Error-Based Switched Fractional Order Model Reference Adaptive Control for MIMO Linear Time Invariant Systems
This paper presents the design and analysis of Switched Fractional Order Model Reference Adaptive Controllers (SFOMRAC) for Multiple Input Multiple Output (MIMO) linear systems with unknown parameters. The proposed controller uses adaptive laws whose derivation order switches between a fractional or...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/2/109 |
| _version_ | 1797298197917335552 |
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| author | Norelys Aguila-Camacho Javier A. Gallegos |
| author_facet | Norelys Aguila-Camacho Javier A. Gallegos |
| author_sort | Norelys Aguila-Camacho |
| collection | DOAJ |
| description | This paper presents the design and analysis of Switched Fractional Order Model Reference Adaptive Controllers (SFOMRAC) for Multiple Input Multiple Output (MIMO) linear systems with unknown parameters. The proposed controller uses adaptive laws whose derivation order switches between a fractional order and the integer order, according to a certain level of control error. The switching aims to use fractional orders when the control error is larger to improve transient response and system performance during large disturbed states, and to obtain smoother control signals, leading to a better control energy usage. Then, it switches to the integer order when the control error is smaller to improve steady state. Boundedness of all the signals in the scheme is analytically proved, as well as convergence of the control error to zero. Moreover, these properties are extended to the case when system states are affected by a bounded non-parametric disturbance. Simulation studies are carried out using different representative plants to be controlled, showing that fractional orders and switching error levels can be found in most of the cases, such as when SFOMRAC achieves a better balance among control energy and system performance than the non-switched equivalent strategies. |
| first_indexed | 2024-03-07T22:31:34Z |
| format | Article |
| id | doaj.art-50122429e5fc46bfbdb239e2534d9af3 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-07T22:31:34Z |
| publishDate | 2024-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-50122429e5fc46bfbdb239e2534d9af32024-02-23T15:17:14ZengMDPI AGFractal and Fractional2504-31102024-02-018210910.3390/fractalfract8020109Error-Based Switched Fractional Order Model Reference Adaptive Control for MIMO Linear Time Invariant SystemsNorelys Aguila-Camacho0Javier A. Gallegos1Department of Electricity, Universidad Tecnológica Metropolitana, Av. José Pedro Alessandri 1242, Santiago 7800002, ChileDepartment of Electrical Engineering, Pontificia Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Santiago 7820436, ChileThis paper presents the design and analysis of Switched Fractional Order Model Reference Adaptive Controllers (SFOMRAC) for Multiple Input Multiple Output (MIMO) linear systems with unknown parameters. The proposed controller uses adaptive laws whose derivation order switches between a fractional order and the integer order, according to a certain level of control error. The switching aims to use fractional orders when the control error is larger to improve transient response and system performance during large disturbed states, and to obtain smoother control signals, leading to a better control energy usage. Then, it switches to the integer order when the control error is smaller to improve steady state. Boundedness of all the signals in the scheme is analytically proved, as well as convergence of the control error to zero. Moreover, these properties are extended to the case when system states are affected by a bounded non-parametric disturbance. Simulation studies are carried out using different representative plants to be controlled, showing that fractional orders and switching error levels can be found in most of the cases, such as when SFOMRAC achieves a better balance among control energy and system performance than the non-switched equivalent strategies.https://www.mdpi.com/2504-3110/8/2/109fractional calculusswitched controllerfractional order adaptive controlmultivariable linear time invariant systemscontrol energy |
| spellingShingle | Norelys Aguila-Camacho Javier A. Gallegos Error-Based Switched Fractional Order Model Reference Adaptive Control for MIMO Linear Time Invariant Systems Fractal and Fractional fractional calculus switched controller fractional order adaptive control multivariable linear time invariant systems control energy |
| title | Error-Based Switched Fractional Order Model Reference Adaptive Control for MIMO Linear Time Invariant Systems |
| title_full | Error-Based Switched Fractional Order Model Reference Adaptive Control for MIMO Linear Time Invariant Systems |
| title_fullStr | Error-Based Switched Fractional Order Model Reference Adaptive Control for MIMO Linear Time Invariant Systems |
| title_full_unstemmed | Error-Based Switched Fractional Order Model Reference Adaptive Control for MIMO Linear Time Invariant Systems |
| title_short | Error-Based Switched Fractional Order Model Reference Adaptive Control for MIMO Linear Time Invariant Systems |
| title_sort | error based switched fractional order model reference adaptive control for mimo linear time invariant systems |
| topic | fractional calculus switched controller fractional order adaptive control multivariable linear time invariant systems control energy |
| url | https://www.mdpi.com/2504-3110/8/2/109 |
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