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

Abstract

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.

Parametrization of electromechanical systems must acknowledge Newton and Maxwell

“…This paper analyzes a common error found in the literature that deals with electromechanical systems. Here, the error is discussed in the context of an galvanometer, but it the literature, the error appears in many different contexts [4][5][6][7]11]. The error is an artifice to simplify the system dynamics.…”

“…They uncouple the mechanical and an electromagnetic subsystems by neglecting the existence of inductance in the electromagnetic subsystem and assuming a functional relation between mechanical and electromagnetic variables. Therefore, the system is characterized by only mechanical variables and the dynamics is reduced to an IVP with only a mechanical equation [4][5][6][7][8]11]. Some references that makes the reduction are references 1, 2 and 3 of [6] and reference 4 of [5].…”

“…Therefore, the system is characterized by only mechanical variables and the dynamics is reduced to an IVP with only a mechanical equation [4][5][6][7][8]11]. Some references that makes the reduction are references 1, 2 and 3 of [6] and reference 4 of [5].…”

On the reduction of nonlinear electromechanical systems

“…In some recent publications, Lima and Sampaio [43], and Lima et al [44] put in check the validity of this electromechanical quasi-steady-state assumption, claiming that, as this simplification decouples the electrical system from its mechanical counterpart, it loses the main features of the system's physics, leading to erroneous predictions. Using the electromechanical system presented in [42] as an example, they give and discuss a limit case in which this model-order reduction approach leads to erroneous predictions.…”

Energy analysis of an electromagnetic loudspeaker

“…When the electromagnetic subsystem and these coupling terms are neglected, the electromechanical system becomes a purely mechanical system described by mechanical variables. The recent published paper [3] discusses about some of the references with mistakes and shows how the neglection of the electromagnetic and coupling terms changes the dynamics.…”