Improving the robustness of Hamiltonian passive control

Abstract

Interconnection and damping assignment passivity based control (IDA-PBC) is a well know technique for port Hamiltonian dissipative systems (PHDS). In this paper we point out the kind of problems that can appear in the closed-loop structure obtained by IDA-PBC methods for relative degree one outputs, when nominal values are used in a system with uncertain parameters. In particular, we show that, in general, the positive semidefiniteness of dissipation matrix breaks down, at least, in a neighborhood of the desired regulation point, preventing thus the use of LaSalle’s theorem. Nevertheless, we present an example where the closed-loop system regulates to a fixed point, albeit different from the desired one. To correct this, we introduce an integral control, which can be cast into Hamiltonian framework. Numerical simulations for our example show that the closed-loop system regulates to the desired point, although a rich dynamical behaviour is obtained when the feedback parameters are varied.