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ANALYSIS AND CONTROL OF BIFURCATIONS IN A DOUBLE PENDULUM

by JAFRI, FIROZ ALI

Abstract (Summary)
The double pendulum is an example of a simple dynamical system that exhibits complex behavior, including chaos. This thesis deals with the analysis and control of dynamic behavior of the double pendulum. The changes in motion of the double pendulum are explored for variations in the system parameters. Sensitivity to changes in parameter values is studied and the irregular behavior that may occur due to these changes is analyzed. Considering the damping present in the system as the bifurcation parameter, the limits on damping for stable behavior are established by performing a bifurcation analysis. The methodology of output feedback control has been used to extend these performance limits on damping. It is a partial state feedback control since, out of the angular position and angular velocities of the two masses, only the angular velocities are used for feedback purpose. It has been demonstrated that a control torque applied at the upper joint of the double pendulum can be effective in stabilizing the system at some parameter values for which the system gives unstable response for the uncontrolled case. In order to maximize the performance of the system, an iterative procedure has been implemented. This procedure gives a feasible set of gain adjustments for the feedback loop that maximize the stable performance range of the system.
Bibliographical Information:

Advisor:

School:University of Cincinnati

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:control bifurcations double pendulum damping state feedback

ISBN:

Date of Publication:01/01/2003

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