Port Hamiltonian Research Articles

Distributed control of spacecraft formation under [formula omitted] perturbation in the port-Hamiltonian framework

To control the relative position and relative velocity of spacecraft formation, a time-varying nonlinear relative motion model under J2 perturbation in an elliptical orbit is established in the port-Hamiltonian (PH) framework, and a distributed control law for spacecraft formation is developed using the consensus algorithm for parameter estimation and the passivity-based control (PBC) method based on the state-error interconnection and damping assignment (IDA) technique. First, the influence of J2 perturbation on the potential energy and orbit parameters in the model is considered when the relative motion model is built in the PH frame, and the expression of the relative motion acceleration under J2 perturbation is given. Second, to solve the problem that the state of the chief spacecraft cannot be directly obtained from the deputy spacecraft under distributed communication, a consensus-based parameter estimation method is introduced, the estimated parameter of the chief spacecraft is applied to the relative motion model in the PH frame, and a state error model with the estimated parameters derived from the consistency algorithm is established. Then, after the stability analysis is conducted on the desired PH system containing the estimated parameter values, the desired Hamiltonian energy function with the estimated parameters is designed according to the time-varying errors of the relative equilibrium states of the deputy spacecraft and the errors between deputy spacecraft, and the distributed control law of spacecraft formation is derived based on the state-error IDA-PBC method. Finally, the expected relative motion trajectory designed based on the TH equation is used to simulate a spacecraft formation under J2 perturbation, and the results indicate that the spacecraft can quickly converge to the expected formation under the influence of the control law.

Interconnection of irreversible port Hamiltonian systems

This paper shows how the interconnection of two controlled Irreversible port Hamiltonian Systems has to be state and co-state modulated in order to ensure the closed-loop Irreversible port Hamiltonian structure, satisfying the first and second laws of Thermodynamics. It proposes a precise parametrization of this modulation from the open-loop systems structures in order to guarantee the consistency of the closed loop energy and entropy balance equations. The results are illustrated by means of the examples of a heat-exchanger, a gas-piston system and a chemical reaction.

A Novel Mixed Finite/Infinite Dimensional Port–Hamiltonian Model of a Mechanical Ventilator

Mechanical ventilation is a life-saving treatment for critically ill patients who are struggling to breathe independently due to injury or disease. Globally, per year, there has always been a large number of individuals who have required mechanical ventilation. The COVID-19 pandemic brought to light the significance of mechanical ventilation, which played a significant role in sustaining COVID-19-infected critically ill patients who could not breathe on their own. The pandemic drew the attention of the world to the shortage of ventilators globally. Some of the challenges to providing an adequate number of ventilators include: increased demand for ventilators, supply chain disruptions, manufacturing constraints, distribution inequalities, financial constraints, maintenance and logistics difficulties, training and expertise shortages, and the lack of design and development of affordable mechanical ventilators that satisfy the stipulated requirements. This research work presents the formulation of a detailed Port–Hamiltonian model of a mechanical ventilator integrated with the human respiratory system. The interconnection and coupling conditions for the various subsystems within the mechanical ventilator and the coupling between the mechanical ventilator and the human respiratory system are also presented. Structure-preserving discretization is provided alongside numerical simulations and results. The obtained results are found to be comparable to results presented in the literature. Future work will include the design of suitable controllers for the system.

Cooperative control of variable damping error port Hamiltonian and backstepping nonsingular terminal sliding mode control for manipulators driven by PMSMs

AbstractTo improve the disadvantages of signal control and energy control, a cooperative control strategy combining signal control and energy control is proposed for manipulators driven by permanent magnet synchronous motors (PMSMs) in this article. The cooperative control strategy is achieved by way of the convex combination of signal controller and energy controller, and Gaussian function is selected as cooperative function. The energy controller applies variable damping error port Hamiltonian and the signal controller uses backstepping nonsingular terminal sliding mode control. The PMSM with loss model is applied to obtain higher efficiency. To deal with modeling errors and joint friction, a nonlinear disturbance observer is used for manipulators system. Simulation and experiment results display that the designed strategy not only increases efficiency, but also enhances dynamic and steady‐state performance of manipulators.

Fixed-time [formula omitted] tracking control of unmanned underwater vehicles with disturbance rejection via Port-Hamiltonian framework

The fixed-time tracking control schemes of unmanned underwater vehicles (UUVs) are investigated in body-fixed coordinates frame based on Port-Hamiltonian (PH) model with external disturbances. The novel locally and globally fixed-time control laws via the interconnection and damping assignment passivity-based control (IDA-PBC) are designed for trajectory tracking in UUVs. The virtual desired equilibria consisted of the tracking error and the desired trajectory are established by the matching conditions. Moreover, the fixed-time stabilization of the UUV induced of variable parameter matrixes is analyzed. Compared with the traditional IDA-PBC controller, the UUV is guaranteed to achieve the reference trajectory within a fixed time regardless of initial conditions. In the presence of external disturbances, the H∞ laws are incorporated in the fixed-time control for the UUV, which can ensure faster trajectory tracking and strong anti-disturbance. Finally, the simulation results demonstrate the effectiveness of the main schemes.

Generalized Maxwell viscoelasticity for geometrically exact strings: Nonlinear port-Hamiltonian formulation and structure-preserving discretization

This contribution proposes a nonlinear and dissipative infinite-dimensional port-Hamiltonian (PH) model for the dynamics of geometrically exact strings. The mechanical model provides a description of large deformations including finite elastic and inelastic strains in a generalized Maxwell model. It is shown that the overall system results from a power-preserving interconnection of PH subsystems. By using a structure-preserving mixed finite element approach, a finite-dimensional PH model is derived. Eventually, midpoint discrete derivatives are employed to deduce an energy-consistent time-stepping method, which inherits discrete-time dissipativity for the irreversible system. An example simulation illustrates the numerical properties of the present approach.

Port-Hamiltonian Modelling of Complex Non-Linear Systems, Application to a Liquid Propelled Rocket Engine

Port-Hamiltonian (PH) systems theory is a well-established framework for modelling the dynamics of non-linear systems. It has been used extensively for complex mechanical systems. Recent developments have extended this representation to multiphysical systems. In this paper, a PH formulation of a Liquid Propelled Rocket Engine model is proposed. Starting from a classical state-space representation, a new model is derived which allows to demonstrate the global passivity feature of the system using the property of passivity inheritance by composition of several PH subsystems. The resulting representation allows to consider passivity-based control perspective for this class of complex thermodynamics system.

Port-Hamiltonian modeling and control of a curling HASEL actuator

This paper is concerned with the modeling and control of a curling Hydraulically Amplified Self-healing Electrostatic (HASEL) actuator using the port-Hamiltonian (PH) approach. For that purpose, we use a modular approach and consider the HASEL actuator as an interconnection of elementary subsystems. Each subsystem is modeled by an electrical component consisting of a capacitor in parallel with an inductor connected through the conservation of volume of the moving liquid to a mechanical structure based on inertia, linear, and torsional springs. The parameters are then identified, and the model is validated on the experimental setup. Position control is achieved by using Interconnection and Damping Assignment-Passivity Based Control (IDA-PBC) with integral action (IA) for disturbance rejection. Simulation results show the Efficiency of the proposed controller.

Evaluation of a Passive-Based Controller for Power Monitoring in Networks of High Voltage Transmission Lines in Direct Current with Voltage Source Converters (VSC–HVDC)

In this paper a tracking Passivity--based Control (PBC) for a multiterminal Voltage Source Converter based High Voltage Direct Current Network (VSC--HVDC) is evaluated. First, the system (an actual multiterminal HVDC) described as a Port Hamiltonian (PH) System and the controller are presented and subsequently three scenarios are proposed to evaluate the closed--loop behavior, namely: (i) load changes; (ii) generation changes and, (iii) DC--bus changes. Numerical simulations are carried out and results shown the robustness of the closed--loop to cope with these common disturbances.

Fixed-Time Control for a Class of Nonlinear PH-DAE Systems

The globally fixed-time stabilization and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> control for the port-Hamiltonian differential algebraic equation (PH-DAE) is addressed by applying the structural properties of the port-Hamiltonian (PH) systems, and the interconnection and damping assignment passivity-based control (IDA-PBC) technique. For fixed-time control design of the differential algebraic equation systems, the main obstacle lies that the algebraic variables are hidden in the system and their dynamics are ambiguous. We propose an available and effective approach to overcome this obstacle. The system variables are decomposed into differential component and the algebraic component, and the explicit representation of the dynamics of algebraic component is obtained. Fist, we investigate the locally fixed-time stabilization control as well as globally attractive for PH-DAE. Second, we focus on solving the globally fixed-time stabilization and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> control problems by jointly taking advantage of the locally fixed-time stabilization control for the origin and the globally fixed-time attractivity control for a predeterminate region. Finally, in order to address fixed-time stabilization control and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> control for PH-DAE, new controllers are designed. Moreover, the convergence time of systems can be easily estimated after external disturbance vanishes. The efficiency of the theoretical results acquired in present article is verified via two examples with numerical simulation.

Observer Design for a Class of Discrete Port Hamiltonian Systems

Observer Design for a Class of Discrete Port Hamiltonian Systems

Energy-Based Modeling and Control of a Piezotube Actuated Optical Fiber

This article presents an energy-based modeling and control design method for a piezotube actuated optical fiber. A nonlinear infinite dimensional port Hamiltonian (pH) formulation of the 3-D flexible optical fiber is derived from the Cosserat rod dynamical equations. Then, the proposed infinite dimensional model is discretized using a pH structure and passivity preserving discretization method for the simulation and control design. This model is then validated against experimental data obtained using a built-in experimental setup equipped with a MEMS Analyzer. A complete pH formulation of the piezotube actuated optical fiber is proposed, combining the Cosserat rod model and actuator dynamics. This model is used for the end-point path control design using an interconnection and damping assignment passivity based control (IDA-PBC) method. Both the proposed pH model of the overall system and the controller are validated in simulation and against experimental results.

Port Hamiltonian based model for platooning applications including air drag effects

This paper deals with platooning modeling considering the force provoked by the air drag in each vehicle. The proposed model is derived using a port-Hamiltonian approach in order to ensure the passivity of the whole system. The relation between the desired platooning formation and its implication on the air drag effect is highlighted. Simulation results illustrate the effect of air drag on the platoon behavior. The results of this work could serve as a basis for a platooning control scheme that explicitly includes the air drag force, as a function of the desired inter-vehicle distance, in the control loop.

Structure preserving discontinuous Galerkin approximation of one-dimensional port-Hamiltonian systems

In this article, we present the structure preserving discretization of linear one-dimensional port-Hamiltonian (PH) systems of two conservation laws using discontinuous Galerkin (DG) methods. We recall the DG discretization procedure which is based on a subdivision of the computational domain, an elementwise weak formulation with up to two integrations by parts, and the interconnection of the elements using different numerical fluxes. We present the interconnection of the element models, which is power preserving in the case of conservative (unstabilized) numerical fluxes, and we set up the resulting global PH state space model. We discuss the properties of the obtained models, including the effect of the flux stabilization parameter on the spectrum. Finally, we show simulations with different parameters for a boundary controlled linear hyperbolic system.

Port maps of Irreversible Port Hamiltonian Systems

Irreversible Port Hamiltonian Systems are a deviation from Port Hamiltonian Systems which embeds the definition of the irreversible phenomena taking place in the system. They are defined with respect to a quasi-Poisson bracket which ensures the positiveness of the entropy generation and is expressed in terms of the total entropy of the system. The port maps, however, associated with the conjugated port variables, were poorly justified and lacked any physical characterization. In this paper, we suggest a novel definition of the port maps which allows to recover not only the energy balance equation (when the Hamiltonian equals the total energy of the system) but also a entropy balance equation including the irreversible entropy creation term at the interface (the port) of the system in addition to the entropy creation term due to internal irreversible phenomena.

Trajectory tracking for nonlinear systems using extended quadratic port-Hamiltonian models without input and state coordinate transformations

In this note, an enhanced trajectory tracking (or equivalently, tracking-error) approach is developed for the control of nonlinear systems whenever the stage of feedback passivation design prior to synthesizing state feedback controllers is impossible. To achieve this purpose while using the original state vector to retain its interpretation, it is possible without the use of input and state coordinate transformations to combine the system dynamics with the so-called extended quadratic port-Hamiltonian (PH) models (including possibly the quadratic pseudo PH models) which are then divided into non-relaxing and relaxing ones for further study on control benefits. Interestingly, both cases are associated to a unifying quadratic Hamiltonian storage function similar to that of electrical, mechanical, or electromechanical systems with a specific insight. Sufficient conditions for the global asymptotic or exponential convergence of the system trajectory to the reference one are shown. In addition, a Proportional–Integral action can be added to the tracking control for improving the closed-loop performance and robustness. The proposed approach is illustrated via two case studies, including the non-minimum phase Van de Vusse reaction system and the 3-DOF SCARA robot.

Model Order Reduction of RLC Circuit System Modeled by Port-Hamiltonian Structure

In this paper, we consider the port-Hamiltonian (PH) modeling of general RLC circuits, then explore the model order reduction (MOR) of corresponding port-Hamiltonian differential algebra equation (PH-DAE) systems. Specifically, by directed graphs, the general RLC circuits are firstly modeled as PH-DAE systems which imply the important passivity property. Based on e-embedding and parametric moment matching techniques, MOR is implemented to the PH-DAE system, and the corresponding reduced system preserves PH-DAE structure and then preserves the passivity property. In addition, we prove that the reduced parametric PH system obtained by only one-side projection can preserve three times moments which indicates better accuracy in theory, and the error estimation between PH-DAE system and parametric PH system is also provided.

From discrete modeling to explicit FE models for port-Hamiltonian systems of conservation laws

Mixed finite element (FE) approaches have proven very useful for the structure-preserving discretization of port-Hamiltonian (PH) distributed parameter systems, but non-uniform boundary conditions (BCs) were treated in an implicit manner up to now. We apply our recent approach from structure mechanics, which relies on the weak imposition of both Neumann and Dirichlet BCs based on a suitable variational principle, to the class of PH systems of two conservation laws. We illustrate (a) starting with the integral conservation laws the transition to an exterior calculus representation suitable for FE approximation according to Farle et al. (2013). Based thereon, we show (b) the variational formulation with weakly imposed BCs of both types. We discuss (c) on a simple example on a quadrilateral mesh the structure and the variables of the resulting FE models compared to the equations derived from a direct discrete approach on dual cell complexes. We (d) provide the corresponding FEniCS code for download.

A perturbed Port-Hamiltonian approach for the stabilization of homogeneous reaction systems via the control of vessel extents

The paper proposes a tracking-error passivity-based control scheme for the asymptotic stabilization of homogeneous reaction systems. The approach uses the concept of vessel extents in the Port-Hamiltonian (PH) framework. Concretely, the extent-based representation that is obtained by linear time-invariant transformation of the reaction model is expressed as a perturbed PH system, whereby the reaction rates constitute unmatched time-varying disturbances.Two scenarios are considered. The first one assumes that the molar numbers of all species and the reaction temperature are measured and, furthermore, the kinetic model is known, while the second scenario relaxes these assumptions and requires only the measurements of a subset of the molar numbers and of the reactor temperature, but no knowledge of reaction kinetics. For the first scenario, the passivity-based method is used to compensate the disturbances, while preserving the PH structure of the error system via simple matrix factorization of the disturbances. For the second scenario, a constructive procedure is proposed to complete the space of vessel extents with the aim of computing an appropriate damping injection for the closed-loop system. It is shown that the proposed strategies guarantee that the system trajectories converge towards the desired setpoints without the need of state observation. A reaction system exhibiting non-minimum phase behavior is used to illustrate the theoretical developments. The closed-loop performance is discussed and compared to that of a PI controller.

Trajectory control of an elastic beam based on port-Hamiltonian numerical models

Abstract We present a systematic approach to realize the precise observer-based trajectory tracking of the tip of a flexible beam using the energy-based port-Hamiltonian (PH) system representation. The first design steps are the structure-preserving spatial discretization by means of a pseudo-spectral method and the structure-preserving order reduction. The model structure is exploited for inversion-based feedforward control, and the control loop is closed via an observer for the friction torque and the state difference. Experimental results for the reference input and the disturbance response illustrate the quality of the design.