Pitfalls in the dynamics of coupled electromechanical systems

Abstract

One of the main features of electromechanical systems is the mutual influence between electrical and mechanical parts. This interaction characterizes coupling. Each part of the system affects the behavior of the other. To properly represent the dynamics of a coupled system, it is necessary to properly characterize how is this interaction between the parts. Any change in model of the interaction affects the behavior of the entire system. Typically, the coupling between electrical 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. Some references in the literature claim that it is possible to reduce the number of equations in initial value problem without changing the interaction between the electrical and mechanical parts. They assume a hypothesis that a term in the equations can be neglected in a way that the coupling between the parts becomes a linear algebraic relationship. This hypothesis reduces the number of equations to be integrated, however it is a pitfall! It implies the decoupling of the motor-cart system, misleading the results as it is shown in this paper.