4 substructural control approach is presented in the control design of large periodic structures with identically repeating substructures. The approach makes use of wave propagation concepts in structural vibrations. After noting relations between vibrational displacements of a large periodic structure, the substructural controller, designed for a reference substructure, is used to assemble the global controller for the entire structure. The accuracy of the method is verified with the example of the control design of a large periodic structure consisting of 9 repetitive substructures. Since only a typical repeating substructure, the reference substructure, is used for the global control design, the technique is expected to be very attractive for the control design engineers of large periodic structures. 0 1997 Elsevier Science Ltd.
NOTATION system matrix input matrix in state space input matrix in configuration space control force vector reaction force vector Extrformance index wave phase change dynamic stiffness matrix typical structure length in x-direction mass matrix solution -matrix to algebraic Riccati equation state weighting matrix input weighting matrix stiffness matrix transformation matrix displacement vector state vector eigenvalue eigenvalue matrix circular frequency du/dt