Application of the Lagrangian Equations to Electrical Circuits

Wells, Dennis

doi:10.1063/1.1710422

Cited by 21 publications

(14 citation statements)

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“…in the books by Neȋmark and Fufaev [28], Wells [31], and Gossick [32]. Articles discussing various aspects of these systems are [33,34,35,36]. We now proceed to some concrete examples of magnetomechanical systems.…”

Section: Electromechanical Systemsmentioning

confidence: 99%

From least action in electrodynamics to magnetomechanical energy—a review

Essén

2009

Eur. J. Phys.

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The equations of motion for electromechanical systems are traced back to the fundamental Lagrangian of particles and electromagnetic fields, via the Darwin Lagrangian. When dissipative forces can be neglected the systems are conservative and one can study them in a Hamiltonian formalism. The central concepts of generalized capacitance and inductance coefficients are introduced and explained. The problem of gauge independence of self-inductance is considered. Our main interest is in magnetomechanics, i.e. the study of systems where there is exchange between mechanical and magnetic energy. This throws light on the concept of magnetic energy, which according to the literature has confusing and peculiar properties. We apply the theory to a few simple examples: the extension of a circular current loop, the force between parallel wires, interacting circular current loops, and the rail gun. These show that the Hamiltonian, phase space, form of magnetic energy has the usual property that an equilibrium configuration corresponds to an energy minimum.

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Section: Electromechanical Systemsmentioning

confidence: 99%

From least action in electrodynamics to magnetomechanical energy—a review

Essén

2009

Eur. J. Phys.

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“…Effectively, the double C fly configuration doubles the current, so it increases the efficiency. The main difference among the three architectures is the minimum output voltage which can be created: The switching nature of charge pump topologies leads to a steady state approach to study the quantities of interest (Vout, Iout, efficiency...), so we have a different set of equations to solve for each phase of the clock [1]; the energy stored in each capacitor is the key to obtain the behavior of the charge stored, and thus the voltages and the currents.…”

Section: Mathematical Modelsmentioning

confidence: 99%

“…Two capacitors are inserted after the amplifier to remove this DC voltage. Bulky and expensive capacitors together with pop noise during start-up of the audio channel make this solution not the best one in terms of performance [1].…”

Section: Introductionmentioning

confidence: 98%

A novel series-parallel inverting charge pump topology in 40nm CMOS technology

Neri¹,

Fazio

Teng³

et al. 2011

2011 IEEE International Conference on Microwaves, Communications, Antennas and Electronic Systems (COMCAS 2011)

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This paper presents an innovative inverting charge pump on a series-parallel architecture, suitable for ground-referenced power supply systems for earphone audio amplifiers. Implemented in a 40nm CMOS technology, the paper illustrates in details the architecture and the final measurement on silicon, highlighting great performance in terms of efficiency and THD when applied as negative power supply for high quality earphone audio amplifier.

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“…where I M and I G are the moments of inertia of the rotor and the gear about their rotation axis respectively. To incorporate the motor dynamics, the kinetic energy of motor circuits [25] is defined by…”

Section: A Continuous-time Modeling Of Wipmentioning

confidence: 99%

Structure-Preserving Constrained Optimal Trajectory Planning of a Wheeled Inverted Pendulum

Albert¹,

Phogat²,

Anhalt³

et al. 2018

Preprint

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The Wheeled Inverted Pendulum (WIP) is an underactuated, nonholonomic mechatronic system, and has been popularized commercially as the Segway. Designing a control law for motion planning, that incorporates the state and control constraints, while respecting the configuration manifold, is a challenging problem. In this article we derive a discrete-time model of the WIP system using discrete mechanics and generate optimal trajectories for the WIP system by solving a discretetime constrained optimal control problem. Further, we describe a nonlinear continuous-time model with parameters for designing a closed loop LQ-controller. A dual control architecture is implemented in which the designed optimal trajectory is then provided as a reference to the robot with the optimal control trajectory as a feedforward control action, and an LQ-controller in the feedback mode is employed to mitigate noise and disturbances for ensuing stable motion of the WIP system. While performing experiments on the WIP system involving aggressive maneuvers with fairly sharp turns, we found a high degree of congruence in the designed optimal trajectories and the path traced by the robot while tracking these trajectories. This corroborates the validity of the nonlinear model and the control scheme. Finally, these experiments demonstrate the highly nonlinear nature of the WIP system and robustness of the control scheme.

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Application of the Lagrangian Equations to Electrical Circuits

Cited by 21 publications

References 0 publications

From least action in electrodynamics to magnetomechanical energy—a review

From least action in electrodynamics to magnetomechanical energy—a review

A novel series-parallel inverting charge pump topology in 40nm CMOS technology

Structure-Preserving Constrained Optimal Trajectory Planning of a Wheeled Inverted Pendulum

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