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

This paper considers robust optimal control of flexible space structures with collocated sensors and actuators. First, we introduce a fourth-order low-pass filter of which relative degree is 1 at each input channel. Then, we temporally feed back output of the filter, displacement and velocity output of the structure to input of the filter, so that we obtain a fourth-order proper controller using only displacement output. By choosing parameters of the proper controller as the controller becomes a phase lead compensator, the 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 can be made not only robustly stable but also optimal for a quadratic cost function by making two feedback gains of the proper controller sufficiently large.