Stabilization of Mechanical Structures With Distributed Sensors and Actuators: A Hamiltonian Approach

Intelligent mechanical structures based on piezoelectricity form an important new group of actuators and sensors for active vibration control. Since this technology allows to construct spatially distributed devices, new design possibilities for the control systems open up. Now the design of the spatially distributed sensors and actuators becomes part of the controller design itself. Several well established approaches, like the PD-, H2- and H∞-design are adapted to solve this problem. They are based on infinite dimensional Hamiltonian systems in conjunction with collocated actuator and sensor pairing. Since this approach is based on the so called Poisson bracket only, one can unify the controller design for finite and for infinite dimensional systems. Of course, the stability investigations are much more complicated in the latter case. Finally, applications to beams and plates demonstrate the power and effectiveness of the proposed methods.