Decentralized robust optimal control of large flexible space structures by local proper controllers using displacement output

Abstract

This paper considers position and attitude control of large flexible space structures composed of a number of subsystems(substructures) which are interconnected by flexible links modeled by springs and dampers. It is assumed that sensors and actuators are collocated in each subsystem. The purpose of the paper is to propose a decentralized control scheme by local proper controllers using only displacement output, which makes both each closed-loop subsystem and an overall closed-loop system not only robustly stable against uncertainty of characteristic parameters such as mass, damping, and stiffness, but also optimal for quadratic cost functions. First, we introduce a second order low-pass filter of which relative degree is 1, at each input channel of each subsystem. Then, we temporarily feed back displacement and velocity output of the substructure and output of the filter to input of the filter locally, so that we obtain a local proper controller using displacement output. By choosing parameters of each local proper controller as it becomes a phase lead compensator, the closed-loop subsystems and the overall closed-loop system become robustly stable. Furthermore, it can be shown the closed-loop subsystems and the overall closed-loop system also become optimal for quadratic cost functions by making two feedback gains in each local proper controller sufficiently large. Finally, numerical examples are presented to show effectiveness of the proposed method.