This paper describes a detailed design procedure for passivity-based controllers developed using the Brayton-Moser framework. Several passivity-based feedback designs are presented for the Voltage-Source Converter, specifically for the H-bridge converter, since nowadays it is one of the preferred solutions to connect direct current (dc) loads or distributed sources to the alternating current (ac) grid. Independent of the operating mode, namely, the rectifier and regenerative operating mode, the achieved control aims are: high power-factor correction in the ac-side and optimal dc voltage regulation capability in the dc-side. The proposed controllers can use series or parallel damping-based solutions for the error dynamics, naturally providing the conditions for stability and tuning of control parameters. Moreover, the Brayton-Moser structure facilitates the addition of virtual RLC filter circuits to the control design for the rejection of low frequency harmonics. The effectiveness of series/parallel damping is investigated in case of abrupt changes in the load, using conductance estimators. Simulation and experimental results validate the analysis.

In this paper we study the stabilization problem of a general class of slow-fast systems with one fast and arbitrarily many slow states. Moreover, the class of systems under study is slowly actuated, meaning that only the slow states are subject to the action of a controller. Furthermore, we are particularly interested in the case where normal hyperbolicity is lost. We show that by using the Geometric Desingularization method, it is possible to design controllers to locally stabilize non-hyperbolic points of any finite degeneracy. The main novelty of this paper is that, unlike previous research on the topic, we make use of more than one chart of the blow up space to enhance the region of attraction of the operating point. A couple of numerical examples highlight our contribution.

Non-hyperbolic points of slow-fast systems (also known as singularly perturbed ordinary differential equations) are responsible for many interesting behavior such as relaxation oscillations, canards, mixed-mode oscillations, etc. Recently, the authors have proposed a control strategy to stabilize nonhyperbolic points of planar slow-fast systems. Such strategy is based on geometric desingularization, which is a well suited technique to analyze the dynamics of slow-fast systems near non-hyperbolic points. This technique transforms the singular perturbation problem to an equivalent regular perturbation problem. This papers treats the nonlinear adaptive stabilization problem of slow-fast systems. The novelty is that the point to be stabilized is non-hyperbolic. The controller is designed by combining geometric desingularization and Lyapunov based techniques. Through the action of the controller, we basically inject a normally hyperbolic behavior to the fast variable. Our results are exemplified on the van der Pol oscillator.

No abstract

In this paper an algorithm for solving the Optimal Power Flow problem for multi-terminal DC networks based on the gradient method is proposed. The aim is seeking the optimal point subject to voltage, current and power constraints. The algorithm is described by a continuous-time port-Hamiltonian model, and the inequality constrains are included by the use of barrier functions. The dynamics of the algorithm is studied and stability conditions are obtained. Finally, the method is used for the offshore wind integration grid in the North Sea and the interconnection with the network dynamics is tested by means of numerical simulations.