High Performance Control of AC Drives with Matlab / Simulink Models

6.4 Multiscalar model (MM) of Induction Motor

An induction motor is a higher-order, non-linear object, as shown in Chapter 2. An internal coupling appears between mechanical and electromagnetic variables. Therefore, it is especially beneficial to use the idea of non-linear control for induction motor control.

6.4.1 Multiscalar Variables

The non-linear control idea using non-linear feedback was first time presented in [1]. It creates a new model of the machine with fewer state variables, which may be linked with the rotor, stator, main flux, etc. If the variables are a function of the rotor flux, then a terminology of non-linear rotor-oriented control systems is presented (i_s, ψ_r). Other options, such as (i_s, ψ_s), (i_s, ψ_m), may also be used. In this book, we will focus on the first option because of its popularity and less complicated decoupling system; however, for extra work, other options could be derived and examined.

The new state variables for the (i_s, ψ_r) option may be interpreted as rotor angular speed, scalar, and vector products of the stator current and rotor flux vectors, and the square of the rotor linkage flux presented in an arbitrary reference frame (i.e. XY) as [1,2,26]

(6.24)

(6.25)

(6.26)

(6.27)

In these equations, are the rotor flux and stator current vectors ...