Synthesis of Boundary Control Laws for Distributed Port-Hamiltonian Systems

Friday, March 18, 2016 - 11:00am - 11:30am
Keller 3-180
Alessandro Macchelli (Universita Di Bologna)
In this talk, a general methodology for the synthesis of asymptotic and exponentially stabilising boundary control laws for a large class of linear, distributed port-Hamiltonian systems defined on a one-dimensional spatial domain is illustrated. The starting point is the energy-Casimir method in which the controller is a passive dynamical system that is interconnected to the boundary of the distributed parameter one. Despite the intrinsic limitations of the approach related to the so-called dissipation obstacle, it is shown how to compute a control action that shapes the closed-loop Hamiltonian to obtain desired stability properties. These considerations lead to the development of a more general passivity-based approach able to perform the energy-shaping task even for system with strong dissipation via state feedback. The idea is to obtain a closed-loop system still in port-Hamiltonian form, but characterized by a new Hamiltonian with an unique and isolated minimum at the desired equilibrium. Asymptotic stability for both methods is then obtained via damping injection at the boundary, while exponential stability is achieved by adding a further integral action.
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