A simple adaptive control application to large flexible structures

This paper addresses the problem of synthesizing a closed-loop controller for attaining robust stabilization and position control of a flexible structure using adaptive control. The usually uncertain number of relevant flexible modes, that could normally be large and their frequencies pretty much unknown, presents a serious challenge for any control methodology. Although it was shown that when sensors and actuators are collocated the structure can be stabilized by output position-plus-velocity feedback, design of controllers requires good knowledge of the (uncertain) plant parameters. On the other hand, implementation of robust adaptive control algorithms, that seem fit to solve such problems with uncertain parameters, require satisfaction of so-called Almost Strictly Positive Realness (ASPR) conditions. The paper will show that the flexible structure with collocated sensors and actuators do satisfy the desired ASPR conditions and thus, robust adaptive control can be used without any other knowledge regarding the frequencies or even the number of modes. An example is also given in order to demonstrate these concepts and the efficiency of Simple Adaptive Control (SAC).