A Chaotic Controller for the Double Pendulum
Here we consider a two link pendulum attached at the top link to a fixed DC motor. A second DC motor provides a bearing between the two links. The torque provided by both motors is limited so that each motor operating under maximum current at steady state will lift each link to an angle of less than 20°. Chaotic motion may be easily produced in this system by driving the system with the first motor under a sine input with no input to the second motor. This paper examines the potential usefulness of using such chaotic motion as a part of an overall control system design strategy in order to achieve target states which would otherwise require more complicated control algorithms (e.g. optimal control theory). In particular we examine the problem of obtaining an inverted position for the second link starting the system with the two links at rest hanging straight down. We demonstrate that an open loop chaotic controller in conjunction with a closed loop controller can indeed result in a useful control design. The key to using such a design depends on having available a simple and accurate method for determining the domain of attraction for the closed loop controller. Results are presented both in terms of a computer simulation of this system and data from an actual two link pendulum.
KeywordsChaotic Motion Open Loop Control Drive Cycle Double Pendulum Unstable Equilibrium Point
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