Passivity-Based Control is a widely recognised control design methodology that has been successfully applied to solve regulation control problems for Port-Controlled Hamiltonian systems. However, the problem of stabilising time-varying trajectories is a topic that still requires further research, in particular for underactuated systems, i.e. systems with fewer control inputs than generalised coordinates. The purpose of this paper is to contribute to the consolidation of this control technique to solve tracking control problems for underactuated Port-Controlled Hamiltonian systems by identifying a novel class of systems for which it is possible to solve the tracking problem. This class is characterised by a quadratic Hamiltonian function and state-dependent interconnection and damping matrices that generate quadratic nonlinearities. It is shown that the desired time-varying trajectories exhibit asymptotic stability properties by applying well-known and simple Lyapunov-based results from the nonlinear systems theory. The usefulness of the contribution is illustrated in a numerical setting by approaching two case studies of practical interest, namely: the three-dimensional Lorenz oscillator system and the model of a surface-mounted Permanent Magnet Synchronous Motor.

The Port-Hamiltonian formalism has demonstrated to be useful in different applications, allowing to explore structural properties to obtain stable controls. A common approach is to design controls in a continuous domain although, in practice, they are implemented in discrete time. However, the study of discrete-time port-Hamiltonian systems is challenging since the system may lose structural properties such as passivity after discretization. This paper shows that passivity is conserved for the backward Euler discretization method when the Hamiltonian is convex, and its gradient is Lipschitz. This result is relevant for power systems applications such as the control of two-area systems, high-voltage direct-current transmission, and microgrids. Although our method is simple and preserves passivity, it does not preserve the symplectic structure of the hamiltonian. Copyright (C) 2024 The Authors.

This paper presents a Hamiltonian model of a direct current microgrid consisting of rectifiers connected in parallel in closed-loop with a Droop-type power-sharing algorithm. The main contribution is to demonstrate that a discretization using the backward Euler method preserves the microgrid’s Hamiltonian structure and passivity properties with a simple implementation of the method. The results are numerically evaluated by comparing the backward and forward Euler methods.

This paper presents a stability analysis for inverter-based renewable resources in multi-converter power systems. Stability conditions are obtained based on the port-Hamiltonian structure of the droop control in grid-forming converters. We show that conventional grid-forming converters have a port-Hamiltonian structure in the multi-converter power system. A simple and direct estimation of the region of attraction is obtained. In addition, we proposed droop control with an angle feedback that ties two converters in order to improve transient response. This control maintains the port-Hamiltonian structure and hence the stability properties of the conventional droop. Numerical experiments show the accuracy of the model and the superior performance of the proposed control.

This paper explores a Passivity-based Control scheme for islanded AC microgrids with detailed power converter dynamics. In contrast to the usual practice, it is proposed to include in the controller design the required power of the loads and the available power of the Distributed Energy Resources by means of a dynamical system whose trajectories asymptotically converge to the solution of the power flow equations. The stability properties of the closed-loop system are formally proved while its usefulness is illustrated numerically.

In this paper, the control problem of microgrids (MGs)operating in islanded mode is approached from a passivity-based control perspective. A control scheme is proposed that, relying only on local measurements for the power converters included in the network representation, achieves both voltage regulation and power balance in the network through the generation of grid-forming and grid-following nodes. From the mathematical perspective, the importance of the contribution lies in the feature that, exploiting a port-controlled Hamiltonian representation of the MG, the closed-loop system's stability properties are formally proved using arguments from the theory of non-linear dynamical systems. Fundamental for this achievement is the decomposition of the system into subsystems that require a control law and another whose variables can evolve in a free way. From the practical viewpoint, the advantage of the proposed controller lies in the feature that the power demanded by the loads is satisfied without neither computing its specific value nor solving the non-linear algebraic equations given by the power flow, avoiding the computational burden associated with this task. The usefulness of the scheme is illustrated via a numerical simulation that includes practical considerations.

In this paper, the stability properties of a microgrid in closed-loop with local inverters’ controllers and a droop power-sharing scheme are studied. The main result is the formal statement that this system is asymptotically stable concerning the equilibrium point that satisfies desired operating conditions. In contrast to the results reported in the literature, neither the stability analysis of the inverter’s dynamics is omitted, nor is it assumed that the only dynamic behavior is that corresponding to the droop scheme. The contribution exploits the inclusion of a passivity-based control law for the inverters and the input-to-state stability properties exhibited by the considered droop algorithm. The validity of the analysis is illustrated via a numerical evaluation.

In this paper, the control problem of Islanded Microgrids is approached. A controller scheme that considers the necessity to assure the generation of grid-forming nodes as well as the proper operation of grid-following nodes is proposed. The main feature of the contribution is the explicit inclusion of the dynamic of the power converters existing in this kind of networks making possible the evaluation of the system performance under sudden and fast changes in the operating conditions typically found in these applications. The scheme uses only the measurement of local variables and guarantees that both voltages and currents of the network achieve the values required to satisfy a prescribed power balance imposed by the loads. The design of the proposed controller is carried out by exploiting a Port-Controlled Hamiltonian representation of the system and applying the Passivity-based Controller design methodology. The stability properties of the closed-loop system are formally proved and its usefulness is illustrated via numerical simulations.

This article introduces an energy-based approach for modeling water distribution networks with faults. The flow in each network pipeline is described by the rigid water column model (RWC), which can be obtained by assuming that the walls of the pipelines are rigid and the flow is incompressible. The key feature of the proposed approach is the modeling of the interactions of the network components (pipelines, faults, and sources), which is done through the use of the graph theory and from an energy point of view. Three examples are given: a pipeline with a partial blockage, a pipeline with a leak, and a pipeline with both faults. The models resulting from this approach can be used for the implementation of realtime applications, for example, for fault diagnosis or for control of valves and pumps in case of faults.

En este artículo se presenta el diseño y la aplicación de la teoría de control basada en pasividad para la integración de recursos energéticos distribuidos (REDs) a través de convertidores controlados por voltaje en redes monofásicas de corriente alterna. La representación Hamiltoniana de estos sistemas facilita el desarrollo de controladores pasivos que garantizan estabilidad en el sentido de Lyapunov para su operación en lazo cerrado. El modelado dinámico no autónomo de estos sistemas es transformado en un modelo incremental, el cual permite resolver el problema de seguimiento de trayectorias como un problema de regulación. La principal contribución de este trabajo radica en la capacidad de controlar el flujo de potencia activa y reactiva entre los REDs y la red eléctrica en función de la disponibilidad del recurso energético primario y la capacidad de los convertidores. Los resultados de simulación muestran que todos los controladores pasivos propuestos logran el objetivo de control, alcanzando el mismo desempeño dinámico que los controladores proporcionales integrales clásicos, garantizando estabilidad asintótica. Todas las simulaciones son desarrolladas bajo el entorno MATLAB/Simulink a través de la librería SimPowerSystems.

Using a well-known Passivity-based controller, in this paper is considered a stabilization scheme that explicitly includes the structure of the network and the dynamics of the power converters, features that are not usually found in the reported results. In addition, a procedure that does not rely on the solution of power flow equations is presented, guaranteeing satisfaction of load power demand with a limited capacity of some of the sources. The usefulness of the proposed control strategy is illustrated via a numerical evaluation although it is also recognized that further work is required in order to fully formalize their properties.

This express brief presents the stability analysis of single-phase microgrids (SP-MG) operating under master-slave connection with constant power terminals. The SP-MG is composed of linear elements, nonlinear loads, and distributed generators modeled as PQ constant terminals interconnected through power electronic converters. Lyapunov's direct method through a Hamiltonian representation of the grid is used to demonstrate stability. The non-autonomous model of the SP-MG is transformed into an autonomous equivalent model based on the dynamics of the error. The proposed analysis shows that if there is an admissible trajectory x* solution of the power flow equations, then the SP-MG is stable in the sense of Lyapunov.

Motivated by the growing interest on microgrids, in this paper, it is presented a numerical evaluation of some robustness properties of a previously reported passivity-based control law. The main feature of the approached controller is that, unlike commonly reported in the literature, dynamics of the power converters are included. Hence, a local control for the power converters is considered and complemented with a secondary control of the well-known droop type, where instead of measuring all the buses powers, as indicated in the original version of the microgrid controller, a state-estimation scheme is included to generate the information required by the former. The estimator allowed to incorporate measurement noise and showed the good performance of the controller in a more realistic scenario.

Microgrids are a special kind of power systems that offer an attractive alternative for sustainable power supply. However, their power electronics based operation still imposes several challenges from a control point of view. This feature usually has been simplified under two main conditions, namely: it is assumed the existence of power converters controllers that decouples the command of the amplitude and frequency of their output voltage and it is assumed that the network operates under a sinusoidal regime. In this paper, exploiting the Hamiltonian structure exhibited by the network, a distributed control scheme is developed for a Mesh Microgrid including the dynamic of the power converters and without assuming a steady state operation. This stabilization result is attained guaranteeing the dispatch of prescribed active and reactive power values.

We study under-actuated Lagrangian systems without dissipative forces, augmented by a chain of integrators. For such systems, we solve the open problem of global tracking control via position measurements only; strictly speaking, we establish uniform global asymptotic stability for the closed loop system. As a corollary, we obtain an original statement for flexible-joint robots, which closes a long-standing open problem of output feedback nonlinear control.

We solve the open problem of global tracking control of 2nd-degree under-actuated lossless (without friction) Lagrangian systems via position measurements only. For flexible-joint robots, we design a dynamic controller which is based on measurements of link and joint positions only. Then, approximate differentiation is used for link velocities and a simple Luenberger observer for rotor velocities. The main results constitute a significant extension of recent work on observerless output-feedback control of Lagrangian systems. Strictly speaking, we establish uniform global asymptotic stability for the closed loop system.

The characterization of a class of electrical circuits is carried out in terms of both stability properties and steady-state behavior. The main contribution is the interpretation of the electrical topology (how the elements that conform the circuits are interconnected) in terms of mathematical properties derived from the structure of their models. In this sense, at what extent the topology by itself defines the dynamic behavior of the systems is explained. The study is based on the graph theory allowing capturing, departing from the well-known Kirchhoff laws, the topology of the circuits into several matrices with specific structure. The algebraic analysis of these matrices permits identifying conditions that determine whether the system is stable in the sense of Lyapunov and the kind of steady-state behavior that it exhibits. The approach is mainly focused on typical topologies widely used in practice, namely, radial, ring, and mesh networks.

In this paper stability and consensus on electrical circuits is approached. The novelty of the presented results lies in the fact that, contrary to the usual practice of establishing these properties for a given circuit, generic features of this class of networks are interpreted in terms of interconnections of the circuit elements to conceive specific topologies for which both stability and consensus are guaranteed. Fundamental for this achievement is the Hamiltonian structure exhibited by the circuits, since the features enjoyed by this kind of dynamical systems allow to systematically state the structural (interconnection) properties under which stability is assured while conditions to conclude consensus are derived from the analysis of its equilibria.

We present a controller for flexible-joint robots without link velocity measurement. Our main result consists in a simple controller of the type proportional-derivative plus feedforward and a series of cascaded filters; the control design is reminiscent of classical backstepping control. To avoid the assumption that link velocities, accelerations and jerks are measured, we use approximate differentiation. The originality of our work lays in establishing uniform global asymptotic stability for the closed-loop system.

SUMMARY We contribute with a linear time‐varying controller for the permanent magnet synchronous motor. We solve the open problem of speed‐tracking control by measuring only stator currents and the rotor angular positions, under parametric uncertainty. Integral action is used to compensate for the effects of the unknown load‐torque, and adaptation is employed to estimate the unknown parameters. In the case that parameters are known (except for the load), we show that the origin of the closed‐loop system is uniformly globally exponentially stable. For the case of unknown parameters, we prove uniform global asymptotic stability; hence, we establish parametric convergence. In contrast to other adaptive control schemes for electrical machines, we use a reduced‐order adaptive controller. Indeed, adaptation is used only for the electrical dynamics equations. Moreover, not surprisingly, the closed‐loop system has a structure well‐studied in adaptive‐control literature. Performance is illustrated in a numerical setting. Copyright © 2013 John Wiley & Sons, Ltd.