Swing-up control for an inverted pendulum with restricted cart rail length

• DOI: 10.1007/s12555-009-0419-x
• Publication Date: 2009-07-31T00:40:06Z
• Authors: Ji-Hyuk Yang; Su-Yong Shim; Jung-Hun Seo; Young-Sam Lee
• Keywords: Square (algebra)

In this paper, we propose a new swing-up strategy for cart inverted pendulums with restricted rail length. The proposed swing-up strategy is derived from a new Lyapunov function. The Lyapunov function is defined as the sum of the square of the pendulum energy and the weighted square of the cart’s velocity. The resulting swing-up strategy is represented in a compact form and has two design parameters. By adjusting these design parameters, we can affect the swing-up strategy such that the restriction on the rail length is satisfied. We also provide a state-dependent transformation to obtain voltage input to a DC motor required to generate the cart’s acceleration obtained from the proposed swing-up strategy. Finally, we illustrate the performance of the proposed swing-up law through simulation and experiments. It is shown that there is quite good correspondence between theory and experiments.