The Experts below are selected from a list of 25812 Experts worldwide ranked by ideXlab platform
Michal Feckan - One of the best experts on this subject based on the ideXlab platform.
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a survey on the melnikov theory for implicit ordinary differential equations with applications to RLC Circuits
2019Co-Authors: Michal FeckanAbstract:Our recent results are presented on the development of the Melnikov theory in investigation of implicit ordinary differential equations with small amplitude perturbations. In particular, the persistence of orbits connecting singularities in finite time is studied provided that certain Melnikov like conditions hold. Achievements on reversible implicit ordinary differential equations are also considered. Applications are given to nonlinear systems of RLC Circuits.
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on the existence of solutions connecting ik singularities and impasse points in fully nonlinear RLC Circuits
Discrete and Continuous Dynamical Systems-series B, 2017Co-Authors: Flaviano Battelli, Michal FeckanAbstract:Higher-dimensional nonlinear and perturbed systems of implicit ordinary differential equations are studied by means of methods of dynamical systems. Namely, the persistence of solutions are studied under nonautonomous perturbations connecting either impasse points with IK-singularities or two impasse points. Important parts of the paper are applications of the theory to concrete perturbed fully nonlinear RLC Circuits.
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on the existence of solutions connecting singularities in nonlinear RLC Circuits
Nonlinear Analysis-theory Methods & Applications, 2015Co-Authors: Flaviano Battelli, Michal FeckanAbstract:Abstract We apply dynamical system methods and Melnikov theory to study small amplitude perturbations of some implicit differential equations arising in RLC Circuits. We find conditions under which solutions joining two singularities persist after a small forcing. Finally, in the last section we extend this result to a wider class of implicit differential equations.
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nonlinear RLC Circuits and implicit odes
Differential and Integral Equations, 2014Co-Authors: Flaviano Battelli, Michal FeckanAbstract:We apply dynamical system methods and Melnikov theory to study small amplitude perturbation of some implicit di!erential equa- tions exhibiting I-singularities (in the sense given in (16, p. 166)). In particular, we show persistence of such I-singularities and orbits con- necting them in finite time provided a Melnikov like condition holds. We start from a concrete example where, we prove that this Melnikov condition actually holds. Then, we extend our results to more general implicit di!erential equations.
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melnikov theory for weakly coupled nonlinear RLC Circuits
Boundary Value Problems, 2014Co-Authors: Flaviano Battelli, Michal FeckanAbstract:We apply dynamical system methods and Melnikov theory to study small amplitude perturbation of some coupled implicit differential equations. In particular we show the persistence of such orbits connecting singularities in finite time provided a Melnikov like condition holds. Application is given to coupled nonlinear RLC system. MSC: Primary 34A09; secondary 34C23; 37G99.
Jacquelien M A Scherpen - One of the best experts on this subject based on the ideXlab platform.
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characterizing inductive and capacitive nonlinear RLC Circuits a passivity test
IFAC Proceedings Volumes, 2004Co-Authors: Eloisa Garcia Canseco, Dimitri Jeltsema, Romeo Ortega, Jacquelien M A ScherpenAbstract:Abstract Linear time invariant RLC Circuits are said to be inductive (capacitive) if the current waveform in sinusoidal steady state has a negative (resp., positive) phase shift with respect to the voltage. Furthermore, it is known that the circuit is inductive (capacitive) if and only if the magnetic energy stored in the inductors dominates (resp., is dominated by) the electrical energy stored in the capacitors. In this paper we propose a framework, based on passivity theory, that allows to extend these intuitive notions to nonlinear RLC Circuits.
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a dual relation between port hamiltonian systems and the brayton moser equations for nonlinear switched RLC Circuits
Automatica, 2003Co-Authors: Dimitri Jeltsema, Jacquelien M A ScherpenAbstract:In the last decades, several researchers have concentrated on the dynamic modeling of nonlinear electrical Circuits from an energy-based perspective. A recent perspective is based on the concept of port-Hamiltonian (PH) systems. In this paper, we discuss the relations between the classical Brayton-Moser (BM) equations-stemming from the early sixties-and PH models for topologically complete nonlinear RLC Circuits, with and without controllable switches. It will be shown that PH systems precisely dualize the BM equations, leading to possible advantages at the level of controller design. Consequently, useful and important properties of the one framework can be translated to the other. Control designs for the PH model cannot be directly implemented since they require observation of flux and charges, which are not directly available through standard sensors, while the BM models require only observation of currents and voltages. The introduced duality allows to pull back PH designs to the space of currents and voltages. This offers the possibility to exchange several different techniques, available in the literature, for modeling, analysis and controller design for RLC Circuits. Illustrative examples are provided to emphasize the duality between both frameworks.
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a novel passivity property of nonlinear RLC Circuits
4th Mathmod Symposium Vienna Austria, 2003Co-Authors: Dimitri Jeltsema, Romeo Ortega, Jacquelien M A ScherpenAbstract:Arbitrary interconnections of passive (possibly nonlinear) resistors, inductors and capacitors define passive systems, with port variables the external sources voltages and currents, and storage function the total stored energy. In this paper we identify a class of RLC Circuits (with convex energy function and weak electromagnetic coupling) for which it is possible to ‘add a differentiation’ to the port terminals preserving passivity—with a new storage function that is directly related to the circuit power. To establish our results we exploit the geometric property that voltages and currents in RLC Circuits live in orthogonal spaces, i.e., Tellegen’s theorem, and heavily rely on the seminal paper of Brayton and Moser published in the early sixties.
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On passivity and power-balance inequalities of nonlinear RLC Circuits
IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2003Co-Authors: Dimitri Jeltsema, Romeo Ortega, Jacquelien M A ScherpenAbstract:Arbitrary interconnections of passive (possibly nonlinear) resistors, inductors, and capacitors define passive systems, with power port variables the external source voltages and currents, and storage function the total stored energy. In this paper, we identify a class of RLC Circuits (with convex energy function and weak electromagnetic coupling), for which it is possible to "add a differentiation" to the port terminals preserving passivity-with a new storage function that is directly related to the circuit power. To establish our results, we exploit the geometric property that voltages and currents in RLC Circuits live in orthogonal spaces, i.e., Tellegen's theorem, and heavily rely on the seminal paper of Brayton and Moser (1964).
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Stabilization of nonlinear RLC Circuits: power shaping and passivation
42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475), 2003Co-Authors: Romeo Ortega, Dimitri Jeltsema, Jacquelien M A ScherpenAbstract:In this paper we prove that for a class of RLC Circuits with convex energy function and weak electromagnetic coupling it is possible to "add a differentiation" to the port terminals preserving passivity - with a new storage function that is directly related to the circuit power. The result is of interest in circuit theory, but also has applications in control problems as it suggests the paradigm of power shaping stabilization as an alternative to the well-known method of energy shaping. We show in the paper that, in contrast with energy shaping designs, power shaping is not restricted to systems without pervasive dissipation and naturally allows to add "derivative" actions in the control. These important features, that stymie the applicability of energy shaping control, make power shaping very practically appealing, as illustrated with examples in the paper. To establish our results we exploit the geometric property that voltages and currents in RLC Circuits live in orthogonal spaces, i.e., Tellegen's theorem, and heavily rely on the seminal paper of Brayton and Moser in 1964.
O. Wing - One of the best experts on this subject based on the ideXlab platform.
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A waveform bounding algorithm for simulation of RLC Circuits
2000 IEEE International Symposium on Circuits and Systems (ISCAS), 2000Co-Authors: Yao-lin Jiang, R.m.m. Chen, O. WingAbstract:A new waveform bounding algorithm to obtain an upper and lower waveform bound of the time response of a class of RLC Circuits is presented. The algorithm produces a sequence of waveforms which converge to the true solution monotonically from above and below. The key step is the choice of the initial guess in the relaxation process. A new method to obtain an initial guess that guarantees monotonic convergence is given. Numerical examples are included to confirm the theoretical results.
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ISCAS - A waveform bounding algorithm for simulation of RLC Circuits
2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353), 2000Co-Authors: Yao-lin Jiang, R.m.m. Chen, O. WingAbstract:A new waveform bounding algorithm to obtain an upper and lower waveform bound of the time response of a class of RLC Circuits is presented. The algorithm produces a sequence of waveforms which converge to the true solution monotonically from above and below. The key step is the choice of the initial guess in the relaxation process. A new method to obtain an initial guess that guarantees monotonic convergence is given. Numerical examples are included to confirm the theoretical results.
Romeo Ortega - One of the best experts on this subject based on the ideXlab platform.
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passivity of nonlinear incremental systems application to pi stabilization of nonlinear RLC Circuits
Systems & Control Letters, 2007Co-Authors: Bayu Jayawardhana, Romeo Ortega, Eloisa Garciacanseco, Fernando CastanosAbstract:Abstract It is well known that if the linear time invariant system x ˙ = A x + B u , y = C x is passive the associated incremental system x ˜ ˙ = A x ˜ + B u ˜ , y ˜ = C x ˜ , with ( · ) ˜ = ( · ) - ( · ) ⋆ , u ⋆ , y ⋆ the constant input and output associated to an equilibrium state x ⋆ , is also passive. In this paper, we identify a class of nonlinear passive systems of the form x ˙ = f ( x ) + gu , y = h ( x ) whose incremental model is also passive. Using this result we then prove that a large class of nonlinear RLC Circuits with strictly convex electric and magnetic energy functions and passive resistors with monotonic characteristic functions are globally stabilizable with linear PI control.
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Passivity of Nonlinear Incremental Systems: Application to PI Stabilization of Nonlinear RLC Circuits
Proceedings of the 45th IEEE Conference on Decision and Control, 2006Co-Authors: Bayu Jayawardhana, Romeo Ortega, Eloisa Garcia-canseco, Fernando CastanosAbstract:It is well known that if the linear time invariant system xdot = Ax + Bu, y = Cx is passive the associated incremental system xtilde = Axtilde + Butilde, ytilde = Cxtilde, with (middot) = (middot) - (middot)*, u*, y*, the constant input and output associated to an equilibrium state x* , is also passive. In this paper, we identify a class of nonlinear passive systems of the form x = f(x) +gu, y = h(x) whose incremental model is also passive. Using this result we then prove that general nonlinear RLC Circuits with convex and proper electric and magnetic energy functions and passive resistors with monotonic characteristic functions are globally stabilizable with linear PI control
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characterizing inductive and capacitive nonlinear RLC Circuits a passivity test
IFAC Proceedings Volumes, 2004Co-Authors: Eloisa Garcia Canseco, Dimitri Jeltsema, Romeo Ortega, Jacquelien M A ScherpenAbstract:Abstract Linear time invariant RLC Circuits are said to be inductive (capacitive) if the current waveform in sinusoidal steady state has a negative (resp., positive) phase shift with respect to the voltage. Furthermore, it is known that the circuit is inductive (capacitive) if and only if the magnetic energy stored in the inductors dominates (resp., is dominated by) the electrical energy stored in the capacitors. In this paper we propose a framework, based on passivity theory, that allows to extend these intuitive notions to nonlinear RLC Circuits.
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a novel passivity property of nonlinear RLC Circuits
4th Mathmod Symposium Vienna Austria, 2003Co-Authors: Dimitri Jeltsema, Romeo Ortega, Jacquelien M A ScherpenAbstract:Arbitrary interconnections of passive (possibly nonlinear) resistors, inductors and capacitors define passive systems, with port variables the external sources voltages and currents, and storage function the total stored energy. In this paper we identify a class of RLC Circuits (with convex energy function and weak electromagnetic coupling) for which it is possible to ‘add a differentiation’ to the port terminals preserving passivity—with a new storage function that is directly related to the circuit power. To establish our results we exploit the geometric property that voltages and currents in RLC Circuits live in orthogonal spaces, i.e., Tellegen’s theorem, and heavily rely on the seminal paper of Brayton and Moser published in the early sixties.
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On passivity and power-balance inequalities of nonlinear RLC Circuits
IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 2003Co-Authors: Dimitri Jeltsema, Romeo Ortega, Jacquelien M A ScherpenAbstract:Arbitrary interconnections of passive (possibly nonlinear) resistors, inductors, and capacitors define passive systems, with power port variables the external source voltages and currents, and storage function the total stored energy. In this paper, we identify a class of RLC Circuits (with convex energy function and weak electromagnetic coupling), for which it is possible to "add a differentiation" to the port terminals preserving passivity-with a new storage function that is directly related to the circuit power. To establish our results, we exploit the geometric property that voltages and currents in RLC Circuits live in orthogonal spaces, i.e., Tellegen's theorem, and heavily rely on the seminal paper of Brayton and Moser (1964).
Yao-lin Jiang - One of the best experts on this subject based on the ideXlab platform.
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A waveform bounding algorithm for simulation of RLC Circuits
2000 IEEE International Symposium on Circuits and Systems (ISCAS), 2000Co-Authors: Yao-lin Jiang, R.m.m. Chen, O. WingAbstract:A new waveform bounding algorithm to obtain an upper and lower waveform bound of the time response of a class of RLC Circuits is presented. The algorithm produces a sequence of waveforms which converge to the true solution monotonically from above and below. The key step is the choice of the initial guess in the relaxation process. A new method to obtain an initial guess that guarantees monotonic convergence is given. Numerical examples are included to confirm the theoretical results.
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ISCAS - A waveform bounding algorithm for simulation of RLC Circuits
2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353), 2000Co-Authors: Yao-lin Jiang, R.m.m. Chen, O. WingAbstract:A new waveform bounding algorithm to obtain an upper and lower waveform bound of the time response of a class of RLC Circuits is presented. The algorithm produces a sequence of waveforms which converge to the true solution monotonically from above and below. The key step is the choice of the initial guess in the relaxation process. A new method to obtain an initial guess that guarantees monotonic convergence is given. Numerical examples are included to confirm the theoretical results.
