Robust Control of Under-actuated Systems via Sliding Modes

Abstract

Underactuated nonlinear systems are always equipped with less number of actua tors than the degree of freedom. This feature offers certain benefits like reduction in weight and minimum energy usage. Majority of the robotic systems (including aerial, underwater and ground robotics) are found to be underactuated in na ture. Therefore, research in such system is still quite demanding and challenging. It is also worthy to mention that the underactuation phenomenon, do not allow the direct design of control input as practiced in fully actuated systems. The two decades have witnessed many control methodologies which include feedback linearization, energy-based, back-stepping, fuzzy logics and sliding mode control. However, majority of these techniques lags behind in the robust stabilization of this class except sliding mode oriented techniques. An extensive simulation study of the underactuated system is carried out in the existing literature while consid ering the examples of translational oscillator with a rotational actuator (TORA), flexible robots, pendulums and surface vessels. In this thesis a simulation as well as experimental study is carried out for a class of underactuated systems. The nonlinear model, of the underactuated systems, is treated generally. The dynamics are either transformed into an input output form and then an integral manifold is devised for the control design purpose or an integral manifold is defined directly for the concerned class. Having defined the integral manifolds discontinuous control laws are designed which are capable to maintain sliding mode from the very beginning. The closed loop stability of these systems is presented in an impressive way. The effectiveness and demand of the designed control laws are proved in term of simulation and experimental results of a ball and beam system. In addition, a comparative experimental study is also performed between three generations of sliding mode control, which includes the conventional first order sliding mode control (FOSMC), second order sliding mode (SOSMC), fast terminal sliding mode (FTSMC), and integral sliding mode (ISMC). The comparative study takes into account certain features like tracking performance, i.e., settling time, overshoots, robustness enhancement, chattering reduction, sliding mode convergences and control efforts.