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

Abstract

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 fourthorder 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. I. INTRODUCTIONAs a method for position and attitude control of flexible space structures such as solar power satellites [1], direct velocity and displacement feedback (DVDFB) [2],[3] has been proposed under the assumption of sensors/actuators collocation. DVDFB can robustly stabilize a closed-loop system and make it optimal. However, both displacement sensors and velocity sensors are needed to implement DVDFB. For reduction of cost, it is desired not to use velocity sensors. To solve this issue, dynamic displacement feedback (DDFB) has been proposed [4] under the assumption that sensors and actuators are collocated. DDFB can also robustly stabilize a closed-loop system. However, DDFB has been proposed as a theoretical scheme in [4] so that it has not been shown how to determine quantitatively the parameters of a DDFB controller.The purpose of this paper is to propose a control method that makes a closed-loop system not only robustly stable but also optimal by introducing a fourth-order controller using only displacement output. We show the closed-loop system becomes robustly stable if the parameters of the proper controller are chosen to make the controller a phase lead compensator to resonant frequencies of the structure. Furthermore, we also show the closed-loop system becomes optimal for a quadratic cost function if two gains of the controller are chosen sufficiently large.