Robust servomechanism output feedback controllers for feedback linearizable systems

Abstract We consider a single-input-single-output nonlinear system which has a uniform relative degree equal to the dimension of the state vector. The system can be transformed into a normal form with no zero dynamics. We allow the system's equation to depend on bounded uncertain parameters which do not change the relative degree. Disturbances are assumed to satisfy a strict-feedback condition which allows us to use a time-varying, disturbance-dependent transformation to transform the system into an error space where disturbances and uncertainties satisfy the matching condition. The nonlinear functions in the error space are used to choose an internal model which is augmented with the system, and a robust state feedback control is designed to drive the error to a positively invariant set that contains the origin. We then show the existence of a zero-error manifold inside this set which attracts all trajectories inside the set. To implement this control using output feedback, we saturate the state feedback control outside a compact set of interest and estimate the state using a high-gain observer. The output feedback controller recovers the robustness and asymptotic tracking properties of the state feedback controller.

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