3,254 research outputs found
Control by interconnection beyond the dissipation obstacle of finite and infinite dimensional port-Hamiltonian systems
No full textBy exploiting the properties of the geometric structure of a port-Hamiltonian system, a general methodology for the definition of a new control port that allows to solve the so-called dissipation obstacle within the control by interconnection framework is discussed. This approach can be applied to a large class of port-Hamiltonian systems, both in the lumped, and in the distributed parameter cases. It is also shown how the limitations of the control by interconnection and energy-shaping via Casimir generation can be removed by interconnecting the controller to a different control port, i.e. how it is possible to compute a new passive output that is instrumental for removing the intrinsic constraints imposed by the dissipative structure of the system
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
Control Design for a Class of Discrete-Time Port-Hamiltonian Systems
No full textThe paper aims at extending the continuous-time energy-shaping plus damping injection control design technique to deal with a class of nonlinear, discrete-time port-Hamiltonian systems. For such systems, the gradient of the Hamiltonian function in the continuous-time dynamics is replaced by a discrete gradient, thus leading to a state equation in implicit form. Its well-posedness is studied both in the autonomous and non-autonomous cases to determine when the dynamical equation admits a solution for the next state. Based on this analysis, the extension of the energy-shaping plus damping injection control methodology is discussed. At first, it is supposed that the control action depends on the discrete gradient of an energy function. Then, this hypothesis is removed, and an algebraic solution to the matching equation is proposed to enlarge the class of stabilising controllers
Brayton-moser formulation of infinite dimensional port-hamiltonian systems with application to boundary control
No full textIn this paper, for a class of distributed port-Hamiltonian systems defined on a one-dimensional spatial domain, an equivalent Brayton-Moser formulation is provided. The dynamic is expressed as a gradient equation with respect to a new storage function, the 'mixed-potential,' with the dimensions of power. The system is then passive with respect to a supply rate that is related to the reactive power, and that depends on the boundary port variables and on their time derivatives. This equivalent representation is the starting point for the development of boundary control laws able to shape the mixed-potential function. Differently from energy-balancing control schemes, this technique allows to deal with pervasive dissipation in the system in an effective way. The general theory is illustrated with the help of an example, the boundary stabilisation of a transmission line with internal dissipation
On the control by interconnection and exponential stabilisation of infinite dimensional port-Hamiltonian systems
No full textThis paper aims at illustrating how the control by interconnection methodology (energy-Casimir method) can be employed in the development of exponentially stabilising boundary control laws for a class of linear, distributed port-Hamiltonian systems with one dimensional spatial domain. The energy-Casimir method is the starting point to determine a state-feedback law able to shape the closed-loop Hamiltonian and achieve simple stability. Then, it is shown how to design a further control loop that guarantees exponential convergence. Thanks to this result, it is possible to overcome a limitation of standard damping injection strategies that, if combined with energy shaping control laws based on energy-balancing, are able to assure, in general, only asymptotic convergence. The methodology is illustrated with the help of a simple example, the boundary stabilisation of a lossless transmission line
A Discrete-Time Formulation of Nonlinear Distributed-Parameter Port-Hamiltonian Systems
No full textThis paper introduces a new framework of nonlinear, discrete-time, boundary control systems (BCSs) in the port-Hamiltonian form. The contribution is twofold. We start with a discrete-time approximation of a nonlinear port-Hamiltonian BCS, i.e. a dynamical system modelled by a nonlinear partial differential equation with boundary actuation and sensing. The most important feature is that the discretisation is performed in time only so that the “distributed nature” of the state is preserved. By approximating the gradient of the Hamiltonian density with its discrete gradient, the obtained sampled dynamics inherit the passivity of the original one. Besides, we prove that, under mild conditions, it is well-posed, i.e. the “next” state always exists. The second contribution deals with control design. More precisely, we have determined sufficient conditions for the plant dynamics and a static output feedback gain to make the closed-loop system asymptotically stable
Trajectory Tracking for Discrete-Time Port-Hamiltonian Systems
No full textThis letter presents a regulator for nonlinear, discrete-time port-Hamiltonian systems that lets the state track a reference signal. Similarly to continuous-time approaches, the synthesis is based on the mapping via state-feedback of the open-loop error system to a target one in port-Hamiltonian form, and with an asymptotically stable origin that corresponds to the perfect tracking condition. The procedure is formally described by a matching equation that, in continuous-time, turns out to be a nonlinear partial differential equation (PDE). This is not the case for sampled-data systems, so an algebraic approach is proposed. The solution is employed to construct a dynamical regulator that performs an “approximated” mapping. The stability analysis relies on Lyapunov arguments
Control by Interconnection of Mixed Port Hamiltonian Systems
No full textIn this note, the regulation problem for mixed finite and infinite dimensional port Hamiltonian systems (m-pH systems) is discussed. A m-pH system results from the power conserving interconnection of finite and infinite dimensional systems in port Hamiltonian form. In particular, the system given by the interconnection of two finite dimensional systems, one of which is the controller, by means of an infinite dimensional connection is studied. The proposed control methodology is a generalization to the infinite dimensional case of a well-established passivity-based control technique for finite-dimensional port Hamiltonian systems, the control by interconnection and energy shaping, according to which the open-loop energy function is shaped so that a minimum in the desired configuration is introduced. This procedure is possible once the state variable of the controller is related to the state variable of the plant by constraining the state of the closed-loop system on a structural invariant (defined by a set of Casimir functions). In this way, the energy function of the controller, which is freely assignable, becomes a function of the configuration of the plant and, then, it can be easily shaped in order to solve the regulation problem
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
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