Harmonic Disturbance Rejection in Tracking Control of Euler-Lagrange Systems: An External Model Approach

We consider the systematic design of tracking controllers for Euler-Lagrange systems which are affected by unmeasurable harmonic disturbances. The problem addressed in this paper departs from the classic setup of the regulator problem and its solution is based on the internal model principle in two aspects. First, the presence of an exogenous disturbance affecting the measurements of the plant output is taken into account. Second, we aim at designing a nominal tracking controller using standard techniques, independently of the device that is used to provide asymptotic rejection of the disturbance. The latter is then added to the stable loop, in such a way that asymptotic cancellation of the disturbance is guaranteed under mild conditions. The device in question is referred to as an external model of the exogenous system, to emphasize the departure from the classic internal model-based design. The external model is endowed with an adaptation mechanism that allows it to deal with uncertainties on the frequencies of the exogenous signals as well. To validate our approach, we provide experimental results for a two-degrees-of-freedom (2-DOF) helicopter model