Robust <i>H</i><sub>∞</sub> Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions
In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-03-01
|
| Series: | Mathematical and Computational Applications |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2297-8747/26/1/21 |
| _version_ | 1797415205942067200 |
|---|---|
| author | Ahmad Taher Azar Fernando E. Serrano Nashwa Ahmad Kamal |
| author_facet | Ahmad Taher Azar Fernando E. Serrano Nashwa Ahmad Kamal |
| author_sort | Ahmad Taher Azar |
| collection | DOAJ |
| description | In this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have a double periodicity. The gain and phase margins of the closed-loop system can be selected appropriately with this new loop shaping design procedure. The loop shaping design methodology consists of implementing suitable filters to obtain a desired frequency response of the closed-loop system by selecting appropriate poles and zeros by the Abel theorem that are fundamental in the theory of the elliptic functions. The elliptic function properties are implemented to facilitate the loop shaping controller design along with their fundamental background and contributions from the complex analysis that are very useful in the automatic control field. Finally, apart from the filter design, a PID controller loop shaping synthesis is proposed implementing a similar design procedure as the first part of this study. |
| first_indexed | 2024-03-09T05:45:23Z |
| format | Article |
| id | doaj.art-bbf530cfc1f04e5ca6e644702dd028ef |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-09T05:45:23Z |
| publishDate | 2021-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-bbf530cfc1f04e5ca6e644702dd028ef2023-12-03T12:22:02ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472021-03-012612110.3390/mca26010021Robust <i>H</i><sub>∞</sub> Loop Shaping Controller Synthesis for SISO Systems by Complex Modular FunctionsAhmad Taher Azar0Fernando E. Serrano1Nashwa Ahmad Kamal2College of Computer & Information Sciences, Prince Sultan University, Riyadh 12435, Saudi ArabiaFaculty of Engineering and Architecture, Universidad Tecnológica Centroamericana (UNITEC), Zona Jacaleapa, Tegucigalpa, HondurasFaculty of Engineering, Cairo University, Giza 12613, EgyptIn this paper, a loop shaping controller design methodology for single input and a single output (SISO) system is proposed. The theoretical background for this approach is based on complex elliptic functions which allow a flexible design of a SISO controller considering that elliptic functions have a double periodicity. The gain and phase margins of the closed-loop system can be selected appropriately with this new loop shaping design procedure. The loop shaping design methodology consists of implementing suitable filters to obtain a desired frequency response of the closed-loop system by selecting appropriate poles and zeros by the Abel theorem that are fundamental in the theory of the elliptic functions. The elliptic function properties are implemented to facilitate the loop shaping controller design along with their fundamental background and contributions from the complex analysis that are very useful in the automatic control field. Finally, apart from the filter design, a PID controller loop shaping synthesis is proposed implementing a similar design procedure as the first part of this study.https://www.mdpi.com/2297-8747/26/1/21<i>H</i>∞ loop shaping controlmodular functionsSISO systemsPID controller |
| spellingShingle | Ahmad Taher Azar Fernando E. Serrano Nashwa Ahmad Kamal Robust <i>H</i><sub>∞</sub> Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions Mathematical and Computational Applications <i>H</i>∞ loop shaping control modular functions SISO systems PID controller |
| title | Robust <i>H</i><sub>∞</sub> Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions |
| title_full | Robust <i>H</i><sub>∞</sub> Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions |
| title_fullStr | Robust <i>H</i><sub>∞</sub> Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions |
| title_full_unstemmed | Robust <i>H</i><sub>∞</sub> Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions |
| title_short | Robust <i>H</i><sub>∞</sub> Loop Shaping Controller Synthesis for SISO Systems by Complex Modular Functions |
| title_sort | robust i h i sub ∞ sub loop shaping controller synthesis for siso systems by complex modular functions |
| topic | <i>H</i>∞ loop shaping control modular functions SISO systems PID controller |
| url | https://www.mdpi.com/2297-8747/26/1/21 |
| work_keys_str_mv | AT ahmadtaherazar robustihisubsubloopshapingcontrollersynthesisforsisosystemsbycomplexmodularfunctions AT fernandoeserrano robustihisubsubloopshapingcontrollersynthesisforsisosystemsbycomplexmodularfunctions AT nashwaahmadkamal robustihisubsubloopshapingcontrollersynthesisforsisosystemsbycomplexmodularfunctions |