External model-based disturbance rejection in tracking control of Euler-Lagrange systems

We consider the systematic design of tracking controllers for Euler-Lagrange systems which are affected by unmeasurable harmonic disturbances. The problem addressed the paper departs from the classic setup of the regulator problem and its solution based on the internal model principle in two aspects. First, the presence of an exogenous disturbance affecting the output channel as well as the input channel of the plant 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. This latter is then placed outside the stabilizing loop, in such a way that stability is preserved, and 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 to deal with uncertainties on the frequencies of the exogenous signals as well. To validate our approach, we provide experimental results for a 2-DOF helicopter model.