Control and trajectory tracking by flatness of a time-variant stator flux motor

By the use of flatness the problem of pole placement, which consists in imposing closed loop system dynamics can be related to tracking. This point of view has been used to enlighten the design of RST controllers in the linear system case with constant parameters. We will see in the present paper that in the case of time-varying linear systems this point of view can also be adopted and leads to design a feedback in terms of the flat output and its derivatives. To implement this feedback a constant gain reduced order observer can be used. The observer poles are also chosen with respect to the trajectory to follow. All these developements are exemplified on a DC motor with a time-variant stator flux, and lead to a simple but powerfull control for tracking a given trajectory for the angular velocity of the motor.