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Title: Design and modelling of nonlinear dynamical system
Researcher: Gupta, Mukul Kumar
Guide(s): Bansal, Kamal and Singh, Arun Kumar
Keywords: Electrical engineering
University: University of Petroleum and Energy Studies (UPES)
Completed Date: 2014
Abstract: The dynamic behavior of double and triple link pendula considering both the lumped and distributed mass has been studied. The system of governing differential equations for double pendulum (DP) and triple pendulum (TP) is derived using the Euler- Lagrange (EL) approach. Effect of damping of pivots is also considered in the model. The governing equations are also derived in the terms of momenta and angular velocity without considering the damping to confirm the results obtained by the E-L approach. Chaotic behavior of these systems was investigated using time series plot, Poincare map and Lyapunov exponent. It is observed that bottom pendulum is most sensitive than other pendula. Further, tendency of chaotic behavior increases with degree of freedom (dof) for the same initial conditions. Nature of Poincare maps of the TP becomes more intricate in comparison to the DP. Interestingly, damping of pivots results in regular motion of the pendulum system. In other words, introduction of damping in the multiple pendula reduces the tendency of chaos. Moreover, there is no qualitative difference between the lumped and distributed pendulum systems as far as the dynamical behavior is concerned. All the observations and results are validated experimentally. The LQR technique was used to control inverted triple pendulum. The control technique was found to be effective. This is also valid for double pendulum newline
Pagination: 123p.
Appears in Departments:Department of Electrical Engineering

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01_titlepage.pdfAttached File29.42 kBAdobe PDFView/Open
02_certficate.pdf19.9 kBAdobe PDFView/Open
03_acknowledgement.pdf20.42 kBAdobe PDFView/Open
04_abstracts.pdf15.89 kBAdobe PDFView/Open
05_summary.pdf19.9 kBAdobe PDFView/Open
06_contents.pdf25.75 kBAdobe PDFView/Open
07_list of figures.pdf80.2 kBAdobe PDFView/Open
08_list of symbols.pdf30.97 kBAdobe PDFView/Open
09_list of tables.pdf14.04 kBAdobe PDFView/Open
10_acronyms.pdf15.05 kBAdobe PDFView/Open
11_list of abbreviations.pdf11.92 kBAdobe PDFView/Open
12_chapter1.pdf691.33 kBAdobe PDFView/Open
13_chapter2.pdf107.45 kBAdobe PDFView/Open
14_chapter3.pdf2.2 MBAdobe PDFView/Open
15_chapter4.pdf3.14 MBAdobe PDFView/Open
16_chapter5.pdf1.48 MBAdobe PDFView/Open
17_chapter6.pdf38.37 kBAdobe PDFView/Open
18_references.pdf130.92 kBAdobe PDFView/Open
19_appendix.pdf677.82 kBAdobe PDFView/Open
20_list of publications.pdf41.58 kBAdobe PDFView/Open

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