Stabilization of Second-Order Non-Minimum Phase System With Delay via PI Controllers: Spectral Abscissa Optimization
This paper addresses the stabilization of a general class of linear single-input/single-output (SISO) second-order non-minimum phase systems with input channel delays using Proportional-Integral (PI) controllers. Such systems arise in various applications, including power electronic circuits and bio...
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| Format: | Article |
| Language: | English |
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IEEE
2024-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10753585/ |
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| author | Diego Torres-Garcia Cesar-Fernando Mendez-Barrios Silviu-Iulian Niculescu |
| author_facet | Diego Torres-Garcia Cesar-Fernando Mendez-Barrios Silviu-Iulian Niculescu |
| author_sort | Diego Torres-Garcia |
| collection | DOAJ |
| description | This paper addresses the stabilization of a general class of linear single-input/single-output (SISO) second-order non-minimum phase systems with input channel delays using Proportional-Integral (PI) controllers. Such systems arise in various applications, including power electronic circuits and biochemical reactors. The primary goal is to enhance system performance by determining optimal control gains that shift the spectral abscissa of the closed-loop system as far to the left as possible, thereby improving its decay rate. To achieve this, we introduce a geometric framework that characterizes the stability region of the closed-loop system in three distinct cases. Our main contribution is a systematic tuning approach to achieve the desired decay rate when feasible. Additionally, we discuss the controller’s fragility and the delay margin of the closed-loop system to ensure practical applicability. The effectiveness of the proposed method is demonstrated through numerical simulations for each scenario. Finally, two practical case studies—a boiler steam drum and a DC-DC boost converter—are presented to illustrate the results’ relevance in practice. |
| format | Article |
| id | doaj-art-42ade0f006604441b4cef9ccdc96905b |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-42ade0f006604441b4cef9ccdc96905b2024-11-23T00:01:17ZengIEEEIEEE Access2169-35362024-01-011217085117086710.1109/ACCESS.2024.349974810753585Stabilization of Second-Order Non-Minimum Phase System With Delay via PI Controllers: Spectral Abscissa OptimizationDiego Torres-Garcia0https://orcid.org/0000-0003-3696-3450Cesar-Fernando Mendez-Barrios1https://orcid.org/0000-0002-1018-3192Silviu-Iulian Niculescu2Facultad de Ingeniería, Universidad Autónoma de San Luis Potosí (UASLP), San Luis Potosi, MexicoFacultad de Ingeniería, Universidad Autónoma de San Luis Potosí (UASLP), San Luis Potosi, MexicoCNRS, CentraleSupélec, Inria, Laboratoire des Signaux et Systèmes (L2S, UMR CNRS 8506), Université Paris-Saclay, Gif-sur-Yvette, FranceThis paper addresses the stabilization of a general class of linear single-input/single-output (SISO) second-order non-minimum phase systems with input channel delays using Proportional-Integral (PI) controllers. Such systems arise in various applications, including power electronic circuits and biochemical reactors. The primary goal is to enhance system performance by determining optimal control gains that shift the spectral abscissa of the closed-loop system as far to the left as possible, thereby improving its decay rate. To achieve this, we introduce a geometric framework that characterizes the stability region of the closed-loop system in three distinct cases. Our main contribution is a systematic tuning approach to achieve the desired decay rate when feasible. Additionally, we discuss the controller’s fragility and the delay margin of the closed-loop system to ensure practical applicability. The effectiveness of the proposed method is demonstrated through numerical simulations for each scenario. Finally, two practical case studies—a boiler steam drum and a DC-DC boost converter—are presented to illustrate the results’ relevance in practice.https://ieeexplore.ieee.org/document/10753585/Linear systemsnon-minimum phasePI controlquasi-polynomialsspectral abscissatime-delay |
| spellingShingle | Diego Torres-Garcia Cesar-Fernando Mendez-Barrios Silviu-Iulian Niculescu Stabilization of Second-Order Non-Minimum Phase System With Delay via PI Controllers: Spectral Abscissa Optimization IEEE Access Linear systems non-minimum phase PI control quasi-polynomials spectral abscissa time-delay |
| title | Stabilization of Second-Order Non-Minimum Phase System With Delay via PI Controllers: Spectral Abscissa Optimization |
| title_full | Stabilization of Second-Order Non-Minimum Phase System With Delay via PI Controllers: Spectral Abscissa Optimization |
| title_fullStr | Stabilization of Second-Order Non-Minimum Phase System With Delay via PI Controllers: Spectral Abscissa Optimization |
| title_full_unstemmed | Stabilization of Second-Order Non-Minimum Phase System With Delay via PI Controllers: Spectral Abscissa Optimization |
| title_short | Stabilization of Second-Order Non-Minimum Phase System With Delay via PI Controllers: Spectral Abscissa Optimization |
| title_sort | stabilization of second order non minimum phase system with delay via pi controllers spectral abscissa optimization |
| topic | Linear systems non-minimum phase PI control quasi-polynomials spectral abscissa time-delay |
| url | https://ieeexplore.ieee.org/document/10753585/ |
| work_keys_str_mv | AT diegotorresgarcia stabilizationofsecondordernonminimumphasesystemwithdelayviapicontrollersspectralabscissaoptimization AT cesarfernandomendezbarrios stabilizationofsecondordernonminimumphasesystemwithdelayviapicontrollersspectralabscissaoptimization AT silviuiulianniculescu stabilizationofsecondordernonminimumphasesystemwithdelayviapicontrollersspectralabscissaoptimization |