Nonlinear compensator synthesis via linear parameter-varying control

For the nonlinear output regulation or servomechanism problem, a nonlinear compensator synthesis framework is presented that merges techniques for linear parameter-varying (LPV) systems with ideas derived from linearization-based gain scheduling. Plant linearizations about zero-error trajectories have an LPV structure upon which the synthesis of an LPV compensator is based. A key issue is whether, loosely speaking, the linearization process can be reversed wherein a nonlinear compensator is sought that linearizes to the LPV compensator about every zero-error trajectory. Necessary and sufficient existence conditions are derived for the existence of compensators satisfying this linearization requirement. Based on this, it is shown that error feedback compensators that contain an internal model of the exosystem are guaranteed to exist under mild hypotheses. A nonlinear compensator is designed for the ball and beam apparatus to illustrate the technique.