A substructural control technique by H∞ method for nonlinear and fuzzy structures

In this paper, a substructural approach is proposed and successfully implemented for H_∞ robust controller design for nonlinear and fuzzy structures. Sensors and actuators are assumed to be discrete, located at some nodal points of the structure, and a nonlinear matrix differential equation is assumed to be the system model. The finite element method (FEM) applied to complex systems, usually results large dimensional models, and as the model dimension becomes larger and larger, controller design algorithms require more and more computation time and start to have numerical problems. To overcome these problems, there are two main research directions: Decentralized and substructural type approaches. In this paper, we adopt a substructural type approach based on the static condensation principle, and study the H_∞ optimal controller design for nonlinear and fuzzy structures. The key point in our approach is doing the static condensation in the abstract state space for linearized models of nonlinear systems and use fuzzy control techniques for nonlinearities. Working with linearized models allows to formulate the problem as a convex optimization one expressed as Linear Matrix Inequalities (LMIs). Because of reduced problem size and hence reduced dimensions of the matrices involved, computation time is reduced and numerical reliability is increased. The proposed method is illustrated on several benchmark problems.