Mathematical structures in the network representation of energy-conserving physical systems

It is shown that network modelling of energy-conserving physical systems naturally leads to the consideration of (nonlinear) implicit generalized Hamiltonian systems. Behavioral systems theory may be invoked to formulate and analyze the system-theoretic properties of these systems.

Nonlinear Model-Based Control of Unstable Wells

This paper illustrates the potential of nonlinear model-based control applied for stabilization of unstable flow in oil wells. A simple empirical model is developed that describes the qualitative behavior of the downhole pressure during severe riser slugging. A nonlinear controller is designed by an integrator backstepping approach, and stabilization for open-loop unstable pressure setpoints is demonstrated. The proposed backstepping controller is shown in simulations to perform better than PI and PD controllers for low pressure setpoints, and is in addition easier to tune. Operation at a low pressure setpoint is desirable since it corresponds to a high production flow rate. The simulation results are presented to illustrate the effectiveness of proposed control scheme

Variational and Geometric Structures of Discrete Dirac Mechanics

In this paper, we develop the theoretical foundations of discrete Dirac mechanics, that is, discrete mechanics of degenerate Lagrangian/Hamiltonian systems with constraints. We first construct discrete analogues of Tulczyjew's triple and induced Dirac structures by considering the geometry of symplectic maps and their associated generating functions. We demonstrate that this framework provides a means of deriving discrete Lagrange-Dirac and nonholonomic Hamiltonian systems. In particular, this yields nonholonomic Lagrangian and Hamiltonian integrators. We also introduce discrete Lagrange-d'Alembert-Pontryagin and Hamilton-d'Alembert variational principles, which provide an alternative derivation of the same set of integration algorithms. The paper provides a unified treatment of discrete Lagrangian and Hamiltonian mechanics in the more general setting of discrete Dirac mechanics, as well as a generalization of symplectic and Poisson integrators to the broader category of Dirac integrators.Comment: 26 pages; published online in Foundations of Computational Mathematics (2011

A Hamiltonian Framework For Interconnected Physical Systems

In the present paper we elaborate on the underlying Hamiltonian structure of interconnected energyconserving physical systems. We show how these systems can be described as implicit generalized Hamiltonian systems (with and without external inputs) using the notion of a generalized Dirac structure. Fundamental mathematical questions concerning the representation and integrability of implicit generalized Hamiltonian systems are addressed. 1 Introduction Modelling of (complex) physical systems such as multibody systems naturally leads to a mathematical description involving differential and algebraic (constraint) equations. As shown in [10, 11], in the case of energyconserving physical systems the resulting set of DAE's has an inherent Hamiltonian structure. Indeed, the network topology of the system determines a geometric structure, called a generalized Dirac structure, the total energy stored in the system defines a Hamiltonian function on the space of energy variables, and together ..