Browsing by Author "Hsu, Tseng-Hsing"
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- Control of a Chaotic Double Pendulum Model for a Ship Mounted CraneHsu, Tseng-Hsing (Virginia Tech, 2000-02-22)An extension of the original Ott-Grebogy-Yorke control scheme is used on a simple double pendulum. The base point of the double pendulum moves in both horizontal and vertical directions which leads to rather complicated behavior.A delay coordinate is used to reconstruct the attractor. The required dimension is determined by the False Nearest Neighbor analysis. A newly developed Fixed Point Transformation method is used to identify the unstable periodic orbit (UPO). Two different system parameters are used to control the motion. Minimum parameter constraints are studied. The use of discrete values for parameter changes is also investigated. Based on these investigations, a new on-off control scheme is proposed to simplify the implementation of the controller and minimize the delay in applying the control.
- The parametrically excited pendulum and the criteria for predicting the onset of chaosHsu, Tseng-Hsing (Virginia Tech, 1991-11-15)A pendulum with its supporting point vibrating in both the x and the y direction is analyzed. Numerical simulation by computer is used to analyze the motion of the pendulum. Chaotic motion of the system is observed. Threshold values for chaos are obtained by simulation. The Lyapunov exponent and the fast Fourier transform ( FFT ) are used as the criteria to determine if the system is chaotic. Two predictive theoretical criteria, the Melnikov criterion and a period-doubling criterion, are then applied to the system. The results obtained by simulation and by theoretical criteria are shown to be in good agreement. A brute-force approach is used to supplement the results. It is found that the motion of this simple driven pendulum will have very complicated behavior. Multiple attractors can be shown to coexist.