© 2022, The Author(s), under exclusive licence to The Brazilian Society of Mechanical Sciences and Engineering.The use of CubeSats is increasing to a wide range of areas in science and technology with some of them requiring an accurate Attitude Determination and Control System (ADCS) and deployable structures such as booms. However, small satellites commonly do not have latching systems to lock their booms, which introduce vibrations and oscillations and might degrade the ADCS performance. Also, some applications propose missions with CubeSats operating in close proximity and coordination, requiring thrusters to perform orbit maneuvers such as the planned ITASAT-2 spacecraft formation flying mission, which will have non-latching booms and a thruster. These thrusters can excite the satellite’s non-latching flexible booms, intensifying their impact on the ADCS. Additionally, on-off thrusters are usually controlled using a Pulse-Width Modulation (PWM), introducing more effects in the system’s dynamic. Hence, motivated by the ITASAT-2 mission, this work aims to understand the impact of a thruster’s PWM parameters in the non-latching flexible booms dynamics. Also, this work presents a framework to obtain the influence of PWM parameters on a satellite, which can be applied to other small spacecraft. The results show that booms’ deformation decreases when the thruster provides a continuous force, compared to a modulated force. Peaks in deformation and rotation were identified near frequencies of the non-latching flexible booms’ system. Further, it was verified that resonances might occur in latched booms at distinct PWM periods. Moreover, the influence of the non-latching mechanism and PWM parameters was observed in the system forming regions of larger deformation.

© American Society for Engineering Education, 2022.Federal grants have been supporting many Brazilian engineering master's students. The availability of these grants is dwindling, so universities on one hand and master's candidates on the other have been looking for alternatives to obtain master's degrees with less grant dependence/support. On the technical university side, this led to the emergence of options to start a master's program in the last semesters of the typical 10-semester undergraduate program. From the university's side and from the student's side it is interesting that such integrated effort is time and resource-efficient. To support this, at Instituto Tecnológico de Aeronáutica (ITA), a new Complementary Training Program (CTP) in Control and Automation Engineering was started in August 2021, serving mainly Mechanical, Electrical, Aeronautical, and Computer Engineering students. The standard goal of CTPs in Brazil is to extend the major undergraduate training in a similar way as a US minor does. Thus, the baseline purpose of the new program is to provide undergraduate students with a complementary education, transversal to engineering courses, which enables them to work as Control and Automation engineers, without the need for training supplementation after graduation. However, by offering a well-designed course choice, this program will also allow for: (a) extending the scope of undergraduate studies, and (b) deepening specific topics that are already part of the undergraduate curriculum. In the scope of the Institute's undergraduate and master's degree integration initiative, this second particularity (item b) may yield anticipated credits for a master's program. Specific features of the program may further benefit students aiming at a master's degree. This paper details the structure of the CTP and the gains expected in terms of incentives for the Institute's Mechanical-Aeronautical Engineering as well as the Electronics and Computer Engineering Master's Programs.

© 2021 Elsevier Masson SASThe Scintillation Prediction Observations Research Task (SPORT) nanosatellite is being developed in partnership with the National Aeronautics and Space Administration agency and the Brazilian Space Agency, with its launch planned for 2022. Its goal is to collect data to improve our understanding of plasma bubbles and the condition that lead to their formation, helping to predict and mitigate their interference in navigation and communication systems. Therefore, to reach this goal, the satellite has several scientific instruments to perform in-situ measurements, with five of them positioned on four booms. These booms do not have a latching system to lock their position; instead, torsional springs are employed to keep them in the deployed state, holding them against their mechanism's structure. This configuration of torsional spring and collision may lead to vibration with the potential to degrade the Attitude Determination and Control System performance, impacting the whole mission. Motivated by the lack of literature covering the non-latching booms dynamics in satellites, this work proposes a framework based on multibody dynamics to simulate satellites with such booms. It also presents a practical method to acquire experimental data and identify the parameters of the booms' deployment mechanism. Later, this work applies the proposed framework and investigates the impact of non-latching booms on the satellite control system to verify if SPORT is able to complete the maneuver. Therefore, experiments were conducted to calibrate both spring and collision models. The multibody model of the satellite was developed and later validated using commercial software. The method for capturing booms' data and determining the mechanisms' parameters shows a satisfactory performance near the booms' deployment position. The proposed framework to simulate satellites with non-latching booms is applied to the SPORT satellite. Simulations in closed-loop indicate that the booms' influence on the SPORT's control system is negligible and the satellite meets its requirements.

© The Author(s) 2020.This paper presents a structure-preserving spatial discretization method for distributed parameter port- Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and geometries. For these systems, a partitioned finite element method (PFEM) is derived, based on the integration by parts of one of the two conservation laws written in weak form. The non-linear one-dimensional shallow-water equation (SWE) is first considered as a motivation example. Then, the method is investigated on the example of the non-linear two-dimensional SWE. Complete derivation of the reduced finite-dimensional port-Hamiltonian system (pHs) is provided and numerical experiments are performed. Extensions to curvilinear (polar) coordinate systems, spacevarying coefficients and higher-order pHs (Euler-Bernoulli beam equation) are provided.

© The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)The dissipative Shallow Water Equations (DSWEs) are investigated as port-Hamiltonian systems. Dissipation models of different types are considered: either as nonlinear bounded operators, or as linear unbounded operators involving a classical diffusion term in 1D, or the vectorial Laplacian in 2D. In order to recast the dissipative SWE into the framework of pHs with dissipation, a physically meaningful factorization of the vectorial Laplacian is being used, which nicely separates the divergent and the rotational components of the velocity field. Finally, the structure-preserving numerical scheme provided by the Partitioned Finite Element Method (PFEM) is applied to the nonlinear bounded dissipative fluid models. For the linear unbounded cases, a change of variables is highlighted, to transform the DSWEs into a new pHs with a polynomial structure, which proves more suitable for numerics.

© The Author(s) 2020. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.The free surface motion in moving containers is an important physical phenomenon for many engineering applications. One way to model the free surface motion is by employing shallow water equations (SWEs). The port-Hamiltonian systems formulation is a powerful tool that can be used for modeling complex systems in a modular way. In this work, we extend previous work on SWEs using the port-Hamiltonian formulation, by considering the two-dimensional equations under rigid body motions. The resulting equations consist of a mixed-port-Hamiltonian system, with finite and infinite-dimensional energy variables and ports.

Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND licenseThe propagation of acoustic waves in a 2D geometrical domain under mixed boundary control is here described by means of the port-Hamiltonian (pH) formalism. A finite element based method is employed to obtain a consistently discretized model. To construct a model with mixed boundary control, two different methodologies are detailed: one employs Lagrange multipliers, the other relies on a virtual domain decomposition to interconnect models with different causalities. The two approaches are assessed numerically, by comparing the Hamiltonian and the state variables norm for progressively refined meshes.

© 2019 IEEE.This work presents the development of the nonlinear 2D Shallow Water Equations (SWE) in polar coordinates as a boundary port controlled Hamiltonian system. A geometric reduction by symmetry is obtained, simplifying the system to one-dimension. The recently developed Partitioned Finite Element Method is applied to semi-discretize the equations, preserving the boundary power-product of both the original 2D and the reduced 1D system. The main advantage of this power-preserving semi-discretization method is that it can be applied using well-established finite element software. In this work, we use FEniCS to solve the variational formulation, including the nonlinearity provided by the non-quadratic Hamiltonian of the SWE. A passive output-feedback controller using damping injection is used to dissipate the water waves.

© 1993-2012 IEEE.In this brief, we develop a mathematical model of a flexible spacecraft system composed of a hub and two symmetrical beams using the port-Hamiltonian framework. This class of system has favorable properties, such as passivity for controller synthesis and stability analysis, where the global Hamiltonian plays the role of a Lyapunov function candidate. The spacecraft model is viewed as a power-conserving interconnection between an infinite (beam) and finite (hub) dimensional system. We show that the interconnection result has a port-Hamiltonian structure and is passive. The introduction of a nonlinear feedback term, which takes into account the beam's flexibility, is developed using the control by an interconnection approach. The closed-loop stability is proven; then, through explicitly solving the partial differential equations of the system, asymptotic stability is obtained. Finally, the experimental results are carried out to assess the validity of the proposed design methodology.

© 2018 European Control Association (EUCA).Quaternion algebra is frequently employed for spacecraft attitude description due to its convenient numerical properties when compared to minimal formulations. In parallel, Linear Quadratic Control (LQR)-based attitude controllers are often applied to underactuated vehicles due to its intuitive tuning process and satisfactory stability robustness properties. However, nonlinear quaternion differential equations of motion linearization yields non-stabilizable systems. Thus, LQR techniques cannot be directly employed since the associated algebraic Riccati equation is ill-posed. The commonplace solution resorts to a reduced quaternion model where only three out of four quaternion coordinates are exploited. The present work shows that such choice exhibits numerically unstable regions that impedes solving the LQR problem for all possible operating points. Additionally, we propose two methods to obtain wellposed LQR problems over all operating points. The first is based on the reduced quaternion model with an appropriate change of coordinates. The second is to append a virtual stabilizing input (VSI) to the nonlinear system to attain controllable linearized systems. The VSI direction should be appropriately chosen to not disturb the controllable modes of the system. Finally, we show that a class of constant angular velocity tracking problems is time-invariant under an appropriate change of variables such that time-invariant LQR techniques are applicable.

© 31st Congress of the International Council of the Aeronautical Sciences, ICAS 2018. All rights reserved.The assumption of small deformations in the formulation of the flight dynamics of flexible aircraft can be very convenient as it allows the use of a reduced number of modes of vibration to represent the structural dynamics with little loss of accuracy. However, depending on the level of structural flexibility, deformations may become large enough to violate this simplifying assumption, making geometrically-nonlinear formulations necessary. Delimiting the range of validity of small deformations is then indispensable for the flight-mechanics engineer in state-of-the-art aircraft design. In this paper, small- and large-deformation formulations are compared in equilibrium conditions and in time-marching simulations for aircraft with different levels of structural flexibility. The importance of geometrical nonlinearities and the range of validity of small deformations are assessed.

© 2018In this paper, the mathematical model of a flexible spacecraft system composed of a hub and two symmetrical beams loaded with tip masses is reconsidered to design a control law for internal disturbance rejection. This model has a port-Hamiltonian structure and is passive. The disturbance rejection is performed by a feedback control law using the angular rates at the two tips of a beam. The closed-loop asymptotic stability of such a collocated / non-collocated control is analyzed through explicitly solving the Partial Differential Equations (PDE) of the system. Finally, the experimental results are carried out to assess the validity of the proposed control methodology.

© 2018Discretizing open systems of conservation laws while preserving the power-balance at the discrete level can be achieved using a new Partitioned Finite Element Method (PFEM), where an integration by parts is performed only on a subset of the variables in the weak formulation. Moreover, since boundary control and observation appear naturally in this formulation, the method is suitable both for simulation and control of infinite-dimensional port-Hamiltonian systems. The method can be applied using FEM software, and comes along with worked-out test cases on the 2D wave equation in different geometries and coordinate systems.

© 2016 Elsevier LtdThis work is motivated by an aeronautical issue: the fuel sloshing in the tank coupled with very flexible wings. Vibrations due to these coupled phenomena can lead to problems like reduced passenger comfort and maneuverability, and even unstable behavior. Port-Hamiltonian systems (pHs) provide a unified framework for the description of multi-domain, complex physical systems and a modular approach for the interconnection of subsystems. In this work, pHs models are proposed for the equations of liquid sloshing in moving containers and for the structural equations of beams with piezoelectric actuators. The interconnection ports are used to couple the sloshing dynamics in the moving tank to the motion the beam. This coupling leads to an infinite-dimensional model of the system in the pHs form. A finite-dimensional approximation is obtained by using a geometric pseudo-spectral method that preserves the pHs structure at the discrete level. Experimental tests on a structure made of a beam and a tank were carried out to validate the finite-dimensional model of liquid sloshing in moving containers. Finally, the pHs model proves useful to design an active control law for the reduction of sloshing phenomena.

© 2017 International Forum on Aeroelasticity and Structural Dynamics (IFASD). All rights reserved.A simple and self-contained methodology to assess the validity of the assumption of small deformations in linear structural-dynamic models was recently proposed. The advantages of the methodology lie in the fact that it does not depend on the availability of higher-fidelity, nonlinear models: it is rather based on the selection of two different structural nodes where the structural motion is to be one at a time completely constrained, typically, a node near the center of mass and another in the region of maximum structural displacements with respect to mean axes. If the two displacement vectors calculated in each case can be transformed between themselves with linear rigid-body modes of the structure, then it is still in the regime of small deformations. In the present paper, in order to demonstrate the value of this methodology, it is applied to the X-HALE aircraft in its four-, six- and eight-meter-span configurations, and the results obtained with the assumption of small deformations are compared with a higher-fidelity model that comprises large structural deformations.

© Emerald Publishing Limited.Purpose: The purpose of this paper is to present a mathematical model of one very flexible transport category airplane whose structural dynamics was modeled with the strain-based formulation. This model can be used for the analysis of couplings between the flight dynamics and structural dynamics. Design/methodology/approach: The model was developed with the use of Hamiltonian mechanics and strain-based formulation. Nonlinear flight dynamics, nonlinear structural dynamics and inertial couplings are considered. Findings: The mathematical model allows the analysis of effects of high structural deformations on airplane flight dynamics. Research limitations/implications: The mathematical model has more than 60 degrees of freedom. The computational burden is too high, if compared to the traditional rigid body flight dynamics simulations. Practical implications: The mathematical model presented in this work allows a detailed analysis of the couplings between flight dynamics and structural dynamics in very flexible airplanes. The better comprehension of these couplings will contribute to the development of flexible airplanes. Originality/value: This work presents the application of nonlinear flight dynamics-nonlinear structural dynamics-strain-based formulation (NFNS-s) methodology to model the flight dynamics of one very flexible transport category airplane. This paper addresses also the way as the analysis of results obtained in nonlinear simulations can be made. Comparisons of the NFNS-s and nonlinear flight dynamics-linear structural dynamics methodologies are presented in this work.

This work addresses the modeling and control of fluid-structure systems. In the first part, the port-Hamiltonian systems (PHS) formulation is used for modeling fluid-structure interactions. This formulation allows describing fluid dynamics and structural dynamics separately and coupling the subsystems easily through physically relevant interconnection ports, which naturally arise in the PHS models. The modeling method is validated on the experimental set-up available at ISAE. The second part is devoted to the control of sloshing using damping injection, that is a classical passivity-based control method, in order to reduce vibrations in flexible structures. One difficulty of this approach is that collocated (and power conjugated) actuators and sensors are needed. This paper presents a method for dealing with damping injection in mechanical systems with non-collocated inputs/outputs making use of a state observer. Finally, control by damping injection is performed, and the overall method is successfully tested on the experimental device.

© 2016A model reduction method for infinite-dimensional port-Hamiltonian systems with distributed ports is presented. The method is applied to the Euler-Bernoulli equation with piezoelectric patches. The voltage is considered as an external input of the system. This gives rise to an unbounded input operator. A weak formulation is used to overcome this difficulty. It also allows defining a discretization method which leads to a finite-dimensional port-Hamiltonian system; the energy flow of the original system is preserved. Numerical results are compared to experimental ones to validate the method. Further work should use this model to couple the approximated equations with a more complex system, and to design active control laws.

© 2015 IFAC.The interactions between fluid and structural dynamics are an important subject of study in several engineering applications. In airplanes, for example, these coupled vibrations can lead to structural fatigue, noise and even instability. At ISAE, we have an experimental device that consists of a cantilevered plate with a fluid tank near the free tip. This device is being used for model validation and active control studies. This work uses the port-Hamiltonian systems formulation for modeling this experimental device. Structural dynamics and fluid dynamics are independently modeled as infinite-dimensional systems. The plate is approximated as a beam. Shallow water equations are used for representing the fluid in the moving tank. The global system is coupled and spatial discretization of the infinite-dimensional systems using mixed finite-element method allows to obtain a finite-dimensional system that is still Hamiltonian.

Structural vibrations can have severe consequences on airplane design like fatigue, aeroelastic instability and reduced maneuverability. Fuel sloshing inside wing tanks can increase these problems. This work is intended to model a system that consists of a cantilever aluminum plate with a fluid tank near the free tip. Piezoelectric patches are used to excite the system. Three different methodologies were used to obtain a state-space model of the system: analytical (exact) solutions of simplified problems, numerical approximated methods and system identification techniques. Results show good agreement between theory and experiments. © 2014 IEEE.

The design of a sailing robot controller is addressed. Based on a simulation model, and validated by experiments with a real sailing robot, three controllers are compared: the classical fuzzy controller, the state machine controller and the fuzzy state machine controller. The fuzzy controller shows poor results because the robot is, like any sailboat, subject to dramatic change in its internal state (tacking, jibe, etc.) The "natural" approach is to describe the transitions between states as a classical state machine with transitions. We improve the concept with fuzzy transition, obtaining the same results in term of behavior but using effectiveness of fuzzy design to transpose human expertise in fuzzy rules. Although these controllers show good results in a wide range of wind force, we conclude that adaptive control is needed. © 2009 IFAC.