Closed-loop actuator and sensor location selection strategies for flexible structures

Abstract

In this thesis, the problem of finding the optimal actuator and sensor locations for vibration control of a flexible structure is studied. An iterative search strategy is used, where the closedloop criteria are selected as the optimization metric. During iterations approximate coprime or low-authority H-infinity-controllers are designed, or alternatively quasi-controller method (residual deformations norm minimization) is used, which does not directly calculate controller but obtains some norms that instead approximate the closed-loop behavior well. In applications with controllers, the controller design is simplified by introducing simple approximate Algebraic Riccati Equation solutions and their derivatives, which are obtained by converting the state space descriptions of the physical system with signal weights into state space representations with decoupled block diagonal state matrices. Hence, based on such approximate solutions, it is possible to design computationally less complex controllers with less computational effort. Since for gradient based search techniques, the partial derivatives of the closed-loop criteria are required, Finite Element sensitivity analysis is utilized. The partial derivatives of the mass, stiffness and electromechanical coupling matrices are defined. Then, the partial derivatives of the open-loop and controller matrices are introduced. For plates with piezoelectric patches, the minimization procedure is enriched with constrained techniques, where Finite Element discretization is done automatically at iteration regarding the constraints. The modified constrained optimization technique is based on Zoutendijk's method and introduces constraints to avoid mesh generation of badly scaled finite elements