Global Optimization based on Mixed H2 and Hinf Approach for Placement of Piezoelectric Actuators and Sensors on Curved Surfaces in Actively Controlled Structures

The presence of actuators and sensors characterizes inevitably all operating processes in engineering, industry or applied research. Careful selection of the actuator/sensor placement can substantially improve performance of systems and contribute in turn to considerable savings. With respect to suppression of unwanted vibrations in lightweight structures by applying appropriate control, piezoelectric films represent convenient solution since they can be easily integrated with structures and due to their lightweight character they do not influence the overall mass of structures, but may contribute to changing stiffness in accordance with applied control and in that way actively perform adapting the structure's properties to changing environmental conditions. In this paper a global optimization procedure for placement of piezoelectric actuators and sensors on lightweight structures prone to vibration is presented. Optimization is model-based and assumes software-in-the-loop coupling of finite element numeric software with corresponding programming solutions to provide iterative exploration of a predefined set of candidate locations with respect to defined objective functions. The objective here is defined in terms of H₂ and H_∞ norms constructed upon the eigenforms of structures, which provides maximization of the control influence or maximal sensing effect. Implementation is illustrated by two examples of structures with curved surfaces - cylindrical and funnel shaped structure.