Disturbance rejection via control by interconnection of port-Hamiltonian systems

Abstract

In this paper we present a new result on rejection of unmatched external disturbances on port-Hamiltonian systems using Control by Interconnection (CbI). The PHS structure is used to design a controller that rejects unmatched constant disturbances from non-passive outputs. In the PHS framework, the disturbance rejection problem has been addressed adding integral action and using a change of coordinates. In our approach, we avoid a change of coordinates keeping the original state vector, which contains variables with physical interpretation. The methodology proposed in this paper is illustrated on an electrical circuit and on a permanent magnet synchronous motor. Simulation of the later example shows the performance of the control design.

Integral Control of Port-Hamiltonian Systems: Nonpassive Outputs Without Coordinate Transformation

“…Proposition 1: Consider system (10) subject to unknown, matched disturbance in closed loop with the controller (11). Then, under Assumptions 1-6, the equilibrium of the closed loop, corresponding to the gradient (16), is globally asymptotically stable.…”

Conditions on shifted passivity of port-Hamiltonian systems

“…In [5] it is shown that pH systems with convex Hamiltonian are also shifted passive provided the input, dissipation and interconnection matrices are all constant. Conditions for shifted passivity of pH systems with state-dependent matrices have been reported in [6] and [21]. In the former case, quite conservative, integrability conditions, are imposed while the latter ones are too general and thus can be difficult to verify.…”

Matched disturbance rejection for energy-shaping controlled underactuated mechanical systems

“…In addition, the control system studied in [14] has a physical interpretation and is shown to be equivalent to a control by interconnection (CbI) scheme, another PBC technique [15]. The method in [13] was shown to be applicable to mechanical systems with constant mass matrix.…”

“…In this paper, we extend the integral action design proposed in [13] to underactuated mechanical systems subject to matched disturbances. The assumption of a constant mass matrix is relaxed, and general mechanical systems are considered.…”