Variable structure control for set-point stabilization of 2-DOF underactuated manipulators

Controlling an underactuated manipulator with less actuators than degree of freedom is a challenging problem, specifically when it is to force the underactuated manipulator to track a given trajectory or to be configurated at a specific position in the work space. This paper presents a cascade sliding mode tracking controller for set-point regulation of 2-DOF underactuated manipulators. This work builds on an observation that an underactuated manipulator can be treated as two subsystems. Consequently, a cascade sliding mode tracking controller can be designed as follows. First, a sliding mode surface is designed for both subsystems, this two sliding surfaces represent a first layer in the design architecture. A second layer sliding mode surface is then constructed based on the first layer sliding surface. The cascaded sliding mode controller is therefor deduced in terms of Lyapunov stability theorem. Robustness issues to bounded disturbances are then investigated. Simulation results on 2-DOF whiling pendulum are presented to demonstrate the effectiveness of the approach.