Robust optimal control of flexible space structures by a proper controller using displacement output

This paper considers robust optimal control of flexible space structures with collocated sensors and actuators. First, we introduce a third order low-pass filter of which relative degree is 1, at each input channel. Then, we feed back output of the filter and displacement and velocity output of the space structure to input of the filter, so that we obtain a third order proper controller using only displacement output. By choosing parameters of the proper controller as the controller becomes a phase lead compensator, a closed-loop system becomes robustly stable against uncertainty of characteristic parameters of the structures such as mass, damping, and stiffness. The purpose of this paper is to show the closed-loop system becomes not only robustly stable but also optimal for a quadratic cost function by making two feedback gains contained in the proper controller sufficiently large.