Modal decoupling conditions for distributed control of flexible structures

Abstract

Introduction T problem of the control of distributed parameter systems can be roughly divided into two approaches: 1) discretize the system in space and then use finite dimensional control theory; and 2) deal with the distributed model directly without discretizing. Recently, Meirovitch and Baruh proposed a scheme for the optimal control of a certain class of conservative distributed parameter systems without resorting to discretization. In particular, they treated the control of self-adjoint conservative systems having known eigensolutions. It is the intent of this Note to point out that their results are applicable to a more general class of problems that includes nonconservative forces and to note that the necessary conditions are available for the existence of decoupling control laws. Decoupling control laws are defined to be those control laws dependent only on the modal state vector of the decoupled equation. This yields an infinite set of independent equations including the feedback control. The use of decoupled controls allows the distributed parameter control problem to be solved by the independent modal-space control method. This method allows each mode to be designed independently of other modes. As a result, the standard control problems involving optimal control and the regulator problem can be solved without difficulty. This method of control is not discussed in detail here, but is mentioned to supply motivation and application for the results that follow.