Dynamic analysis of brushless motors based on compact representations of the equations of motion

Formulation of the equations of motion for brushless motors in the compact form is considered. It is demonstrated that, by incorporating a combination of time scaling and linear state transformations, compact representations for the equations of motion can be obtained. It is shown that, by nondimensionalizing the equations of motion for brushless motors, one can significantly reduce the number of parameters in the model, and thus significantly reduce the complexity associated with the dynamic analysis procedure. Using the compact representations, it is demonstrated that the systems under investigation, subject to constant inputs and loads, possess multiple equilibrium states which characterize the global stability. As a by-product of the proposed scheme, an equivalence relationship between brushless motors and the Lorenz system is presented