Transfer Matrix Modeling of Systems With Noncollocated Feedback

Abstract

The transfer matrix method (TMM) can be a powerful tool for modeling flexible structures under feedback control. It is particularly well suited to modeling structures composed of serially connected elements. The TMM is capable of modeling continuous elements such as beams or flexible robot links without discretization. The ability to incorporate controller transfer functions into the transfer matrix model of the system makes it a useful approach for control design. A limitation of the traditional formulation of the TMM is that it can only model feedback where the actuators and sensors are strictly collocated. The primary contribution of this paper is an algorithm for modeling noncollocated feedback with the TMM. Two cases of noncollocated sensors are considered (upstream and downstream). The approach is experimentally verified on a flexible robot that has one upstream and one downstream sensor in its feedback loops.