Robust Approach for Global Stabilization of a Class of Underactuated Mechanical Systems in Presence of Uncertainties

Abstract

Underactuated mechanical systems offer complex dynamic behavior and poses control challenges, especially in the presence of uncertainties in the system. To cope with such systems, control mechanisms are required, which needs to be robust. In this research, an algorithm based on sliding mode control (SMC) is presented. The algorithm design offer a methodical way to handle underactuation, while the robustness properties of SMC suppresses the effect of norm bounded uncertainties and external disturbances. To proceed with the design, an underactuated system is converted into cascaded subsystems, a linear one and reduced-order nonlinear subsystem. The proposed SMC design is backed by rigorous mathematical presentation and based on Lyapunov theory, so that the global stabilization of overall system is ensured. Numerical simulations are performed, on the laboratory test bench underactuated systems (Inertial Wheel, Furuta Pendulum, TORA, and an Overhead Crane), to validate the efficacy of the proposed design. In addition, a novel sliding surface is presented for Inertial Wheel and Furuta Pendulum to achieve swingup control and global stabilization subjected to uncertainties.

Adaptive second-order backstepping control for a class of 2DoF underactuated systems with input saturation and uncertain disturbances

“…For the intelligent control algorithms, the fuzzy or fuzzy-based control algorithms are proposed 4 , 5 , and neural network (NN) or NN-based controllers are proposed 6 – 8 . For the nonlinear control algorithms, the partial feedback linearization 1 , the adaptive control methods 7 , 9 , the energy- or passivity-based control methods 10 , 11 , the robust control methods 12 , 13 , and the sliding mode-based methods 14 , 15 are proposed. Despite the control classifications made for the above literature, almost all are a combination of multiple control algorithms.…”