Poincaré Map-Based Design

In this chapter, Poincare maps were used, to the best knowledge of the authors, for the first time as a design tool: to find controller parameters that provide the desired amplitude and frequency of the periodic motion of in systems having nonlinear plants, through the use of the TRC . We present application to an underactuated mechanical system via generating a self-excited oscillation of a desired amplitude and frequency of the unactuated position variable. Poincare map design provides values of the TRC parameters and ensures local orbital stability of the periodic motions, for an arbitrary mechanical plant. The proposed approach is illustrated by the controller design for and experiments on the inertia wheel pendulum.