port-Hamiltonian Framework Research Articles

Stabilisation of a Nonlinear Flexible Beam in Port-Hamiltonian Form

The aim of this paper is to present a simple extension of the theory of linear, distributed, port-Hamiltonian systems to the nonlinear scenario. More precisely, an algebraic nonlinear skew-symmetric term has now been included in the PDE. It is then shown that the system can be equivalently written in terms of the scattering variables, and that these variables are strictly related with the Riemann invariants that appear in quasi-linear hyperbolic PDEs. For this class of PDEs, several results about the existence of solutions, and asymptotic stability of equilibria have already been presented in literature. Here, these results have been extended and applied within the port-Hamiltonian framework, where are suitable of a nice physical interpretation. The final scope is the boundary asymptotic stabilisation of a nonlinear flexible beam with a free-end, and full actuation on the other side.

Discrete IDA-PBC design for 2D port-Hamiltonian systems

We address the discrete-time passivity-based control laws synthesis within port-Hamiltonian framework. We focus on IDA-PBC design for canonical port-Hamiltonian systems with separable energy being quadratic in momentum. For this class of systems, we define a discrete Hamiltonian dynamics that exactly satisfies a discrete energy balance. We then derive a discrete controller following the IDA-PBC procedure. The proposed methodology relies on an energy discretization scheme with suitable discrete conjugate port variables. The main result is illustrated on two examples: a nonlinear pendulum in order to compare with some simulation results of the literature, and the impact oscillator which requires robust discretization scheme.

Structure Preserving Adaptive Control of Port-Hamiltonian Systems

In this technical note, an adaptive control scheme is presented for general port-Hamiltonian systems. Adaptive control is used to compensate for control errors that are caused by unknown or uncertain parameter values of a system. The adaptive control is also combined with canonical transformation theory for port-Hamiltonian systems. This allows for the adaptive control to be applied on a large class of systems and for being included in the port-Hamiltonian framework.

A port-Hamiltonian approach to image-based visual servo control for dynamic systems

This paper introduces a port-Hamiltonian framework for the design of image-based visual servo control for dynamic mechanical systems. The approach taken introduces the concept of an image effort and provides an interpretation of energy exchange between the dynamics of the physical system and virtual potentials or ‘image Hamiltonians’ posed in the image space. The port-Hamiltonian framework leads to an elegant algorithm to estimate unknown image depth on-line even when the translational velocity of the camera is not measured.

Dynamic positioning of marine craft using a port-Hamiltonian framework

Dynamic positioning of marine craft refers to the use of the propulsion system to regulate the vessel position and heading. This type of motion control is commonly used in the offshore industry for surface vessels, and it is also used for some underwater vehicles. In this paper, we use a port-Hamiltonian framework to design a novel nonlinear set-point-regulation controller with integral action. The controller handles input saturation and guarantees internal stability, rejection of unknown constant disturbances, and (integral-)input-to-state stability.

A Class of Standard Mechanical System with Force Feedback in the port-Hamiltonian Framework

In this paper we show force feedback and position control of a class of standard mechanical system in the port-Hamiltonian framework. Furthermore, we show how to derive an extended port-Hamiltonian system with structure preservation which can be used for force feedback purposes besides providing the closed-loop system asymptotically stable. We also show the usefulness of the extended port-Hamiltonian system by showing its disturbance attenuation properties. Finally, we present simulation results obtained for the proposed control laws.

Port hamiltonian modeling of MSMA based actuator: toward a thermodynamically consistent formulation

This paper presents a thermodynamically consistent model of MSMA (Magnetic Shape Memory Alloys) under port Hamiltonian framework. It is based on previous works on MSMA proposed in (Gauthier et al., 2008; Calchand et al., 2011). The main difference lies in the choice of the state variables and manipulated thermodynamic forces. Furthermore in (Gauthier et al., 2008), subsequent experiments revealed a highly hysteretic behavior of these materials. Here, the simplified hysteretic behavior is incorporated into the port-hamiltonian model to obtain a finer and more precise model. Such modeling will allow the use of a wide range of energy based methods to design the associated control system. The paper ends with some extensions to more complex hysterestic phenomena by using Preisach like model. First ideas are proposed to extend the previous physical model to systems with internal hysteretic loops.

On port-Hamiltonian Modeling of the Synchronous Generator and Ultimate Boundedness of its solutions

In this paper starting with bond graph techniques a nonlinear mathematical model of the synchronous generator in port-Hamiltonian framework is derived. This leads to an energy–based description of the system which we later use for stability analysis. We use Park's state transformation to decouple the dynamics of other state variables from the dynamics of rotor angle, resulting in a quotient system admitting equilibria. We show that the solutions of this quotient system are bounded and provide closed form expression for the ultimate bound of these solutions. We will also give some preliminary results on stability analysis of these equilibria using energy shaping techniques.

On damping models preserving the eigenfunctions of conservative systems: a port-Hamiltonian perspective

In this paper, a special class of damping model is introduced for second order dynamical systems. This class is built so as to leave the eigenfunctions invariant, while modifying the dynamics: for mechanical systems, well-known examples are the standard fluid and structural dampings.In the finite-dimensional case, the so-called Caughey series are a general extension of these standard damping models; the damping matrix can be expressed as a polynomial of a matrix, which depends on the mass and stiffness matrices. Damping is ensured whatever the eigenvalues of the conservative problem if and only if the polynomial is positive for positive scalar values. This can be recast in the port-Hamiltonian framework by introducing a port variable corresponding to internal energy dissipation (resistive element). Moreover, this formalism naturally allows to cope with systems including gyroscopic effects (gyrators).In the infinite-dimensional case, the previous polynomial class can be extended to rational functions and more general functions of operators (instead of matrices), once the appropriate functional framework has been defined. In this case, the resistive element is modelled by a given static operator, such as an elliptic PDE. These results are illustrated on several PDE examples: the Webster horn equation, the Bernoulli beam equation; the damping models under consideration are fluid, structural, rational and generalized fractional Laplacian or bi-Laplacian.

Manoeuvring Control of Underactuated Surface Vessels using Manifold Regulation for Port-Hamiltonian Systems

This paper considers the manoeuvring of underactuated surface vessels. The control objective is to steer the vessel to reach a manifold which encloses a waypoint. A transformation of configuration variables and a potential field are used in a Port-Hamiltonian framework to design an energy-based controller. With the proposed controller, the geometric task associated with the manoeuvring problem depends on the desired potential energy (closed-loop) and the dynamic task depends on the total energy and damping. Therefore, guidance and motion control are addressed jointly, leading to model-energy-based trajectory generation.

Modeling of Systems With Position-Dependent Mass Revisited: A Port-Hamiltonian Approach

It is known that straightforward application of the classical Lagrangian and Hamiltonian formalism to systems with mass varying explicitly with position may lead to discrepancies in the formulation of the equations of motion. Systems with mass varying explicitly with position often arise from situations where the partitioning of a closed system of constant mass leads to open subsystems that exchange mass among themselves. One possible solution is to introduce additional nonconservative generalized forces that account for these effects. However, it remains unclear how to systematically interconnect the Lagrangian or Hamiltonian subsystems. In this note, systems with mass varying explicitly with position and their properties are studied in the port-Hamiltonian modeling framework. The port-Hamiltonian formalism combines the classical Lagrangian and Hamiltonian approach with network modeling and is applicable to various engineering domains. One of the strong aspects of the port-Hamiltonian formalism is that power-preserving interconnections between port-Hamiltonian subsystems results in another port-Hamiltonian system with composite energy and interconnection structure. The motion of a heavy cable being deployed from a reel by the action of gravity is used as an example.

Mastering the complexity of an Ultrasonic Sealing System: The port-Hamiltonian approach

This paper deals with the problem of simulating an Ultrasonic Sealing System (USS). The USS is a complex electromechanical system used to seal aseptic packages for liquid foods that is the core of the most advanced filling machines. Since the overall device is the result of the interconnection of several sub-systems that belong to different physical domains, the problem is tackled within the port-Hamiltonian framework, which is naturally multi-domain and multi-scale. On the other hand, the simulation of the whole sealing process is not a trivial task due to the presence of a Compact Transducer (CT) that can be modeled only by means of commercial finite-element software. Then, only extremely high-order models are available, which makes the simulation of the complete system impractical. Consequently, a novel model reduction procedure for port-Hamiltonian systems has been developed. The method is able to preserve the frequency behavior of the original system in a neighborhood of a predefined set of frequencies of interest. In this way, simulation times have been drastically shortened without loosing the essential dynamical information. The reduced order model can be adopted to test the validity of the controller, and to simulate and perform the diagnosis of the entire sealing process. The results of the model reduction algorithm have been experimentally validated. Moreover, also the complete USS model has been derived.

Reaction-Diffusion Systems in the Port-Hamiltonian Framework

Reaction-diffusion systems model the evolution of the constituents distributed in space under the influence of chemical reactions and diffusion. These systems arise naturally in chemistry, but can also be used to model dynamical processes beyond the realm of chemistry such as in biology, ecology, geology, and physics. In this paper, by adopting the viewpoint of port-based modeling, we cast reaction-diffusion systems into the port-Hamiltonian framework. Aside from offering conceptually a clear geometric interpretation formalized by a Stokes-Dirac structure, a port-Hamiltonian perspective allows to treat these dissipative systems as interconnected and thus makes their analysis, both quantitative and qualitative, more accessible from a modern dynamical systems and control theory point of view. This modeling approach permits us to draw immediately some conclusions regarding passivity and stability of reaction-diffusion systems. Furthermore, by adopting a discrete differential geometry-based approach and discretizing the reaction-diffusion system in the port-Hamiltonian form, apart from preserving a geometric structure, a compartmental model analogous to the standard one is obtained.

Memristive port-Hamiltonian Systems

The port-Hamiltonian modelling framework is extended to a class of systems containing memristive elements and phenomena. First, the concept of memristance is generalised to the same generic level as the port-Hamiltonian framework. Second, the underlying Dirac structure is augmented with a memristive port. The inclusion of memristive elements in the port-Hamiltonian framework turns out to be almost as straightforward as the inclusion of resistive elements. Although a memristor is a resistive element, it is also a dynamic element since the associated Ohmian laws are rather expressed in terms of differential equations. This means that the state space manifold, as naturally defined by the storage elements, is augmented by the states associated with the memristive elements. Hence the order of complexity is, in general, defined by the number of storage elements plus the number of memristors in the system. Apart from enlarging our repertoire of modelling building blocks, the inclusion of memristive elements in the existing port-Hamiltonian formalism possibly opens up new ideas for controller synthesis and design.

Control of port Hamiltonian systems by dissipative devices and its application to improve the semi-active suspension behaviour

The port Hamiltonian framework is a powerful tool for modeling a wide class of nonlinear systems such as robots and, more generally, mechatronic systems. The standard approaches used for the control of the port Hamiltonian systems are not applicable to a wide variety of mechatronic systems. This happens, for example, when the input control variable acts directly on some dissipative components of the system. In these cases the controlled devices can only dissipate power and the problem is to find a proper control law in order to meet the control requirements. This paper proposes four control laws for the controlled dissipative components which allow to satisfy a set of control requirements by acting on the energy stored in a subsection of the given system or by controlling the power flowing through a physical section of the system. Although some important issues remain open, the example of the semi-active suspension shows that some positive results can be achieved by applying the proposed approach.

Port-based Simulation of Flexible Multi-body Systems

This 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 OF PORT HAMILTONIAN SYSTEMS BY DISSIPATIVE DEVICES AND ITS APPLICATION TO IMPROVE THE SEMI-ACTIVE SUSPENSION BEHAVIOUR

The port Hamiltonian framework is a powerful tool for modeling a wide class of nonlinear systems such as robots and, more generally, mechatronic systems. A wide variety of mechatronic systems are controlled by operating dissipative components and the standard approaches for the control of port Hamiltonian systems are not applicable. Facing the limitation that the controlled devices can only dissipate power, the issue is to find a proper control law to satisfy the control requirements. This paper proposes to choose the control inputs to lead the input power of a subsystem in oder to satisfy the requirements by controlling the energy stored or the power dissipated in that subsystem. A slight extension of the definition of port Hamiltonian system is proposed to allow the description of a larger set of mechatronic systems. Although some important issues remain open, the example of the semi-active suspension shows that some positive results can be achieved by applying the proposed approach.