پديد آورنده :
قرقاني، فرشته
عنوان :
آناليز انشعابات يك آونگ معكوس
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
دستگاههاي ديناميكي
محل تحصيل :
اصفهان : دانشگاه صنعتي اصفهان
صفحه شمار :
هفت، 92 ص. : نمودار، مصور، جدول
استاد مشاور :
رضا رضاييان فراشاهي
توصيفگر ها :
آنگ معكوس , كنترل فيدبك , تاخير زماني , انشعاب هاپف
استاد داور :
رسول عاشقي، رضا مزروعي سبداني
تاريخ ورود اطلاعات :
1398/07/07
رشته تحصيلي :
رياضي كاربردي
تاريخ ويرايش اطلاعات :
1398/07/07
چكيده انگليسي :
د Bifurcation analysis of an inverted pendulum FERESHTEH GHARAGHANI fereshteh gharaghani@math iut ac ir August 6 2019 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Majid Gazor mgazor@cc iut ac irAdvisor Mr Reza Rezaeean Farashahi farashahi@cc iut ac ir2000 MSC 70K50 93D15 34K18 34K20 70Q50Keywords inverted pendulum time delay feedback control stability analysis Hopf bifurca tion Abstract This abstract and thesis is exctracted from the following papers Dynam M L S A C K M C O A ics of an Inverted Pendulum with Delayed Feedback Control SIAM J Applied Dynamical Systems 4 2005 No 2 333 351 Bifurcation Analysis and Dynamic Behaviour of an Inverted Pen S N dulum with Bounded Control Theoretical and Applied Mechanics So a 46 2016 No 1 17 32 An experimental system consisting of a pendulum is considered which is free to rotate 360degrees attached to a cart The cart can move in one dimension A model for this systemis presented and is used to design a feedback control law that stabilizes the pendulum in theupright position Then a time delay is introduced into the feedback and proved that for valuesof the delay below a critical delay the system remains stable Using a center manifold reduction the system undergoes a supercritical Hopf bifurcation at the critical delay Both the critical valueof the delay and the stability of the limit cycle are veri ed experimentally Experimental data isillustrated with plots and videos While our model reproduces most of the behavior of the experimental system it is not perfect Incertain situations the experimental system exhibits low amplitude low frequency oscillations notpredicted by the model An explanation for this is that this phenomenon is due to noise excitingmodes corresponding to eigenvalues with small negative real parts An alternative explanationis the presence of stick slip friction between the cart and the track A thorough investigation ofthese ideas would require reformulating the model and hence the authors of the original paperleft this for future work The interpretation of experimental results can be subject to debate The authors of the abovementioned paper are convinced that the results shown in Figure 6 of their paper support the pre diction of the presented model that the system exhibits a supercritical Hopf bifurcation How ever it is also possible to interpret this gure as showing bistability between a steady state andperiodic orbit This is not something they claim to observe in their model Thus this latter inter pretation might suggest that there are unmodeled nonlinear effects in the experimental system
استاد مشاور :
رضا رضاييان فراشاهي
استاد داور :
رسول عاشقي، رضا مزروعي سبداني
