Distributed Parameter-Dependent Control of Non-Uniform Flexible Structures

Abstract

In this thesis, we consider the distributed parameter-dependent modeling and control of non-uniform flexible structures, which are classified under spatially varying distributed systems. A distributed state space model of a non-uniform flexible cantilever beam is developed, in which the spatial variation of the beam parameters is treated as parametric uncertainty, assuming that the system depends on the spatially varying parameters in linear fractional manner. We are particularly interested in the systems discretized in spatial dimension for practical reasons. Spatial discretization is obtained via the central finite difference scheme. We assume that the displacements at each discretized node are measurable in real time for controller use. Based on the proposed distributed model, sufficient conditions for analysis and synthesis of a distributed output-feedback controller are presented using the induced L2 norm as the performance criterion. The controller synthesis condition is characterized in terms of linear matrix inequalities, which are convex optimization problems and can be solved efficiently using available software. The distributed controller inherits the same structure as the plant, which results in a localized control architecture and a simple implementation. Each local controller unit processes the available local displacement measurement while sharing information with its adjacent units. We present the main advantage of distributed control; its reliability in the case of malfunctioning actuators or sensors, where many other control techniques would probably fail.