On the driven inverted pendulum

22Citations
Citations of this article
7Readers
Mendeley users who have this article in their library.
Get full text

Abstract

We explore the solutions of the driven inverted pendulum system lφ̈ = g sin φ -al(t)cosφ where al(·) is a bounded lateral acceleration. We show that, for lateral accelerations that are constant before some initial time, an inverted trajectory always exists and remains within a diamond shaped region in the state space. Functional analytic techniques are also developed to provide further insight into the nature of the inverted pendulum trajectories. Associated to the driven inverted pendulum is a time varying linear system. We show that this system always possesses an exponential dichotomy, allowing for the development of a successive approximation algorithm for finding the desired inverted pendulum trajectory. We show that the curve obtained from one iteration of this algorithm is a very good estimate of the required inverted trajectory. As that curve is obtained by filtering the quasi-static angle trajectory by a noncausal time varying low pass filter with weighting function with a shape similar to h(t) = exp -α0|t|, we find that the current pendulum angle is influenced by the values of the lateral acceleration within only a few seconds of the current time. These results are important as the driven inverted pendulum is a common susbsystem in systems ranging from motorcycles and bicycles to rockets and aircaft. © 2005 IEEE.

Cite

CITATION STYLE

APA

Hauser, J., Saccon, A., & Frezza, R. (2005). On the driven inverted pendulum. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC ’05 (Vol. 2005, pp. 6176–6180). https://doi.org/10.1109/CDC.2005.1583150

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free