Feedback Linearization and Application to Electric Motors

Abstract

Having obtained nonlinear dynamical models for various electric motors in Chap. 3, various new tools in synthesizing nonlinear controllers may be considered. One approach is feedback linearization, i.e., application of a nonlinear change of coordinates and a nonlinear redefinition of inputs so that the system is equivalent to a linear system in the new coordinates. In the first part of this chapter, we discuss the theory of feedback linearization. En route to the presentation of feedback linearization, we shall encounter various notions of the modern geometric theory of nonlinear control [9, 83, 99, 160, 179] . In the second part of the chapter, we shall apply the developed feedback linearization techniques to the various stepper motors. Feedback linearization for brushless DC and induction motors will be considered in Chaps. 11 and 12, respectively. As will be seen, the feedback linearization approach requires exact knowledge of the parameters and the dynamics and availability of all states. In the subsequent chapters of the book, we will remove these restrictions in order to develop robust nonlinear control designs to achieve high performance for motors.