Title :
Time-varying port-representation of dissipative structures with gauge transformations
Author :
Nishida, Gou ; Yamakita, Masaki ; Zhi-wei Luo
Author_Institution :
Bio-Mimetic Control Res. Center, RIKEN(The Inst. of Phys. & Chem. Res.), Nagoya, Japan
Abstract :
A distributed-port-Hamiltonian system is a generalized model for passivity-based controls. The system representation has been extended to an infinite-dimensional conservative system derived from variational calculus, which is called a field-port-Lagrangian system. A lot of practical systems for control engineering include dissipative elements; however such a non-conservative structure usually cannot be defined by a variational problem. This paper shows that a system with the dissipative structure can be defined as a time-varying fieldport-Lagrangian system by a gauge transformation. First, we show that the gauge transformation generates a time-dependent Lagrangian density functional that introduces the time-varying port-representation. Next, we present that a class of dissipative systems can be identified with a conservative system possessing an internal irreversible energy flow. Finally, we illustrate an equation of elastic films with viscosity damping with the time-varying port-representation.
Keywords :
distributed parameter systems; multidimensional systems; time-varying systems; variational techniques; control engineering; dissipative element; dissipative structure; dissipative system; distributed-port-Hamiltonian system; elastic film; field-port-Lagrangian system; gauge transformation; generalized model; infinite-dimensional conservative system; internal irreversible energy flow; nonconservative structure; passivity-based control; practical system; system representation; time-dependent Lagrangian density functional; time-varying fieldport-Lagrangian system; time-varying port-representation; variational calculus; variational problem; viscosity damping; Damping; Equations; Indexes; Mathematical model; Time-varying systems; Vectors; Viscosity; Algebraic/geometric methods; Distributed parameter systems; Nonlinear systems;
Conference_Titel :
Control Conference (ECC), 2007 European
Conference_Location :
Kos
Print_ISBN :
978-3-9524173-8-6