Designing Limit-Cycle Suppressor Using Dithering and Dual-Input Describing Function Methods
This paper described a method to design a limit-cycle suppressor. The dithering technique was used to eliminate self-sustained oscillations or limit cycles. Otherwise, the Dual Input Describing Function (DIDF) method was applied to design dither parameters and analyze the existence of limit cycles....
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/11/1978 |
| _version_ | 1827702740823834624 |
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| author | Elisabeth Tansiana Mbitu Seng-Chi Chen |
| author_facet | Elisabeth Tansiana Mbitu Seng-Chi Chen |
| author_sort | Elisabeth Tansiana Mbitu |
| collection | DOAJ |
| description | This paper described a method to design a limit-cycle suppressor. The dithering technique was used to eliminate self-sustained oscillations or limit cycles. Otherwise, the Dual Input Describing Function (DIDF) method was applied to design dither parameters and analyze the existence of limit cycles. This method was done in a nonlinear system with relay nonlinearity using three standard dither signals, namely sine, triangle, and square waves. The aim of choosing varying dithers was to investigate the effect of dither shapes and the minimum amplitude required for the quenching strategy. First, the possibility and amplitude of limit cycles were determined graphically on the DIDF curve. Then, the minimum amplitude of dither was calculated based on the DIDF analysis. Finally, a simulation was built to verify the analytical work using a digital computer. The simulation results were related to the analysis results. It was evident that the dithering technique is a simple way to suppress limit cycles in a nonlinear system. This paper also presented that dither is an amplitude function, and square-wave dither has the minimum amplitude to quench limit cycles. |
| first_indexed | 2024-03-10T15:02:48Z |
| format | Article |
| id | doaj.art-155aa68409d5434983791d02e43f26cd |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:02:48Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-155aa68409d5434983791d02e43f26cd2023-11-20T20:01:23ZengMDPI AGMathematics2227-73902020-11-01811197810.3390/math8111978Designing Limit-Cycle Suppressor Using Dithering and Dual-Input Describing Function MethodsElisabeth Tansiana Mbitu0Seng-Chi Chen1Electrical Engineering Department, Southern Taiwan University of Science and Technology, Tainan City 71005, TaiwanElectrical Engineering Department, Southern Taiwan University of Science and Technology, Tainan City 71005, TaiwanThis paper described a method to design a limit-cycle suppressor. The dithering technique was used to eliminate self-sustained oscillations or limit cycles. Otherwise, the Dual Input Describing Function (DIDF) method was applied to design dither parameters and analyze the existence of limit cycles. This method was done in a nonlinear system with relay nonlinearity using three standard dither signals, namely sine, triangle, and square waves. The aim of choosing varying dithers was to investigate the effect of dither shapes and the minimum amplitude required for the quenching strategy. First, the possibility and amplitude of limit cycles were determined graphically on the DIDF curve. Then, the minimum amplitude of dither was calculated based on the DIDF analysis. Finally, a simulation was built to verify the analytical work using a digital computer. The simulation results were related to the analysis results. It was evident that the dithering technique is a simple way to suppress limit cycles in a nonlinear system. This paper also presented that dither is an amplitude function, and square-wave dither has the minimum amplitude to quench limit cycles.https://www.mdpi.com/2227-7390/8/11/1978limit cyclesDIDFdither signalnonlinearityrelay system |
| spellingShingle | Elisabeth Tansiana Mbitu Seng-Chi Chen Designing Limit-Cycle Suppressor Using Dithering and Dual-Input Describing Function Methods Mathematics limit cycles DIDF dither signal nonlinearity relay system |
| title | Designing Limit-Cycle Suppressor Using Dithering and Dual-Input Describing Function Methods |
| title_full | Designing Limit-Cycle Suppressor Using Dithering and Dual-Input Describing Function Methods |
| title_fullStr | Designing Limit-Cycle Suppressor Using Dithering and Dual-Input Describing Function Methods |
| title_full_unstemmed | Designing Limit-Cycle Suppressor Using Dithering and Dual-Input Describing Function Methods |
| title_short | Designing Limit-Cycle Suppressor Using Dithering and Dual-Input Describing Function Methods |
| title_sort | designing limit cycle suppressor using dithering and dual input describing function methods |
| topic | limit cycles DIDF dither signal nonlinearity relay system |
| url | https://www.mdpi.com/2227-7390/8/11/1978 |
| work_keys_str_mv | AT elisabethtansianambitu designinglimitcyclesuppressorusingditheringanddualinputdescribingfunctionmethods AT sengchichen designinglimitcyclesuppressorusingditheringanddualinputdescribingfunctionmethods |