Stabilisation of a class of 2-DOF underactuated mechanical systems via direct Lyapunov approach

Abstract

This paper represents an alternative stabilisation procedure for a class of two degree-of-freedom underactuated mechanical systems based on a set of transformations and a Lyapunov function. After simplifying dynamic equations of the system via partial feedback linearisation and coordinate changes, the stability of the system is provided with Lyapunov’s direct method. Proposed control scheme is used on two different examples and asymptotic convergence for each system is proven by means of La Salle’s invariance principle. The designed controller is successfully illustrated through numerical simulations for each example.

Keywords:

• Lyapunov-based stabilisation
• underactuated mechanical systems
• pendulum on a cart
• Furuta pendulum

Notes

For all expressions from now on, the dependence will be indicated only for the first appearance to simplify the notation.