Controlling underactuated mechanical systems using direct Lyapunov approach by solving for the potential function

Abstract

Underactuated Mechanical System (UMS) is the system with n degrees of freedom out of which only m < n are actuated. Among various methods for controlling UMS, the Direct Lyapunov Approach (DLA) is one. In this method, the time derivative of the candidate Lyapunov function produces a relation that is solved via a matching method. The equation of motion corresponding to a system is applied to the matching conditions of the DLA method. The potential of the system is calculated by solving these matching conditions. The Conditions of stability are analyzed to find bounds on the parameters. Control Law is formulated and applied to the system to see the result of the system under the DLA method. Two underactuated systems being controlled with the DLA method have been studied which are, Inertia Wheel System and Inverted Pendulum Cart system.