Structure preserving reduction of port hamiltonian system using a modified LQG method

This paper proposes a controller reduction method for the port Hamiltonian system by using a modified LQG method. We first use the LQG method to design two passive type controllers which are equivalent to the control of port Hamiltonian system by interconnection. One of these LQG type method permit us to define a LQG balanced realization by computing its LQG Grammians. Then we use the effort-constraint method to achieve a reduced order port Hamiltonian system and design a reduced order passive type LQG controller. Finally, the method is illustrated on a mass-spring system by numerical simulations of the closed loop system with the full order passive LQG controller and with its reduced order controller.