port-Hamiltonian Framework 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.

Trajectory tracking PID passivity-based control of spacecraft formation flying around Sun-Earth L2 point in the port-Hamiltonian framework

Spacecraft formation flying for interferometric observations around the 2nd Lagrange point in the Sun-Earth system (SEL2) is currently focal point in deep space exploration research, which demands high precision in relative position control of spacecraft. This paper proposes the relative motion dynamics of satellite formations around the L2 point in the port-Hamiltonian framework, and establishes a high-precision nonlinear dynamics model. PID passivity-based control (PID-PBC) is widely used in engineering. However, existing methods of PID-PBC cannot address the trajectory tracking issues in port-Hamiltonian systems. Utilizing the contraction properties of the port-Hamiltonian system, this paper proposes the trajectory tracking PID-PBC (tPID-PBC) approach, effectively resolving trajectory tracking issues for formation dynamics around L2 point in port-Hamiltonian framework. The paper details explicit solutions of the Partial Differential Equations (PDE) for the tPID-PBC method and its controller structure, and references the trajectories of interferometric observation formations, to verify the method’s effectiveness through numerical simulation. The presented control approach is applicable across generic port-Hamiltonian systems, offering substantial theoretical value.

Passivity-Based Control with Disturbance Observer of Electromagnetic Formation Flight Spacecraft in the Port-Hamiltonian Framework

Satellite formation flying technology currently represents a focal point in space mission research. Traditional spacecraft payload performance and lifespan are often constrained by propellant limitations. Electromagnetic Formation Flying (EMFF), a propellant-free formation flying technique, has garnered widespread attention. Its inherent strong nonlinearity and coupling present challenges for high-precision control within EMFF. This paper presents the relative motion dynamics of a two-satellite EMFF in the port-Hamiltonian framework and constructs an accurate nonlinear model of the dynamics. Utilizing the concept of Interconnection and Damping Assignment and nonlinear disturbance observer, a composite disturbance-rejection passivity-based controller is designed, offering a method for controlling the magnetic dipole strength of formation satellites. Finally, numerical simulations are conducted to demonstrate the viability of the proposed dynamics model and control strategy.

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.

Reduced order in domain control of distributed parameter port-Hamiltonian systems via energy shaping

An in-domain finite dimensional controller for a class of distributed parameter systems on a one-dimensional spatial domain formulated under the port-Hamiltonian framework is presented. Based on (Trenchant et al. 2017) where positive feedback and a late lumping approach is used, we extend the Control by Interconnection method and propose a new energy shaping methodology with an early lumping approach on the distributed spatial domain of the system. Our two main control objectives are to stabilize the closed-loop system, as well as to improve the closed-loop dynamic performances. With the early lumping approach, we investigate two cases of the controller design, the ideal case where each distributed controller acts independently on the spatial domain (fully-actuated), and the more realistic case where the control action is piecewise constant over certain intervals (under-actuated). We then analyze the asymptotic stability of the closed-loop system when the infinite dimensional plant system is connected with the finite dimensional controller. Furthermore we provide simulation results comparing the performance of the fully-actuated case and the under-actuated case with an example of an elastic vibrating string.

Control Design of Passive Grid-Forming Inverters in Port-Hamiltonian Framework

Control Design of Passive Grid-Forming Inverters in Port-Hamiltonian Framework

Structure-preserving spatial discretization of a coupled Heat-Wave system formulated as an irreversible port-Hamiltonian system.

The port-Hamiltonian (pH) framework allows one to properly model, interconnect, simulate and control various types of systems. Yet, properly modeling irreversibility remains a challenge as one has to include a nonlinear relation between flows and efforts, leading to a nonlinear Dirac structure. In this work, we will focus on the modelling of a distributed coupling of the heat and wave equations as pH systems. In particular, the representation of the coupled dynamics as an irreversible pH system is presented and its properties discussed. A discretization in space which preserves both the second and first principles of thermodynamics is detailed. Finally some numerical results are presented.

A Casimir based Analysis of a Class of the General Actuator Model

The paper discusses a Casimir based analysis of the General Actuator Model by Neville Hogan in which all actuators are classified into only two types: the Norton type and the Thevenin (Thévenin) type. Since the original version of the General Actuator Model was very weakly defined, the link to the fruitful port Hamiltonian framework is not clarified yet. First, a subset of the General Actuator Model is focused and we discuss a new port based modeling of the two types of the General Actuator Model. To clarify the link, a relation using the Casimir function between the two types is found as their structural properties. Second, a special mechatronic example whose energy is non-quadratic is analyzed as well as the popular mass-spring example. A hidden energy structure in these two examples is revealed unexpectedly. Not only a new observation for the special mechatronic example but also a new look at the popular mass-spring example are provided.

Minimal port-Hamiltonian modeling of voice production: choices of fluid flow hypotheses, resulting structure and comparison

Voice production results from the interaction between expelled airflow and soft tissues in the larynx and the vocal tract. Among the large literature on this topic over the last fifty years, a few nonlinear fluid-structure interaction models have been proposed in the port-Hamiltonian framework for passivity purposes. In this paper, we examine, compare and discuss two lumped-element port-Hamiltonian models from the literature, both derived from distributed parameter descriptions and simplifying assumptions chosen to integrate the minimal relevant phenomena involved in the larynx (for self-oscillations) or the vocal tract (during articulation). These models are recalled and reformulated using common terminology and notations. This leads to equivalent circuit representations, the components and the structure of which allow direct comparison (about causality, dimension, nonlinear laws, coupling) and physical interpretation. These results highlight important properties to consider and provide guidelines for future modelling improvement to be used in simulation.

Passivity-Based Trajectory Tracking and Formation Control of Nonholonomic Wheeled Robots Without Velocity Measurements

This note proposes a passivity-based control method for trajectory tracking and formation control of nonholonomic wheeled robots without velocity measurements. Coordinate transformations are used to incorporate the nonholonomic constraints, which are then avoided by controlling the front end of the robot rather than the center of the wheel axle into the differential equations. Starting from the passivity-based coordination design, the control goals are achieved via an internal controller for velocity tracking and heading control and an external controller for formation in the port-Hamiltonian framework. This approach endows the resulting controller with a physical interpretation. To avoid unavailable velocity measurements or unreliable velocity estimations, we derive the distributed control law with only position measurements by introducing a dynamic extension. In addition, we prove that our approach is suitable not only for acyclic graphs but also for a class of non-acyclic graphs, namely, ring graphs. Simulations are provided to illustrate the effectiveness of the approach.

Energy-based trajectory tracking control of under-actuated unmanned surface vessels

In this paper, a novel energy-based trajectory tracking control strategy for under-actuated unmanned surface vessels (USVs) in the presence of unknown environmental disturbances is presented. The port-Hamiltonian framework is utilized to propose a passivity-based control model in body-fixed coordinates of the USVs. An adaptive disturbance estimation method is detailed and used to accurately estimate the environmental disturbances affecting USV motion. Furthermore, a passive and Hamiltonian structure-preserving controller is employed to achieve the desired trajectory of the USV system, and the stability of the desired target dynamic system is rigorously proven. The effectiveness of the proposed controller is demonstrated through simulations and experiments on a USV experimental platform, showcasing its capability of trajectory tracking performance and mitigating the effects of disturbances.

Control of port-Hamiltonian differential-algebraic systems and applications

We discuss the modelling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control. The structure is ideal for automated network-based modelling since it is invariant under power-conserving interconnection, congruence transformations and Galerkin projection. Moreover, stability and passivity properties are easily shown. Condensed forms under orthogonal transformations present easy analysis tools for existence, uniqueness, regularity and numerical methods to check these properties.After recalling the concepts for general linear and nonlinear descriptor systems, we demonstrate that many difficulties that arise in general descriptor systems can be easily overcome within the port-Hamiltonian framework. The properties of port-Hamiltonian descriptor systems are analysed, and time discretization and numerical linear algebra techniques are discussed. Structure-preserving regularization procedures for descriptor systems are presented to make them suitable for simulation and control. Model reduction techniques that preserve the structure and stabilization and optimal control techniques are discussed.The properties of port-Hamiltonian descriptor systems and their use in modelling simulation and control methods are illustrated with several examples from different physical domains. The survey concludes with open problems and research topics that deserve further attention.

Tracking control design for fractional order systems: A passivity-based port-Hamiltonian framework

This article focuses on the design of tracking control for chaotic fractional order systems subjected to perturbations in a port-Hamiltonian framework. The fractional order systems of general form are modeled into port-controlled Hamiltonian form. Then, the extended results on the dissipativity, energy balance, and passivity of the fractional order systems are proved and presented in this paper. The port-controlled Hamiltonian form of the fractional order systems are proved to be asymptotically stable via energy balancing concept. Furthermore, a tracking controller is designed for the fractional order port-controlled Hamiltonian form by utilizing the matching conditions of the port-Hamiltonian systems. Stability of the system is established and analyzed explicitly for the closed-loop system with the help of direct Lyapunov method. Finally, an application example is solved with simulation results and discussions to prove the effectiveness of the propounded control design approach.

Increasing the region of attraction in DC microgrids

Based on the port-Hamiltonian framework, this paper proposes a novel control scheme for stabilising the voltage in DC networks affected by (i) unknown ZIP-loads, i.e., nonlinear loads consisting of the parallel combination of constant impedance (Z), current (I) and power (P) load types, and (ii) unknown (but bounded) time-varying disturbances. Differently from the results existing in the literature, where restrictive (sufficient) conditions on the load parameters, voltage trajectory and voltage reference are assumed to be satisfied, this is the first paper (to the best of our knowledge) proposing a controller that relaxes such conditions and guarantees the exponential stability of the desired equilibrium point, whose region of attraction can be increased by simply tuning the control gains. In the case the network is affected by unknown time-varying disturbances, local input-to-state stability (l-ISS) is ensured. Furthermore, if non-ideal P-loads are considered, excluding the unrealistic possibility that the load absorbs infinite current when the voltage approaches zero, the aforementioned stability results hold globally.

Backstepping stabilization of a clamped string with actuation inside the domain

In this paper, we consider the stabilization of a clamped string with actuation located inside the domain. Such a model can represent the simplified dynamics of a microendoscope. Inspired by the Port Hamiltonian framework, we use the Riemann invariants of the energy states to reformulate this problem as stabilizing a chain of two coupled hyperbolic subsystems with actuation at the in-between boundary. After applying successive transforms, it is shown to be equivalent to stabilizing a neutral-type delay-differential equation. A suitable controller is derived using the backstepping methodology with a Fredholm integral transform. Some simulations illustrate this approach.

Multi-scale description of pedestrian collective dynamics with port-Hamiltonian systems

<abstract><p>Port-Hamiltonian systems (PHS) theory is a recent but already well-established modelling approach for non-linear physical systems. Some studies have shown lately that PHS frameworks are relevant for modelling and control of swarm and multi-agent systems. We identify in this contribution a general class of microscopic force-based pedestrian models that can be formulated as a port-Hamiltonian system. The pedestrian PHS has linear structure and dissipation components. Non-linear effects come from isotropic pedestrian interactions. Simulation results on a torus with disordered initial states show that the port-Hamiltonian pedestrian model can exhibit different types of dynamics. They range from relaxed speed models with no interaction, dynamical billiards, or crystallization dynamics to realistic pedestrian collective behaviors, including lane and strip formation for counter and crossing flow. The port-Hamiltonian framework is a natural multiscale description of pedestrian dynamics as the Hamiltonian turns out to be a generic order parameter that allows us to identify specific behaviours of the dynamics from a macroscopic viewpoint. Particular cases even enable through energy balance to determine the Hamiltonian behavior without requiring the tedious computation of the microscopic dynamics. Using PHS theory, we systematically identify a critical threshold value for the Hamiltonian, which relies only on exogenous input and can be physically interpreted.</p></abstract>

Energy Aware Impedance Control of a Flying End-Effector in the Port-Hamiltonian Framework

This work addresses the interaction control problem of a fully actuated aerial vehicle considered as a flying end-effector. We tackle the problem using geometrically consistent variable-stiffness impedance control for safe wrench regulation using the concept of energy tanks, where both the modeling and the control are carried out in the port Hamiltonian framework. We exploit previous well-known results in the literature of ground manipulators and extend them to be applied for novel and challenging aerial physical interaction with a focus on quasi-static applications. The energy-awareness of the presented control method guarantees the stability of the aerial robot in both free-flight and in-contact scenarios together with a level of safety in the case of contact-loss with the unknown environment. Furthermore, by utilizing bond graphs we demonstrate how the closed-loop passivity can be graphically conducted. The validity of our proposed approach is shown via several experiments. We also provide several insights on how the proposed framework could be extended to a generic dynamic aerial physical interaction.

Current-Sensorless Control Strategy for the MPPT of a PV Cell: An Energy-Based Approach

A novel energy-based modelling and control strategy is developed and implemented to solve the maximum power point tracking problem when a photovoltaic cell array is connected to consumption loads. A mathematical model that contains key characteristic parameters of an energy converter stage connected to a photovoltaic cell array is proposed and recast using the port-Hamiltonian framework. The system consists of input-output power port pairs and storage and dissipating elements. Then, a current-sensorless control loop for a maximum power point tracking is designed, acting over the energy converter stage and following an interconnection and damping assignment passivity-based strategy. The performance of the proposed strategy is compared to a (classical) sliding mode control law. Our energy-based strategy is implemented in a hardware platform with a sampling rate of 122 Hz, resulting in lower dynamic power consumption compared to other maximum power point tracking control strategies. Numerical simulations and experimental results validate the performance of the proposed energy-based modelling and the novel control law approach.

Modeling and Position Control of the HASEL Actuator via Port-Hamiltonian Approach

This paper deals with the modeling and control problem of a Hydraulically Amplified Self-healing Electrostatic (HASEL) actuator based on the port-Hamiltonian framework. A nonlinear spring-damper system is used to approximate the mechanical deformation of the actuator due to the motion of the fluid while a nonlinear capacitance is used to approximate the electric behavior of the system. The actuator position control strategy is investigated based on the Interconnection Damping Assignment-Passivity Based Control (IDA-PBC) method, with further Integral Actions (IA) added to cope with load uncertainties. The proposed model and control laws are validated on an experimental benchmark. The experimental tests demonstrate that the proposed model is accurate up to 94% of fitness. The controllers allow assigning the actuator position with ramp and sinusoidal references with the relative error less than 5%. At last, the robustness of the proposed IDA-PBC controller with IA has been shown with the experimental result for the unknown load disturbance rejection.

Virtual contractivity-based control of fully-actuated mechanical systems in the port-Hamiltonian framework

We present a trajectory tracking control design method for a class of mechanical systems in the port-Hamiltonian framework. The proposed solution is based on the virtual contractivity-based control (v-CBC) method, which employs the notions of virtual systems and of contractivity. This approach leads to a family of asymptotic tracking controllers that are not limited to those that preserve the pH structure of the closed-loop system nor require an intermediate change of coordinates. Nevertheless, structure preservation and other properties (e.g., passivity) are possible under sufficient conditions. The performance of the proposed v-CBC scheme is experimentally evaluated on a planar robot of two degrees of freedom (DoF).