Fractional Control of a Class of Underdamped Fractional Systems with Time Delay—Application to a Teleoperated Robot with a Flexible Link
This work addresses the robust control of processes of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mrow><mo>(</mo><mi>s</mi><mo>)<...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-08-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/9/646 |
| _version_ | 1797580056920326144 |
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| author | Saddam Gharab Vicente Feliu Batlle |
| author_facet | Saddam Gharab Vicente Feliu Batlle |
| author_sort | Saddam Gharab |
| collection | DOAJ |
| description | This work addresses the robust control of processes of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>=</mo><mi>K</mi><mo>·</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>τ</mi><mo>·</mo><mi>s</mi></mrow></msup><mo>/</mo><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>T</mi><mo>·</mo><msup><mi>s</mi><mi>λ</mi></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>λ</mi><mo>≤</mo><mn>2</mn></mrow></semantics></math></inline-formula>. A new method for tuning fractional-order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>I</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>D</mi></mrow></semantics></math></inline-formula> controllers is developed. The stability is assessed based on the frequency domain tuning of the regulators to control such delayed fractional-order underdamped processes. In order to analyze the closed-loop stability and robustness, the new concept of <i>Robust High-Frequency Condition</i> is introduced. The analysis based on that demonstrates that each controller has a different region of feasible frequency specifications, and, in all cases, they depend on their fractional integral or derivative actions. Finally, an application example, the position control of a teleoperated manipulator with a flexible link, is presented. Simulations and experiments illustrate that the region of feasible frequency specifications defined at low and high frequencies allows us to obtain robust controllers that fulfill frequency requirements. |
| first_indexed | 2024-03-10T22:44:55Z |
| format | Article |
| id | doaj.art-f7e37fe84ecd4df3bf84986af2697d15 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T22:44:55Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-f7e37fe84ecd4df3bf84986af2697d152023-11-19T10:48:14ZengMDPI AGFractal and Fractional2504-31102023-08-017964610.3390/fractalfract7090646Fractional Control of a Class of Underdamped Fractional Systems with Time Delay—Application to a Teleoperated Robot with a Flexible LinkSaddam Gharab0Vicente Feliu Batlle1Instituto de Investigaciones Energéticas y Aplicaciones Industriales, 13005 Ciudad Real, SpainEscuela Técnica Superior de Ingeniería Industrial, Universidad de Castilla La Mancha, 13071 Ciudad Real, SpainThis work addresses the robust control of processes of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mrow><mo>(</mo><mi>s</mi><mo>)</mo></mrow><mo>=</mo><mi>K</mi><mo>·</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>τ</mi><mo>·</mo><mi>s</mi></mrow></msup><mo>/</mo><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>T</mi><mo>·</mo><msup><mi>s</mi><mi>λ</mi></msup><mo>)</mo></mrow></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>λ</mi><mo>≤</mo><mn>2</mn></mrow></semantics></math></inline-formula>. A new method for tuning fractional-order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>I</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mi>D</mi></mrow></semantics></math></inline-formula> controllers is developed. The stability is assessed based on the frequency domain tuning of the regulators to control such delayed fractional-order underdamped processes. In order to analyze the closed-loop stability and robustness, the new concept of <i>Robust High-Frequency Condition</i> is introduced. The analysis based on that demonstrates that each controller has a different region of feasible frequency specifications, and, in all cases, they depend on their fractional integral or derivative actions. Finally, an application example, the position control of a teleoperated manipulator with a flexible link, is presented. Simulations and experiments illustrate that the region of feasible frequency specifications defined at low and high frequencies allows us to obtain robust controllers that fulfill frequency requirements.https://www.mdpi.com/2504-3110/7/9/646time delayfractional order systemsflexible robotsteleoperated robotsfractional order control |
| spellingShingle | Saddam Gharab Vicente Feliu Batlle Fractional Control of a Class of Underdamped Fractional Systems with Time Delay—Application to a Teleoperated Robot with a Flexible Link Fractal and Fractional time delay fractional order systems flexible robots teleoperated robots fractional order control |
| title | Fractional Control of a Class of Underdamped Fractional Systems with Time Delay—Application to a Teleoperated Robot with a Flexible Link |
| title_full | Fractional Control of a Class of Underdamped Fractional Systems with Time Delay—Application to a Teleoperated Robot with a Flexible Link |
| title_fullStr | Fractional Control of a Class of Underdamped Fractional Systems with Time Delay—Application to a Teleoperated Robot with a Flexible Link |
| title_full_unstemmed | Fractional Control of a Class of Underdamped Fractional Systems with Time Delay—Application to a Teleoperated Robot with a Flexible Link |
| title_short | Fractional Control of a Class of Underdamped Fractional Systems with Time Delay—Application to a Teleoperated Robot with a Flexible Link |
| title_sort | fractional control of a class of underdamped fractional systems with time delay application to a teleoperated robot with a flexible link |
| topic | time delay fractional order systems flexible robots teleoperated robots fractional order control |
| url | https://www.mdpi.com/2504-3110/7/9/646 |
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