One Alone Makes No Coupling

Roberta Lima, Rubens Sampaio, Peter Hagedorn


Electromechanical systems deal with the mutual interaction between electromagnetic and mechanical parts. In this paper, it simply means the connection of a DC motor and a mechanical part by some mechanism. This interaction is called coupling. The mechanical and the electromagnetic subsystems interact. To properly represent the dynamics of a coupled system, it is necessary to properly characterize this interaction between the parts. Any change in the modeling of the interaction affects the behavior of the entire system. Typically, the coupling between electromagnetic and mechanical parts is expressed by a set of coupled differential equations. The dynamics of the coupled system is given by an initial value problem comprising this set of coupled differential equations. In this paper, we discuss three mistakes found in the literature on electromechanical systems. The three mistakes somehow decouple the system. They maim the initial value problem of the coupled system, in a way that it looses one differential equation and the initial condition related to the lost equation. The remaining equations represent only the dynamics of the mechanical part. The dynamics of the motor is ignored in a way that the electromagnetic part is decoupled from the system. Apparently they are useful hypotheses, since they simplify the problem greatly. However they lead to wrong results, as is shown in this paper. To exemplify how the hypotheses mislead and change the dynamics, numerical simulations are performed for an simple electromechanical system. Observing the results, one sees, immediately, the inadequacy of them. The oldest of these misleading hypotheses was first made at least 75 years ago still persist in the literature. It seems that lately these hypotheses are used more than ever.

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