08c20d0dc91e9faa42e4ca62a9ae1cb1 mathematics-11-04040.pdf ef8977f1f77296cfb6824d15864f90d870b6cf20 mathematics-11-04040.pdf ac48a76c226a99e2152dcd64de28d42c8c3a7814dfcbc7a2b1b4367d4871bac4 mathematics-11-04040.pdf Title: Design a Robust Proportional-Derivative Gain-Scheduling Control for a Magnetic Levitation System Subject: This study focuses on the design of a robust PD gain-scheduling controller (PD-GS-C) for an unstable SISO (single-input, single-output) magnetic levitation system with two electromagnets (MLS2EM). Magnetic levitation systems offer various advantages, including friction-free, reliable, fast, and cost-effective operations. However, due to their unstable and highly nonlinear nature, these systems require sophisticated feedback control techniques to ensure optimal performance and functionality. To address these challenges, in this study, we derive the nonlinear state-space mathematical model of the MLS2EM and linearize it around five different operating points. The PD-GS-C controller aims to stabilize the system and improve steady-state control error. The strategy for obtaining the PD controller gains involves a parameter space technique, which specifies performance requirements. This technique results in ranges of proportional (KP) and derivative (KD) gains that are used by the PD-GS-C structure. To optimize the controller's performance further, we utilize the big bang–big crunch optimization technique (BB-BC) to determine the optimal PD gains within the specified ranges. The optimization process focuses on achieving optimal performance in terms of a specific performance index function. This function quantifies the system's time-domain step response criteria, which include minimizing overshoot percentage, settling time, and rising time. The index function is inversely proportional to the desired performance criteria, meaning that the goal is to maximize the index function to optimize the system's performance. To validate the effectiveness and viability of the proposed strategy, we conducts MATLAB simulations and real-time experiments. The simulations and experimental findings serve to demonstrate the controller's performance and verify its capabilities in stabilizing the MLS2EM magnetic levitation system. Keywords: magnetic levitation system; proportional-derivative controller; robust PD gain-scheduling controller (PD-GS-C); parameter space technique; Big Bang–Big Crunch optimization technique (BB-BC); real-time experiment Author: Moayed Almobaied, Hassan S. Al-Nahhal, Orlando Arrieta, and Ramon Vilanova Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Sat Sep 23 10:17:32 2023 CEST ModDate: Sat Sep 23 10:44:54 2023 CEST Tagged: no UserProperties: no Suspects: no Form: none JavaScript: no Pages: 21 Encrypted: no Page size: 595.276 x 841.89 pts (A4) Page rot: 0 File size: 4604811 bytes Optimized: no PDF version: 1.7 name type encoding emb sub uni object ID ------------------------------------ ----------------- ---------------- --- --- --- --------- AIXDAA+URWPalladioL-Bold Type 1 Custom yes yes no 10 0 YJWQPB+URWPalladioL-Roma Type 1 Custom yes yes no 15 0 QGQCRP+URWPalladioL-Ital Type 1 Custom yes yes no 19 0 DVTHKG+TimesNewRomanPS-BoldItalicMT Type 1C WinAnsi yes yes no 37 0 SOSTRQ+CMR10 Type 1 Builtin yes yes no 65 0 ZXCWJD+CMSY10 Type 1 Builtin yes yes no 69 0 YECWWF+CMEX10 Type 1 Builtin yes yes no 78 0 NFZFQP+PazoMath Type 1 Builtin yes yes no 82 0 NOWDKC+PazoMath-Italic Type 1 Builtin yes yes no 95 0 QDTWCG+MSBM10 Type 1 Builtin yes yes no 99 0 XSXHIJ+URWPalladioL-BoldItal Type 1 Custom yes yes no 108 0 BJQDNG+CMBX10 Type 1 Builtin yes yes no 112 0 QIELJB+CMMI10 Type 1 Builtin yes yes no 136 0 Jhove (Rel. 1.22.1, 2019-04-17) Date: 2023-11-14 02:30:43 CET RepresentationInformation: mathematics-11-04040.pdf ReportingModule: PDF-hul, Rel. 1.12.1 (2019-04-17) LastModified: 2023-11-06 14:13:20 CET Size: 4604811 Format: PDF Version: 1.7 Status: Well-Formed and valid SignatureMatches: PDF-hul MIMEtype: application/pdf PDFMetadata: Objects: 360 FreeObjects: 1 IncrementalUpdates: 0 DocumentCatalog: PageLayout: SinglePage PageMode: UseNone Outlines: Item: Title: Introduction Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@87f383f Item: Title: Magnetic Levitation and Modeling Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@4eb7f003 Item: Title: Stability Analysis Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@eafc191 Item: Title: Controller Design Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@612fc6eb Children: Item: Title: The Big Bang Big Crunch Optimization Algorithm Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@1060b431 Item: Title: The Proportional-Derivative Gain-Scheduling Controller (PD-GS-C) Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@612679d6 Item: Title: Simulation Results Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@11758f2a Item: Title: Conclusions Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@e720b71 Item: Title: References Destination: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject@1b26f7b2 Info: Title: Design a Robust Proportional-Derivative Gain-Scheduling Control for a Magnetic Levitation System Author: Moayed Almobaied, Hassan S. Al-Nahhal, Orlando Arrieta, and Ramon Vilanova Subject: This study focuses on the design of a robust PD gain-scheduling controller (PD-GS-C) for an unstable SISO (single-input, single-output) magnetic levitation system with two electromagnets (MLS2EM). Magnetic levitation systems offer various advantages, including friction-free, reliable, fast, and cost-effective operations. However, due to their unstable and highly nonlinear nature, these systems require sophisticated feedback control techniques to ensure optimal performance and functionality. To address these challenges, in this study, we derive the nonlinear state-space mathematical model of the MLS2EM and linearize it around five different operating points. The PD-GS-C controller aims to stabilize the system and improve steady-state control error. The strategy for obtaining the PD controller gains involves a parameter space technique, which specifies performance requirements. This technique results in ranges of proportional (KP) and derivative (KD) gains that are used by the PD-GS-C structure. To optimize the controller's performance further, we utilize the big bang big crunch optimization technique (BB-BC) to determine the optimal PD gains within the specified ranges. The optimization process focuses on achieving optimal performance in terms of a specific performance index function. This function quantifies the system's time-domain step response criteria, which include minimizing overshoot percentage, settling time, and rising time. The index function is inversely proportional to the desired performance criteria, meaning that the goal is to maximize the index function to optimize the system's performance. To validate the effectiveness and viability of the proposed strategy, we conducts MATLAB simulations and real-time experiments. The simulations and experimental findings serve to demonstrate the controller's performance and verify its capabilities in stabilizing the MLS2EM magnetic levitation system. Keywords: magnetic levitation system; proportional-derivative controller; robust PD gain-scheduling controller (PD-GS-C); parameter space technique; Big Bang Big Crunch optimization technique (BB-BC); real-time experiment Creator: LaTeX with hyperref Producer: pdfTeX-1.40.21 CreationDate: Sat Sep 23 10:17:32 CEST 2023 ModDate: Sat Sep 23 10:44:54 CEST 2023 ID: 0x696c1a724d73f38d250e29d4ec8cc5c1, 0x696c1a724d73f38d250e29d4ec8cc5c1 Filters: FilterPipeline: FlateDecode FilterPipeline: DCTDecode Images: Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 300 ImageHeight: 321 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Image: NisoImageMetadata: FormatName: image/jpg CompressionScheme: JPEG ImageWidth: 500 ImageHeight: 392 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Image: NisoImageMetadata: FormatName: image/png ImageWidth: 757 ImageHeight: 226 ColorSpace: RGB BitsPerSample: 8 BitsPerSampleUnit: integer Filter: FlateDecode 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