optimization |
| title_short | Variable Time Step Algorithm for Transient Response Analysis for Control and Optimization |
| title_sort | variable time step algorithm for transient response analysis for control and optimization |
| topic | control theory algorithms step response analysis fractional order systems inverse Laplace transform |
| url | https://www.mdpi.com/2504-3110/8/12/710 |
| work_keys_str_mv | AT igorreznichenko variabletimestepalgorithmfortransientresponseanalysisforcontrolandoptimization AT primozpodrzaj variabletimestepalgorithmfortransientresponseanalysisforcontrolandoptimization AT aljosapeperko variabletimestepalgorithmfortransientresponseanalysisforcontrolandoptimization |