Active Control Model for the “FAST” Reflecting Surface Based on Discrete Methods
Radio telescopes are important for the development of society. With the advent of China’s Five-hundred-meter Aperture Spherical radio Telescope (FAST), adjusting the reflector panel to improve the reception ability is becoming an urgent problem. In this paper, an active control model of the reflecto...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/2/252 |
| _version_ | 1797476504622333952 |
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| author | Yanbo Wang Yingchang Xiong Jianming Hao Jiaqi He Yuchi Liu Xinpeng He |
| author_facet | Yanbo Wang Yingchang Xiong Jianming Hao Jiaqi He Yuchi Liu Xinpeng He |
| author_sort | Yanbo Wang |
| collection | DOAJ |
| description | Radio telescopes are important for the development of society. With the advent of China’s Five-hundred-meter Aperture Spherical radio Telescope (FAST), adjusting the reflector panel to improve the reception ability is becoming an urgent problem. In this paper, an active control model of the reflector panel is established that considers the minimum sum of the radial offset of the actuator and the non-smoothness of the working paraboloid. Using the idea of discretization, the adjusted position of the main cable nodes, the ideal parabolic equation, and the expansion of each actuator are obtained by inputting the elevation and azimuth angle of the incident electromagnetic wave. To find the ideal parabola, a univariate optimization model is established, and the Fibonacci method is used to search for the optimal solution <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>h</mi><mo>=</mo><mo>−</mo><mn>0.33018</mn></mrow></semantics></math></inline-formula> (offset in the direction away from the sphere’s center) and the focal diameter ratio <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>=</mo><mn>0.4671</mn></mrow></semantics></math></inline-formula> of the parabolic vertex. The ideal two-dimensional parabolic equation is then determined as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>555.25</mn><mi>z</mi><mo>−</mo><mn>166757.2</mn><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>, and the ideal three-dimensional paraboloid equation is determined to be <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>z</mi><mo>=</mo><mrow><mo>(</mo><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow><mo>/</mo><mn>555.25</mn><mo>−</mo><mn>300.33018</mn></mrow></semantics></math></inline-formula>. Moreover, the amount of the nodes and triangular reflection panels are calculated, which were determined to be 706 and 1325, respectively. The ratio reception of the working paraboloid and the datum sphere are <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>9.434</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.3898</mn><mo>%</mo></mrow></semantics></math></inline-formula>, respectively. The latter is calculated through a ray tracing simulation using the optical system modeling software LightTools. |
| first_indexed | 2024-03-09T20:58:46Z |
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| id | doaj.art-dc5dc1b519dd497d99952e88178f7b2e |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T20:58:46Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-dc5dc1b519dd497d99952e88178f7b2e2023-11-23T22:15:43ZengMDPI AGSymmetry2073-89942022-01-0114225210.3390/sym14020252Active Control Model for the “FAST” Reflecting Surface Based on Discrete MethodsYanbo Wang0Yingchang Xiong1Jianming Hao2Jiaqi He3Yuchi Liu4Xinpeng He5Chang’an Dublin International College of Transportation, Chang’an University, Xi’an 710064, ChinaChang’an Dublin International College of Transportation, Chang’an University, Xi’an 710064, ChinaSchool of Highway, Chang’an University, Xi’an 710064, ChinaChang’an Dublin International College of Transportation, Chang’an University, Xi’an 710064, ChinaChang’an Dublin International College of Transportation, Chang’an University, Xi’an 710064, ChinaChang’an Dublin International College of Transportation, Chang’an University, Xi’an 710064, ChinaRadio telescopes are important for the development of society. With the advent of China’s Five-hundred-meter Aperture Spherical radio Telescope (FAST), adjusting the reflector panel to improve the reception ability is becoming an urgent problem. In this paper, an active control model of the reflector panel is established that considers the minimum sum of the radial offset of the actuator and the non-smoothness of the working paraboloid. Using the idea of discretization, the adjusted position of the main cable nodes, the ideal parabolic equation, and the expansion of each actuator are obtained by inputting the elevation and azimuth angle of the incident electromagnetic wave. To find the ideal parabola, a univariate optimization model is established, and the Fibonacci method is used to search for the optimal solution <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>h</mi><mo>=</mo><mo>−</mo><mn>0.33018</mn></mrow></semantics></math></inline-formula> (offset in the direction away from the sphere’s center) and the focal diameter ratio <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>=</mo><mn>0.4671</mn></mrow></semantics></math></inline-formula> of the parabolic vertex. The ideal two-dimensional parabolic equation is then determined as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>555.25</mn><mi>z</mi><mo>−</mo><mn>166757.2</mn><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>, and the ideal three-dimensional paraboloid equation is determined to be <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>z</mi><mo>=</mo><mrow><mo>(</mo><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup></mrow><mo>)</mo></mrow><mo>/</mo><mn>555.25</mn><mo>−</mo><mn>300.33018</mn></mrow></semantics></math></inline-formula>. Moreover, the amount of the nodes and triangular reflection panels are calculated, which were determined to be 706 and 1325, respectively. The ratio reception of the working paraboloid and the datum sphere are <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>9.434</mn><mo>%</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1.3898</mn><mo>%</mo></mrow></semantics></math></inline-formula>, respectively. The latter is calculated through a ray tracing simulation using the optical system modeling software LightTools.https://www.mdpi.com/2073-8994/14/2/252radio telescopeleast square methodunivariate optimization modelthe idea of discretizationFibonacci method |
| spellingShingle | Yanbo Wang Yingchang Xiong Jianming Hao Jiaqi He Yuchi Liu Xinpeng He Active Control Model for the “FAST” Reflecting Surface Based on Discrete Methods Symmetry radio telescope least square method univariate optimization model the idea of discretization Fibonacci method |
| title | Active Control Model for the “FAST” Reflecting Surface Based on Discrete Methods |
| title_full | Active Control Model for the “FAST” Reflecting Surface Based on Discrete Methods |
| title_fullStr | Active Control Model for the “FAST” Reflecting Surface Based on Discrete Methods |
| title_full_unstemmed | Active Control Model for the “FAST” Reflecting Surface Based on Discrete Methods |
| title_short | Active Control Model for the “FAST” Reflecting Surface Based on Discrete Methods |
| title_sort | active control model for the fast reflecting surface based on discrete methods |
| topic | radio telescope least square method univariate optimization model the idea of discretization Fibonacci method |
| url | https://www.mdpi.com/2073-8994/14/2/252 |
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