Active Unmatched Disturbance Cancellation and Estimation by State–Derivative Feedback for Plants Modeled as an LTI System

We design adaptive algorithms for both cancellation and estimation of unknownperiodic disturbance, by feedback of state–derivatives (i.e., withoutposition information for mechanical systems) for the plants which are modeledas a linear time invariant system. We consider a series of unmatched unknownsinusoidal signals as the disturbance. The first step of the design consists ofthe parametrization of the disturbance model and the development of observerfilters. The result obtained in this step allows us to use adaptive control techniquesfor the solution of the problem. In order to handle the unmatchedcondition, a backstepping technique is employed. Since the partial measurementof the virtual inputs is not available, we design a state observer and theestimates of these signals are used in the backstepping design. Finally, thestability of the equilibrium of the adaptive closed loop system with the convergenceof states is proven. As a numerical example, a two-degree of freedomsystem is considered and the effectiveness of the algorithms are shown.

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