Design and Control of Adaptive Structures Using the Finite Element Method

Current work develops and presents a clear methodology for all stages of adaptive structure design using a commercially available FE program. A procedure for replacing the induced strain actuation of the piezo-elements by mechanical forces is developed and validated numerically using the ANSYS^R coupled field piezoelectric 3-D solid elements, as well as experimentally. The use of reduced FE analysis as a spatial discretization tool for controller design is addressed and shown to be advantageous in many cases. Balanced order reduction schemes are applied to the discrete structural model in state space in order to ensure controllability and observability, as well as to maintain a low number of states for the controller design and implementation. Linear quadratic (LQ) and H_∞ controller designs are presented and implemented using computer simulations of the controlled structure. The methodology is applied to a simply supported beam as a bench-mark case, and is shown to effectively control the beam vibrations.