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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Main Authors: Diego Torres-Garcia, Cesar-Fernando Mendez-Barrios, Silviu-Iulian Niculescu
Format: Article
Language:English
Published: IEEE 2024-01-01
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.
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institution Kabale University
issn 2169-3536
language English
publishDate 2024-01-01
publisher IEEE
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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