Control of propagating waves in rods by piezoelectric actuators and sensors

This paper deals with active control of propagating waves in rods. The mechanical models under consideration are characterized by hyperbolic equations with source terms. The latter ones describe the control or disturbance inputs. Piezoelectric layers are used as actuators and sensors to affect the dynamic behavior of the system. The controller design is based on the theory of Lagrangian systems with inputs. One can show that a special pairing of the actuators and sensors simplifies the controller design significantly, but this approach requires a specific design of the actuators and sensors. Smart structures based on piezoelectricity allow to construct spatially distributed devices, which are the prerequisites for the realization of so designed control laws.