Port-Hamiltonian systems’ modelling in electrical engineering. - In: Scientific computing in electrical engineering, (2024), S. 133-143
The port-Hamiltonian (pH) modelling framework allows for models that preserve essential physical properties such as energy conservation or dissipative inequalities. If all subsystems are modelled as pH systems and the inputs are related to the output in a linear manner, the overall system can be modelled as a pH system, too, which preserves the properties of the underlying subsystems. If the coupling is given by a skew-symmetric matrix, as usual in many applications, the overall system can be easily derived from the subsystems without the need of introducing dummy variables and therefore artificially increasing the complexity of the system. Hence the framework of pH systems is especially suitable for modelling multiphysical systems.
https://doi.org/10.1007/978-3-031-54517-7_15
Experimental validation for the combination of funnel control with a feedforward control strategy. - In: Multibody system dynamics, ISSN 1573-272X, Bd. 0 (2024), 0, S. 1-19
Current engineering design trends, such as lightweight machines and human-machine interaction, often lead to underactuated systems. Output trajectory tracking of such systems is a challenging control problem. Here, we use a two-design-degree of freedom control approach by combining funnel feedback control with feedforward control based on servo-constraints. We present experimental results to verify the approach and demonstrate that the addition of a feedforward controller mitigates drawbacks of the funnel controller. We also present new experimental results for the real-time implementation of a feedforward controller based on servo-constraints on a minimum phase system.
https://doi.org/10.1007/s11044-024-09976-2
Structure-preserving model reduction for dissipative mechanical systems. - In: Calm, smooth and smart, (2024), S. 209-230
Suppressing vibrations in mechanical systems, usually described by second-order dynamical models, is a challenging task in mechanical engineering in terms of computational resources even nowadays. One remedy is structure-preserving model order reduction to construct easy-to-evaluate surrogates for the original dynamical system having the same structure. In our work, we present an overview of recently developed structure-preserving model reduction methods for second-order systems. These methods are based on modal and balanced truncation in different variants, as well as on rational interpolation. Numerical examples are used to illustrate the effectiveness of all described methods.
https://doi.org/10.1007/978-3-031-36143-2_11
Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems. - In: Numerische Mathematik, ISSN 0945-3245, Bd. 155 (2023), 1, S. 1-34
A dynamic iteration scheme for linear differential-algebraic port-Hamiltonian systems based on Lions-Mercier-type operator splitting methods is developed. The dynamic iteration is monotone in the sense that the error is decreasing and no stability conditions are required. The developed iteration scheme is even new for linear port-Hamiltonian systems governed by ODEs. The obtained algorithm is applied to a multibody system and an electrical network.
https://doi.org/10.1007/s00211-023-01369-5
Passivity, port-Hamiltonian formulation and solution estimates for a coupled magneto-quasistatic system. - In: Evolution equations and control theory, ISSN 2163-2480, Bd. 12 (2023), 4, S. 1208-1232
In this paper, we study a quasilinear coupled magneto-quasistatic model from a systems theoretic perspective. First, by taking the injected voltages as input and the associated currents as output, we prove that the magneto-quasistatic system is passive. Moreover, by defining suitable Dirac and resistive structures, we show that it admits a representation as a port-Hamiltonian system. Thereafter, we consider dependence of the solution on initial and input data. We show that the current and the magnetic vector potential can be estimated by means of the initial magnetic vector potential and the voltage. We also analyse the free dynamics of the system and study the asymptotic behavior of the solutions for $ t\to\infty $.
https://doi.org/10.3934/eect.2023008
Analysis of a quasilinear coupled magneto-quasistatic model: solvability and regularity of solutions. - In: Journal of mathematical analysis and applications, ISSN 1096-0813, Bd. 523 (2023), 2, 127033
We consider a quasilinear model arising from dynamical magnetization. This model is described by a magneto-quasistatic (MQS) approximation of Maxwell's equations. Assuming that the medium consists of a conducting and a non-conducting part, the derivative with respect to time is not fully entering, whence the system can be described by an abstract differential-algebraic equation. Furthermore, via magnetic induction, the system is coupled with an equation which contains the induced electrical currents along the associated voltages, which form the input of the system. The aim of this paper is to study well-posedness of the coupled MQS system and regularity of its solutions. Thereby, we rely on the classical theory of gradient systems on Hilbert spaces combined with the concept of E-subgradients using in particular the magnetic energy. The coupled MQS system precisely fits into this general framework.
https://doi.org/10.1016/j.jmaa.2023.127033
Port-Hamiltonian system nodes. - In: Extended abstracts presented at the 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022, (2022), S. 441-444
We present a framework to formulate infinite dimensional port-Hamiltonian systems by means of system nodes, which provide a very general and powerful setting for unbounded input and output operators that appear, e.g., in the context of boundary control or observation. One novelty of our approach is that we allow for unbounded and not necessarily coercive Hamiltonian energies. To this end, we construct finite energy spaces to define the port-Hamiltonian dynamics and give an application in case of multiplication operator Hamiltonians where the Hamiltonian density does not need to be positive or bounded. In order to model systems involving differential operators on these finite energy spaces, we show that if the total mass w.r.t. the Hamiltonian density (and its inverse) is finite, one can define a unique weak derivative.
https://doi.org/10.15495/EPub_UBT_00006809
Systems theoretic properties of linear RLC circuits. - In: Extended abstracts presented at the 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022, (2022), S. 108-111
We consider the differential-algebraic systems obtained by modified nodal analysis of linear RLC circuits from a systems theoretic viewpoint. We derive expressions for the set of consistent initial values and show that the properties of controllability at infinity and impulse controllability do not depend on parameter values but rather on the interconnection structure of the circuit. We further present circuit topological criteria for behavioral stabilizability. This extended abstract is a shortened version of the full paper Glazov and Reis (2020) which has been accepted for the cancelled MTNS 2020 in Cambridge.
https://doi.org/10.15495/EPub_UBT_00006809
Flat outputs for funnel control of non-minimum-phase systems. - In: Extended abstracts presented at the 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022, (2022), S. 85-86
We consider adaptive ouput feedback tracking control of linear time-invariant systems which are not necessarily minimum phase. The zero dynamics is split into a stable and an unstable part, we show that a flat output of the unstable part can contribute to the design of a funnel controller of the system. More precisely, we consider an auxiliary output based of the ”true output” of the system and the flat output of the unstable part of the zero dynamics. The funnel controller is designed for this auxiliary output, and the consequences for the true output are discussed.
https://doi.org/10.15495/EPub_UBT_00006809
A Jordan-like decomposition for linear relations in finite-dimensional spaces. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2022. - 1 Online-Ressource (34 Seiten). - (Preprint ; M22,05)
A square matrix A has the usual Jordan canonical form that describes the structure of A via eigenvalues and the corresponding Jordan blocks. If A is a linear relation in a finite-dimensional linear space H (i.e., A is a linear subspace of H × H and can be considered as a multivalued linear operator), then there is a richer structure. In addition to the classical Jordan chains (interpreted in the Cartesian product H × H), there occur three more classes of chains: chains starting at zero (the chains for the eigenvalue infinity), chains starting at zero and also ending at zero (the singular chains), and chains with linearly independent entries (the shift chains). These four types of chains give rise to a direct sum decomposition (a Jordan-like decomposition) of the linear relation A. In this decomposition there is a completely singular part that has the extended complex plane as eigenvalues; a usual Jordan part that corresponds to the finite proper eigenvalues; a Jordan part that corresponds to the eigenvalue infinity; and a multishift, i.e., a part that has no eigenvalues at all. Furthermore, the Jordan-like decomposition exhibits a certain uniqueness, closing a gap in earlier results. The presentation is purely algebraic, only the structure of linear spaces is used. Moreover, the presentation has a uniform character: each of the above types is constructed via an appropriately chosen sequence of quotient spaces. The dimensions of the spaces are the Weyr characteristics, which uniquely determine the Jordan-like decomposition of the linear relation.
https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2022200249