On Singular Perturbations of Unstable Underactuated Mechanical Systems With Underactuation Degree ≥ 1

Abstract

10 years ago, K.J. Åström proposed that the essence of the complex control problem originated by the joint of the pilot–&–aircraft can be captured on labs, by means of unstable underactuated mechanical systems. Thus, the unactuated part describes the autonomous aircraft dynamics and the actuated the piloted one. In this constructive approach we propose a nonlinear controller based on classical feedback linearization and singular perturbation theory, which has a compact and explicit expression, providing the designer a handle to address transient performance and robustness issues to dominate undesirable friction and/or drag effects, even in the unactuated coordinates. Further, partial differential equations need not to be solved. A multivariable example and successful experiments on the Furuta's pendulum are reported. To the best of authors’ knowledge it has the largest attraction basin experimentally tested so far.