Pitfalls in the dynamics of coupled electromechanical systems

Lima, Roberta; Sampaio, Rubens

doi:10.5540/03.2018.006.02.0310

Cited by 13 publications

(35 citation statements)

References 6 publications

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“…While for the reduced IVP, there is no functional relation between ̇ and c, for the reduced IVP, there is a linear relation between ̇ and c, given by Eq. (16). Remark that this linear relation is the same relation given by Eq.…”

Section: Results For Different Values Of the Source Voltagementioning

confidence: 64%

See 1 more Smart Citation

Comments on the paper “On nonlinear dynamics behavior of an electro-mechanical pendulum excited by a nonideal motor and a chaos control taking into account parametric errors” published in this journal

Lima

Sampaio

Hagedorn

et al. 2019

J Braz. Soc. Mech. Sci. Eng.

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Electromechanical systems are an interesting type of coupled systems. The mutual influence between electromagnetic and mechanical subsystems characterizes coupling. Each subsystem affects the behaviour of the other. Typically, the dynamics of an electromechanical system is expressed by an initial value problem (IVP) that comprises a set of coupled differential equations involving electrical and mechanical variables, as for example, current and angle. This article discusses a hypothesis found in a recent paper published in this journal ("On nonlinear dynamics behavior of an electromechanical pendulum excited by a nonideal motor and a chaos control taking into account parametric errors") and in some thesis. The hypothesis is that it is possible to consider the derivative of the current equal to zero in the IVP that gives the dynamics of an electromechanical system without changing the system dynamics. The hypothesis is based only on some parameter values and, also, does not depend on the electromechanical system being analysed. Apparently, it is a nice hypothesis since it simplifies the dynamics greatly. With the hypothesis, the number of equations in the IVP that gives the dynamics is reduced. The hypothesis results in a reduced system, a simplification of the complete one. However, the hypothesis contradicts itself and changes the dynamics. The reduced system does not represent the complete system, and, moreover, it decouples the electromagnetic and mechanical subsystems. The reduction eliminates the mutual interaction between the subsystems, i.e., eliminates the coupling. To highlight the problems of the reduction, self-contradiction and dynamical change, we analyse the effects of the hypothesis for a simple electromechanical system, a motor-cart system. For the chosen system, the equations of the two IVP, reduced and complete, are presented and numerical simulations are performed. Considering just the results of simulations of the reduced IVP, it is possible to verify the self-contradiction of the hypothesis made. Comparing the results of simulations of the reduced and complete IVPs, it is possible to see, immediately, the big difference between the two dynamics.

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Section: Results For Different Values Of the Source Voltagementioning

confidence: 64%

“…Typically, the coupling between electromagnetic and mechanical subsystems is expressed by a set of coupled differential equations [9,[11][12][13]20]. The dynamics of the coupled system is given by an initial value problem (IVP) comprising this set of coupled differential equations [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Comments on the paper “On nonlinear dynamics behavior of an electro-mechanical pendulum excited by a nonideal motor and a chaos control taking into account parametric errors” published in this journal

Lima

Sampaio

Hagedorn

et al. 2019

J Braz. Soc. Mech. Sci. Eng.

Self Cite

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“…Equation 11is obtained consideringα = 0 andα = 0 in Eq. (10). Remark that during the stick-mode, the frictional force varies and depends on the angular position of the motor.…”

Section: Dynamics Of the Electromechanial System With Dry-frictionmentioning

confidence: 99%

“…Electromechanical systems present an interesting behavior characterized by the mutual influence between the electrical and mechanical parts of the system, that is, the dynamics of the motor is heavily influenced by the mechanical system and the dynamics of the mechanical system depends on the dynamics of the motor [1][2][3]11] Each part of the system affects the behavior of the other, i.e., they interact. The coupling varies with the coupling conditions, it is not a functional relation and depends on the initial conditions [5,6] The dynamics of the coupled system is given by an initial value problem comprising a set of coupled differential equations [9,10], in which the coupling torque appears as a parametric excitation, i.e., a time variation of the system parameters. The problem becomes even more interesting if it is considered the existence of dry-friction in the electromechanical system.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of a coupled system with dry-friction

Lima¹,

Sampaio²

2020

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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This work analyzes the nonlinear dynamics of a coupled system with dry-friction. The system has a mechanical part and an electromagnetic part. It is composed of a cart, whose motion is excited by a DC motor. The coupling between the motor and the cart is made by a mechanism called scotch yoke, so that the motor rotational motion is transformed in horizontal cart motion in a rail. It is considered the existence of dry-friction between the cart and the rail. The friction is modeled as Coulomb friction. The resulting motion of the motor can be characterized by two qualitatively different and alternate modes, the stick-and slip-modes, with a non-smooth transition between them. The focus of the work is to find the stick-and slip-mode parts of the trajectory for different values of the system parameters.

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“…The objective of this project was to formulate a Lagrangian for electromechanical systems. It is not possible to deal with electromechanical systems without knowing the electrical part, please see [15]. Some incorrect methods consist in mimicking the standard derivations of purely mechanical systems to electromechanical systems .…”

Section: Discussionmentioning

confidence: 99%

Lagrangians for Electromechanical Systems

MANHAES¹

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Lagrangians for Electromechanical SystemsElectromechanical systems are very common. The importance of constructing the dynamical equations of motors coupled with mechanical subsystems suggests a new strategy . In the literature, often, the derivation of the dynamical equations is wrong. One thinks that the standard derivations of the dynamical equations of purely mechanical systems can be mimicked to electromechanical systems. Unfortunately, it cannot. The main reason is that in electromechanical systems one deals with the presence of electromagnetic fields, continuous entities. These fields store electrical and mechanical energies. In purely mechanical systems the conservative mechanical energy is stored as elastic or gravitational energy , and the nonconservative terms enter the equation as nonconservative forces. This cannot be done in electromechanical systems. This project shows the right way to derive the dynamical equations applying the results for systems formed by a motor, a coupling mechanism, and a mechanical subsystem.

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Pitfalls in the dynamics of coupled electromechanical systems

Cited by 13 publications

References 6 publications

Comments on the paper “On nonlinear dynamics behavior of an electro-mechanical pendulum excited by a nonideal motor and a chaos control taking into account parametric errors” published in this journal

Comments on the paper “On nonlinear dynamics behavior of an electro-mechanical pendulum excited by a nonideal motor and a chaos control taking into account parametric errors” published in this journal

Nonlinear dynamics of a coupled system with dry-friction

Lagrangians for Electromechanical Systems

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