1,354,209 research outputs found
Port-based Simulation of Flexible Multi-body Systems
No full textThis paper is devoted to simulation aspects of complex multi-body systems resulting from the interconnection of rigid and flexible links. This work is the natural complement of Macchelli et al. [2006, 2007a], in which only the mathematical modeling aspects of such kind of devices have been discussed. This paper tries to show how the port Hamiltonian framework can be instrumental also for the easy implementation of efficient simulations if proper packages able to deal with the a-causality of port-based modeling techniques are used. In fact, once the main components (i.e. rigid and flexible links and kinematic pairs) have been created, the complete model just follows by port interconnection in a plug-and-play fashion. Then, it is the simulation engine that solves the causality of the overall scheme and generate the simulation code. The main steps are illustrated in detail with an example
On the Synthesis of Discrete-time Energy-based Regulators for Port-Hamiltonian Systems
No full textThis paper aims at describing a synthesis procedure of discrete-time, energy-based regulators for continuous-time port-Hamiltonian systems. The methodology consists of three steps. The first twos deal with the definition of a discrete-time approximation of the plant to be successively employed in the development of the control law. Here, the focus is mainly on the last step, i.e. on how to interconnect digital controller and plant. The coupling is implemented via a zero-order hold and relies on the solution of an optimisation problem that determines the “best” and “minimal” correction to be applied to the nominal action to achieve the same performances obtained when the regulator is in closed-loop with the discrete-time model of the plant. This is the reference scenario used by the designer to develop and tune the control law. The procedure (time-discretisation, control design and coupling implementation) is illustrated in an example
Dirac Structures on Hilbert Spaces and Boundary Control of Distributed Port-Hamiltonian Systems
No full textAim of this paper is to show how the Dirac structure properties can be exploited in the development of energy-based boundary control laws for distributed port-Hamiltonian systems. Usually, stabilization of non-zero equilibria has been achieved by looking at, or generating, a set of structural invariants, namely Casimir functions, in closed-loop. Since this approach fails when an infinite amount of energy is required at the equilibrium (dissipation obstacle), this paper illustrates a novel approach that enlarges the class of stabilizing controllers. The starting point is the parametrization of the dynamics provided by the image representation of the Dirac structure, that is able to show the effects of the boundary inputs on the state evolution. In this way, energy-balancing and control by state-modulated source methodologies are extended to the distributed parameter scenario, and a geometric interpretation of these control techniques is provided. The theoretical results are discussed with the help of a simple but illustrative example, i.e. a transmission line with an RLC load in both serial and parallel configurations. In the latter case, energy-balancing controllers are not able to stabilize non-zero equilibria because of the dissipation obstacle. The problem is solved thanks to a (boundary) state-modulated source
Brayton-Moser formulation of high-order distributed port-Hamiltonian systems with one-dimensional spatial domain
No full textFor a class of distributed port-Hamiltonian systems with dissipation characterised by high-order differential operators, one-dimensional domain, and boundary actuation and sensing, an equivalent Brayton-Moser formulation is obtained. The result is that the state evolution is described by a gradient equation with respect to a storage function, the "mixed-potential," that has the dimensions of power. This is the main difference with respect to the port-Hamiltonian form, where the dynamic depends on the derivatives up to a certain order and with respect to the spatial coordinate of the gradient of the Hamiltonian function, i.e. of the total energy. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved
Distributed-Parameter Port-Hamiltonian Systems in Discrete-Time
No full textThis paper presents a design framework of discrete-time regulators for linear, port-Hamiltonian, boundary control systems. The contribution is twofold. At first, a discrete-time approximation of the plant dynamics originally described by a linear PDE with boundary actuation is introduced. The discretisation is performed in time only. Thus, the 'distributed nature' of the state is maintained. Such a system inherits the passivity of the original one and is well-posed, namely the 'next' state always exists. The second result is the characterisation of discrete-time, linear controllers in the port-Hamiltonian form that render the closed-loop dynamics asymptotically stable. A numerical example illustrates the effectiveness of the proposed framework
Distributed control for infinite dimensional port-Hamiltonian systems
No full textThe aim of the paper is twofold. At first, a class of autonomous port-Hamiltonian systems whose dynamic is described by coupled PDEs and (nonlinear) ODEs is presented, and some properties (i.e., well-posedness and asymptotic stability of the origin) investigated. Secondly, an energy-based control design methodology is discussed. The finite-dimensional subsystem is equipped with an input, and a procedure for designing a state-feedback control action that maps the open-loop dynamic to a target one still in port-Hamiltonian form is illustrated. The idea is that the corresponding error system meets the requirements regarding the asymptotic stability of the origin stated in the first part of the paper. In this way, asymptotic convergence of the trajectories to the desired equilibrium configuration can be proved
Dirac structures and control by interconnection for distributed Port-Hamiltonian systems
No full textThe aim of this work is to show how the Dirac structure properties can be exploited in the development of energy-based boundary control laws for distributed port-Hamiltonian systems. Stabilisation of non-zero equilibria has been achieved by looking at, or generating, a set of structural invariants, namely Casimir functions, in closed-loop, and geometric conditions for the problem to be solved are determined. However, it is well known that this method fails when an infinite amount of energy is required at the equilibrium (dissipation obstacle). So, a novel approach that enlarges the class of stabilising controllers within the control by interconnection paradigm is also discussed. In this respect, it is shown how to determine a different control port that is instrumental for removing the intrinsic constraints imposed by the dissipative structure of the system. The general theory is illustrated with the help of two related examples, namely the boundary stabilisation of the shallow water equation with and without distributed dissipation
Boundary Energy Shaping of Linear Distributed Port-Hamiltonian Systems
No full textThis paper deals with the stabilization via Casimir generation and energy shaping of linear, lossless, distributed port-Hamiltonian systems. Once inputs and outputs of the distributed port-Hamiltonian system have been chosen to obtain a well-defined boundary control systems, conditions for the existence of Casimir functions in closed-loop and of the associated semigroup are given, together with a criterion to be used to check asymptotic stability. Casimir functions suggest how to select the controller Hamiltonian to introduce a minimum at the desired equilibrium, while stability is ensured if proper "pervasive" boundary damping is present. The methodology is illustrated with the help of a Timoshenko beam with full-actuation on one side
Infinite-Dimensional Port-Hamiltonian Systems
No full textThis chapter presents the formulation of distributed parameter systems
in terms of port-Hamiltonian system. In the first part it is shown, for different examples of physical systems defined on one-dimensional spatial domains, how the Dirac structure and the port-Hamiltonian formulation arise from the description of distributed parameter systems as systems of conservation laws. In the second part we consider systems of two conservation laws, describing two physical domains in reversible interaction, and it is shown that they may be formulated as port-Hamiltonian systems defined on a canonical Dirac structure called canonical Stokes-Dirac structure. In the third part, this canonical Stokes-Dirac structure is generalized for the examples of the Timoshenko beam, a nonlinear flexible link, and the ideal compressible fluid in order to encompass geometrically complex configurations and the convection of momentum
Asymptotic stability of forced equilibria for distributed port-Hamiltonian systems
No full textThe main contribution of this paper is an energy shaping procedure for the stabilization of forced equilibria for linear, lossless, distributed port-Hamiltonian systems via Casimir generation. Once inputs and outputs have been properly chosen to have a well-posed boundary control system, conditions for the existence of Casimir functions in closed-loop are given, together with their relation with the controller structure. These invariants suggest how to select the controller Hamiltonian to introduce a minimum at the desired equilibrium. Such equilibrium can be made asymptotically stable via damping injection, if proper 'pervasive' damping injection conditions are satisfied. The methodology is illustrated with the help of a Timoshenko beam with constant non-zero force applied at one side of the spatial domain, and full-actuation on the other one
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