Design of Dynamical Controllers for Linear Hamiltonian Systems

Linear Hamiltonian control systems with collocation of sensor and actuator are considered. Based on a frequency domain approach a controller design algorithm is stated. The design leads to a controller with internal dynamics which uses the output of the system and its first time derivative. The presence of internal dynamics in the controller is an extension of the usual PD-control law and a main result of the work. The design is based on the special properties of the proposed class of systems. In particular, these Hamiltonian systems are passive. It is shown that the design leads to strictly passive controllers for a certain choice of the design parameters. This is another sigificant result and offers a way for robust L2-stabilization even in the case of infinte dimensional systems. Some features of the controller design are discussed with respect to an application, the control of a composite circular plate.