Dynamics of an inverted pendulum with delayed feedback control
Campbell, Sue Ann
Aguilar, Cesar O.
MetadataShow full item record
We consider an experimental system consisting of a pendulum, which is free to rotate 360 degrees, attached to a cart. The cart can move in one dimension. We describe a model for this system and use it to design a feedback control law that stabilizes the pendulum in the uprigiht position. We then introduce a time delay into the feedback and prove that for values of the delay below a critical delay, the system remains stable. Using a center manifold reduction, we show that the system undergoes a supercritical Hopf bifurcation at the critical delay. Both the critical value of the delay and the stability of the limit cycle are verified experimentally. Our experimental data is illustrated with plots and videos.
The article of record as published may be found at: http://dx.doi.org/10.1137/030600461Approved for public release; distribution is unlimited
Showing items related by title, author, creator and subject.
Bradford, Ellen M. (Monterey, California: Naval Postgraduate School, 2017-06);The inverted pendulum, a popular problem of study, is presented in many textbooks as a nonminimum phase system. The majority of control algorithms for this problem include linearizing the system about a fixed operating ...
Harding, Richard Warren (Monterey, California. Naval Postgraduate School, 1981);In a space booster on takeoff, a control system must be employed to prevent the rocket from falling over as it is forced upward by the engines. One accurate dynamic model of the space booster on takeoff is the inverted ...
Lewis, Laird-Philip Ryan (Monterey, California. Naval Postgraduate School, 2006-12);This work introduces the use of optimal control methods for path planning and control of autonomous vehicles in an obstacle-rich environment. Traditional techniques harbor non-optimal, closed architectures primarily ...