Controller design for a class of underactuated mechanical systems

This study proposes a strategy for the control of a class of underactuated mechanical systems. The Olfati transformation is applied firstly to represent the system into a special cascade form. Since, in general cases, some of the terms in the system dynamic equation represented in the new space might become too complex to derive, they are regarded as uncertainties. These uncertainties would enter the system in a mismatched fashion, and their variation bounds are not available; therefore, most conventional robust or adaptive designs fail to stabilise the closed-loop dynamics. A backstepping-like adaptive controller based on function approximation technique (FAT) is designed so that the system in the new space can be stabilised with uniformly ultimately bounded performance which further implies the same stability property to the system in the original space. Simulation cases for the control of an inverted pendulum and a translational oscillator/rotational actuator (TORA) system are presented to justify the proposed design.