The minimal analytical form of the characteristic polynomial of an asynchronous drive system

In studies of the robust stability of induction motor drive systems, it is often necessary to know the analytical form of the characteristic polynomial of such a drive system. Such a form makes it possible to reveal, symbolically, the relation between the coefficients of the characteristic polynomial of the drive studied and the parameters of the induction motor. During analysis of the various feedback loops existing in the multidimensional control system studied, the nontrivial problem of minimization of the order of the matrix transfer function characteristic polynomial may arise. In the paper, a method which considerably simplifies the procedure of determining the minimal, as regards order, analytical form of the characteristic polynomial of a drive system is presented. From this method, general formulae are obtained, which make it possible to determine simply and quickly the analytical forms of any complex, as regards structure and number of controlled output signals, transfer function types of induction motor control systems