Nested Saturation Based Control of Ultra-Compliant Cantilever with Tip Mass mounted on a Cart

Abstract

Ultra-compliant mechanical systems are widely deployed in flexible link robots, compliant mechanisms, antenna structures, and so on for their advantages such as lower inertia, low energy requirement, and high speeds. Mathematically however, they represent a class underactuated of systems with both compliant and distributed parameters and pose challenges for control. A representative system in this class: a vertical inverted ultra-flexible beam with tip mass on cart, exhibiting highly nonlinear dynamics, is considered here. Control task is defined to be stabilization of central unstable equilibrium along with regulation of cart to a desired position. Two coordinate transformations are proposed to obtain a mathematical structure suitable to employ nested saturation based control. Asymptotic stability of the unstable equilibrium is established with the proposed controller and is demonstrated in simulation as well as in the experimental implementation. Nested saturation based controller is found to be relatively robust in experiments although system dynamics is very sensitive to parametric uncertainities.