Distributed Parameter-Dependent Modeling and Control of Flexible Structures

In this paper, distributed parameter-dependent modeling and control approaches are proposed for flexible structures. The distributed model is motivated from distributed control design, which is advantageous in reducing control implementation cost and increasing control system reliability. This modeling approach mainly relies on a central finite difference scheme to capture the distributed nature of the flexible system. Based on the proposed distributed model, a sufficient synthesis condition for the design of a distributed output-feedback controller is presented using induced $L2$ norm as the performance criterion. The controller synthesis condition is formulated as linear matrix inequalities, which are convex optimization problems and can be solved efficiently using interior-point algorithms. The distributed controller inherits the same structure as the plant, which results in a localized control architecture and a simple implementation scheme. These modeling and control approaches are demonstrated on a non-uniform cantilever beam problem through simulation studies.