Stabilization of Unstable Distributed Port-Hamiltonian Systems in Scattering Form
—In this letter, we consider the exponential stabilization of a distributed parameter port-Hamiltonian system interconnected with an unstable finite-dimensional linear system at its free end and control input at the opposite one. The infinite-dimensional system can also have in-domain anti-damping. The control design passes through the definition of a finite-dimensional linear system that “embeds” the response of the distributed parameter model, and that can be stabilized by acting on the available control input. The conditions that link the exponential stability of the latter system with the exponential stability of the original one are obtained thanks to a Lyapunov analysis. Simulations are presented to show the pros and cons of the proposed synthesis methodology.
Modelling and control of an IPMC actuated flexible structure: A lumped port Hamiltonian approach
This paper deals with the finite dimensional modelling and control of an electro-active polymer (EAP) actuated flexible structure. This model reproduces the basic mechanical properties of a class of one dimensional flexible endoscope. The flexible structure and the EAP actuator are both modelled as port-Hamiltonian systems. The EAP actuator is interconnected with the flexible structure in a power preserving manner such that the global system is again a PHS. Using the obtained model, two passivity based control strategies are applied to derive the controllers which achieve a desired equilibrium configuration with desired dynamic behaviour. An experimental benchmark composed of the Ionic Polymer Metal Composites patches glued to a flexible beam is used to validate the proposed model and control law.
